Satellite Network Providing Continuous Communications to Support

SATELLITE NETWORK PROVIDING CONTINUOUS COMMUNICATIONS TO SUPPORT

MANNED AND UNMANNED EXPLORATION OF THE INNER- PLANETS

A Master Thesis

Submitted to the Faculty

American Public University

Ralph Leroy Spangler, Jr.

In Partial Fulfillment of the

Requirements for the Degree

Master of Science

July 26, 2016

American Public University

Charles Town, WV

The author hereby grants the American Public University System the right to display these contents for educational purposes.

The author assumes total responsibility for meeting the requirements set by United States copyright law for the inclusion of any materials that are not the author’s creation or in the public domain.

DEDICATION

I dedicate this thesis to my wife and sons. Without their encouragement, patience, understanding, support, and most of all, love, the completion of this work would not have been possible. I cannot leave out my faithful furry companion, Veritas, who patiently laid at my feet while I worked.

ACKNOWLEDGMENTS

I wish to thank the instructors, administration, and fellow students of American Military

University for their support, insight, differing viewpoints, openness, and sometimes humor. Their commitment and involvement in my time of studies has been most appreciated. From the beginning, they reinforced the confidence I have in my abilities not only to complete a Master’s degree, but to complete it with excellence.

I have found my course work throughout the Space Studies program to be stimulating and thoughtful, providing me with the tools and knowledge with which to explore past, present and future ideas and issues.

ABSTRACT OF THE THESIS

SATELLITE NETWORK PROVIDING CONTINUOUS COMMUNICATIONS TO SUPPORT

MANNED AND UNMANNED EXPLORATION OF THE INNER- PLANETS

Ralph Leroy Spangler, Jr.

American Public University System, July 26, 2016

Charles Town, West Virginia

Professor Dimitry Bizyaev, Thesis Professor

This thesis provides an evaluation of a possible inner-planetary communications network that would provide continuous coverage of manned and unmanned missions. It examines the network’s ability to provide continuous coverage during times of occultation, or being obscured by an astronomical body from Earth’s reference point. The examination is conducted using computer simulation and mathematical modeling. The results show that a network of satellites that include Earth ground stations, relay satellites at Earth-Sun Lagrange points L4 and L5, and a minimal constellation around the planet or moon can provide continuous coverage. Due to the extreme distances involved, a real-time communications network will not be possible, regardless, the benefit of a continuous communications satellite network will provide a solution to signal loss during times of occulting, reduce signal acquisition times, allow for smaller receiving antennas, redundancy, and survivability.

Table Of Contents

Table Of Contents ...... 6

Table of Figures ...... 8

Table of Tables ...... 10

1 INTRODUCTION ...... 11

1.1 Research Goal ...... 11

1.2 Research Motivation ...... 12

1.3 Summary ...... 13

2 LITERATURE REVIEW ...... 15

2.1 Introduction ...... 15

2.2 Moon and Beyond ...... 17

2.2.1 Moon Constellation ...... 18

2.3 Mars ...... 19

2.3.1 Mars Constellation ...... 20

2.4 Lagrange Points ...... 22

2.5 Inner-Planetary Network Connectivity, Performance, Reliability ...... 23

2.6 Summary ...... 24

3 APPROACH TO ANALYSIS ...... 25

3.1 Introduction ...... 25

3.2 Modeling Occulting of Mars ...... 26

3.3 Mars Constellation Modeling ...... 31

3.4 Earth-Mars Network Modeling ...... 32

6 3.4.1 Network Performance, Survivability ...... 35

3.5 Summary ...... 39

4 DATA ANALYSIS ...... 40

4.1 Introduction ...... 40

4.2 Occulting of Mars ...... 40

4.3 Mars Constellations ...... 46

4.4 Network Performance, Survivability ...... 47

4.5 Summary ...... 51

5 DISCUSSION and CONCLUSION ...... 53

5.1 Introduction ...... 53

5.2 Restatement of Research Goal ...... 53

5.3 Research Motivation ...... 53

5.4 Conclusions ...... 54

5.5 Significant Results of Research ...... 55

5.6 Recommendations for Future Research ...... 55

APPENDIX A ...... 57

A.1 GMAT Occulting Model Configuration Parameters ...... 57

References ...... 62

7 Table of Figures

FIGURE 1: DIAGRAM ILLUSTRATING THE CONFIGURATION OF THE EARTH-SUN LAGRANGE POINTS. S IS THE SUN, E IS THE EARTH, L1 – L5 ARE THE LAGRANGE POINTS. L4 AND L5 ARE STABLE, EQUILIBRIUM POINTS IN SPACE REQUIRING MINIMAL STATION KEEPING DUE AND ALLOW SIGNALS TO BE ROUTED AROUND THE SUN...... 23

FIGURE 2: AREA ZONE OF SIGNAL LOSS CAUSED BY OCCULTATION OF MARS BY THE SUN (NOT TO SCALE). PERIODIC SIGNAL LOSS WILL OCCUR AS THE SUN COMES BETWEEN THE EARTH AND MARS. THIS IS A TEMPORARY CONCERN AS THE PLANETS CONTINUE IN THEIR ORBITS...... 27

FIGURE 3: THE SHADOW CAST OR ZONE OF SIGNAL LOSS INCREASES AS THE DISTANCE TO SUN DECREASES. WHEN MARS IS AT ITS PERIHELION THE DISTANCE THAT EARTH WILL TRAVEL THROUGH WILL INCREASE...... 28

FIGURE 4: THE POSITION OF RELAY SATELLITES AT EARTH-SUN LAGRANGE POINTS L4 AND L5 PROVIDES FOR ROUTING OF THE COMMUNICATIONS AROUND THE SUN AND UNOBSTRUCTED PATH TO MARS. (NOT TO SCALE) .. 29

FIGURE 5: IN DETERMINING THE LENGTH OF SHADOW, ZONE OF SIGNAL LOSS, EARTH TRAVELS THROUGH, SEVERAL PARAMETERS NEED TO BE USED AS INDICATED IN THE DIAGRAM. RELATIVISTIC EFFECTS OF THE STRONG GRAVITATIONAL EFFECT OF THE SUN ARE NOT CONSIDERED...... 30

FIGURE 6: DIAGRAM SHOWING THE COMMUNICATIONS PATH USING THE RELAY SATELLITES AT EARTH-SUN L4 AND L5. COMMUNICATIONS WILL BE ROUTED THROUGH EITHER OR BOTH OF THE RELAY SATELLITES WHEN THE SUN OCCULTS MARS. THERE WILL BE AN INCREASE IN LATENCY DUE TO THE ADDED DISTANCE TO THE PATH. (NOT TO SCALE) ...... 33

FIGURE 7: THE EARTH-MARS COMMUNICATIONS NETWORK IS DEPICTED IN THIS DIAGRAM. TRANSMISSION FROM THE EARTH HAVE MULTIPLE PATHS THAT CAN BE USED. NORMAL COMMUNICATIONS WILL USE A DIRECT PATH UNTIL OCCULTED, THEN AN ALTERNATE PATH THROUGH THE L4, L5 RELAY. THE MULTIPLE PATHS PROVIDE REDUNDANCY, GUARANTEED DELIVERY, AND PRIORITY BASED TRANSMISSIONS. (NOT TO SCALE) ...... 34

FIGURE 8: THE DIRECT PATH BETWEEN EARTH AND MARS PROVIDES A SHORTER DISTANCE AND LESS SIGNAL DELAY THAN THE L4/L5 PATH BETWEEN EARTH AND MARS. THE EARTH-L4/L5 PATH IS A CONSTANT WHILE THE MARS-L4/L5 PATH VARIES IN RELATIONSHIP TO EARTH AS MARS ORBITS THE SUN. THE VALUES SHOWN INDICATE THE WORST CASE DISTANCES AND TIMES...... 38

FIGURE 9: THE NETWORK DIAGRAM DEPICTED IS PROVIDES A GRAPHICAL REPRESENTATION OF THE PATHS OF THE EARTH-MARS SATELLITE NETWORK AND IS USED TO LINK ANALYSIS AND SINGLE POINTS OF

8 FAILURE. MC REFERS TO THE MARS CONSTELLATION, L4/L5 ARE THE RELAYS AT THE EARTH-SUN LAGRANGE POINTS L4 AND L5, AND DSN REPRESENTS THE EARTH BASED NETWORK. THERE ARE THREE PATHS TO BE MODELED...... 39

FIGURE 10: CUMULATIVE OCCULTING BY MARS FOR A PERIOD OF TEN YEARS. THE X-AXIS IS THE DATE AND Y-AXIS INDICATES WHETHER SIGNAL LOSS OCCURRED (1) OR WAS RECEIVED (0). THIS GRAPH INDICATES THAT MARS WILL BE THE PRIMARY CAUSE OF SIGNAL LOSS...... 42

FIGURE 11: A ONE MONTH FOCUSED VIEW OF OCCULTING CAUSED BY MARS REVEALS CONTINUOUS PERIODS OF SIGNAL LOSS (1) INTERSPERSED THROUGHOUT. REPEATING PATTERNS CAN BE SEEN WITHIN THE GRAPH. SIGNAL LOSS ON THIS ORDER CAN BE OVERCOME BY A MARS CONSTELLATION...... 43

FIGURE 12: OCCULTING CAUSED BY THE SUN OVER THE TEN-YEAR PERIOD IS NOT A COMMON PHENOMENON DUE TO THE ORBITAL DANCE AND INCLINATION OF MARS. THE SUN CREATES THE LONGEST DURATION OF SIGNAL LOSS (1) DURING THE OCCULTING ON 17 NOVEMBER 2023. THE DURATION BETWEEN 2 AND 24 AUGUST 2018 IS AN ANOMALOUS INDICATION THAT WAS NOT INVESTIGATED...... 44

FIGURE 13: FOCUSED VIEW OF SUN OCCULTING PERIOD SHOWS THAT FROM 17 TO 19 NOVEMBER 2023, SIGNAL LOSS (1) OCCURS FOR 1.61 DAYS. THIS IS A SIGNIFICANT PERIOD OF TIME OF LOST COMMUNICATIONS ESPECIALLY DURING MANNED MISSIONS...... 44

FIGURE 14: OCCULTING CAUSED BY THE MOON OVER THE TEN-YEAR PERIOD IS NOT A COMMON PHENOMENON DUE TO THE ORBITAL DANCE AND INCLINATION OF MARS. THE MOON CREATES MULTIPLE SIGNAL LOSS (1) SCENARIOS, THE LONGEST OCCURS ON 8 DECEMBER 2022 FOR APPROXIMATELY 3 HOURS. THE DURATION BETWEEN 2 AND 24 AUGUST 2018 IS AN ANOMALOUS INDICATION THAT WAS NOT INVESTIGATED...... 45

FIGURE 15: FOCUSED VIEW OF MOON OCCULTING PERIOD SHOWS THAT WITHIN A TWO MONTH TIME FRAME, SIGNAL LOSS (1) OCCURS THREE SEPARATE TIME WITH THE LONGEST BEING ALMOST 3. THIS IS A SIGNIFICANT PERIOD OF TIME OF LOST COMMUNICATIONS ESPECIALLY DURING MANNED MISSIONS...... 45

FIGURE 16: THE TRANSMISSION DELAY TIME PERCENTAGE INCREASES THROUGH L4 OR L5 AS THE DISTANCE TO MARS INCREASES. AS THE TOTAL DISTANCE APPROACHES THE MAXIMUM DISTANCE THE SIGNAL TRAVELS THROUGH THE L4/L5 RELAYS, THE DELAY BECOMES ACCEPTABLE...... 49

FIGURE 17: GRAPH OF SIGNAL LOSS FOR A RANGE OF WAVELENGTHS INDICATES THAT COMPARED TO DIRECT TO MARS MINIMUM, THE MARS, L4/L5, EARTH

9 MINIMUM WILL INCUR ADDITIONAL SIGNAL LOSS WITH THE PRIMARY LOSS IS IN THE L4/L5 TO MARS PATH...... 50

Table of Tables

TABLE 1: IN DESIGNING A MARS NETWORK CONSTELLATION THERE ARE HIGH- LEVEL PERFORMANCE GOALS THAT NEED TO BE CONSIDERED...... 20

TABLE 2: OCCULTATION DISTANCES AND TIMES CAN BE CALCULATED FOR THE EARTH-MARS SYSTEM USING THE VALUES IN THIS TABLE. THE VALUES FOR MERCURY AND VENUS ARE PROVIDE FOR COMPARISON, WHILE MARS IS USED THROUGHOUT AS AN EXEMPLAR. DISTANCE TO EARTH IS DETERMINED BY THE EARTH AT APHELION AND THE OTHER PLANET AT PERIHELION TO THE SUN IN A DIRECT PATH THROUGH THE SUN...... 30

TABLE 3: DISTANCES TO EARTH FOR LARGE INNER-SOLAR SYSTEM OBJECTS USED IN DETERMINING THE SIGNAL PATH DELAY. IN THEIR RESPECTIVE ORBITS, AS THE PLANETS APPROACH EARTH THE DISTANCE DECREASES DRAMATICALLY...... 36

TABLE 4: DISTANCES AND TIMES ALONG THE ORBIT OF EARTH THAT SIGNAL LOSS WILL OCCUR FROM THE OCCULTING CAUSED BY THE SUN. THE PARE USED AS THEY FORM THE LARGEST ZONE OF SIGNAL LOSS AND DURATION THAT EARTH WILL TRAVEL THROUGH THE ZONE...... 41

TABLE 5: CUMULATIVE AND MAXIMUM OCCULTING TIMES OF MARS. MARS CAN BE SEEN TO HAVE THE MOST ACCUMULATIVE TIME WHEREAS THE SUN CREATES THE LONGEST SINGLE DURATION OF SIGNAL LOSS DUE TO OCCULTING...... 41

TABLE 6: COMPARISON OF SATELLITE CONSTELLATIONS USING A MINIMAL QUANTITY OF REQUIRED SATELLITES TO PROVIDE FULL COVERAGE OF THE MARTIAN SURFACE...... 46

TABLE 7: TIME FOR ONE-WAY TRANSMISSION BASED ON THE DISTANCES TO EARTH FROM VARIOUS LARGE INNER-SOLAR SYSTEM OBJECTS. AT ITS CLOSEST, EARTH-MARS IS APPROXIMATELY 3 MINUTES, BUT EXTENDS TO 22 MINUTES. L4/L5 EXHIBITS A RELATIVE CONSTANT IN THE TIME FOR A ONE- WAY TRANSMISSION...... 47

10 1 INTRODUCTION

1.1 Research Goal

The goal of this research is to evaluate an inner-planetary communications network comprised of a satellite constellation, inner-planetary relay satellites, and the Earth-based ground stations that will provide a continuous communications network for voice, video, and data which will provide continuous coverage and support the increasing communications demands of unmanned and manned missions to the inner-solar system.

The definition of inner-solar system used in this thesis can be easily defined as the space and astronomical bodies that are inclusive within the imaginary sphere that has its center at the center of the Sun and extends out to a radius inclusive of what is known as the asteroid belt. The inner-planetary system and inner-planets are contained within that sphere and include the four planets Mars, Earth, Venus, and Mercury, the 2 moons of Mars: Phobos and Deimos, and Earth’s moon. The term inner-planetary communications will be used to refer to the communications within this sphere between ground stations, satellites, probes, landers, rovers, and other manned or unmanned spacecraft. Lastly, communications will refer to the transmission of both digital and analog signals that are used for data, voice, video, telemetry, and other such uses.

This research will look at the possibility of implementing a communications network to support exploration within the inner-solar system. As humans look toward space for resources such as water, metals, and minerals, continued and future studies of this region, and possible habitation beyond the Earth, having the ability to continually communicate voice, video, and data with Earth will be become vital. The distances that will be involved will make instantaneous communications, which is taken for granted, impossible due to the limitation imposed by the velocity of a photon in free space and thus the propagation of electromagnetic waves. Not

11 withstanding, having the ability to continually communicate will provide advantages to these missions. With the inception of a continuous satellite network will come resiliency, alternate paths, guaranteed delivery, and a very human need, connectedness though with a large delay.

1.2 Research Motivation

As the missions to the inner-planets, Mercury, Venus, Mars, Moon and other bodies such as asteroids and comets continue and increase, along with current missions, the need to communicate with Earth on a continuous basis will become paramount to the mission success.

There are certain aspects of any space communications network that will not be overcome due to the limits of our known physical universe, namely the speed at which a photon travels in free space, which is approximately 3.0 x108 meters per second. Regarding communications on Earth, in near-Earth orbit, and out to the Moon, this limitation is typically not an issue, but as the distance in which we communicate increases far beyond the Moon, the delay or latency, becomes a major issue for real-time or near real-time communications.

The issue of occulting is a factor that will need to be addressed. Even missions to the

Moon will have to contend with this. As exploration of the “far side” of the Moon are conducted, signal loss will occur. This is easily overcome by placing a constellation of satellites around the

Moon, but when dealing with objects out to that of Mars and beyond, other astronomical bodies can occult, or block communications for a period of time. A communications network between

Earth and the various spacecraft, probes, satellites, landers and rovers throughout the inner-solar system can be developed and deployed which will provide a continuous communications network even with latency of tens of minutes by taking advantage of the Earth-Sun Lagrange L4 and L5 points.

12 There is much focus in exploring and possible manned missions to Mars. With this as a focus, research will be conducted using Mars as an exemplar and the primary mission destination to determine a minimum constellation, interplanetary relays, latency, and routing requirements for a network that will provide continuous communications. The Earth based portion of the communications network will utilize the Deep Space Network (DSN) as the Earth-based ground stations (GS).

There are several aspects of an Earth-Mars communications network that will be considered and modeled in support of this research. One area of concern, called occulting, is an issue in which an astronomical body comes in between the Earth and other communicating body and blocks the transmitted signal. This will be investigated to provide information on the occurrence and severity of the issue. Along with understanding the occulting issue, an analysis of the latency and free-space path loss for signal transmissions will be performed. This will provide additional information required to understand and determine the placement and number of satellites in the communications network.

1.3 Summary

A continuous satellite communications network using the Earth-Sun Lagrange L4 and L5 points along with a satellite constellation orbiting an astronomical body, such as Mars, is possible. The distances between Earth and the body will prohibit real-time communications and the phenomenon of occulting will place a body in between Earth and the satellite or lander.

Utilizing the Earth-Sun Lagrange L4 and L5 points will provide a method of routing around the object maintaining communications. The use of these Lagrange points and subsequent increase in distance due to routing will increase the latency by a constant 500 seconds, which is manageable, and as the total distance of the network reaches approximately 485 x 106 km, the

13 percentage increase becomes more acceptable. There are several advantages of using these points such as alternate paths for communications, redundancy and survivability in case of up to two paths loss, guaranteed delivery, and priority selection.

14 2 LITERATURE REVIEW

2.1 Introduction

With the renewed interest in manned missions to Mars, the need to have continuous communications is becoming an area of paramount importance. There are two primary areas of concern: latency and signal loss. Latency, or delay, is inherent in communication networks and a common phenomenon, but at distances beyond Earth orbit, this delay becomes problematic.

Overcoming the delay would be an exercise in instantaneous communications, of which there is ongoing research regarding quantum entanglement, but otherwise beyond the scope of this thesis.

The second primary area of concern in inter-planetary communications, signal loss, is the main focus of this thesis. Even with the delay within the communications network, continuous communications are possible and will provide certain benefits: continuous telemetry, continuous data transfer, reduced acquisition time, redundancy, survivability, alternate paths, guaranteed delivery, and more. A continuous communications network between Earth and Mars will be used as an exemplar in this thesis. This network will consist of Earth based ground stations, relay satellites, and a Martian constellation.

This chapter will begin with a current history of inter-planetary communications and networks that exist and are in use today. A look at each stage of the network will be conducted beginning with Earth ground stations. Location of relay satellites will be characterized along with the advantages and disadvantages. The Martian constellation will be characterized and the advantages and disadvantages discussed. Several constellation configurations will be considered.

There is not much regarding history. From the early days of space exploration and travel, direct line-of-sight communications with Earth based ground stations was the only practical method of communicating. During the Apollo missions that landed on the Moon, the Lunar

15 Module (LM) was used to relay signals and video from the astronauts on the surface of the

Moon. When the astronauts’ missions involved the Lunar Rover, it was equipped with transceivers and antennas for direct Earth communications.

Prior to the deployment of the Tracking and Data Relay System (TDRS), communications with spacecraft and satellites in Earth orbit relied on direct line of sight to ground stations at fixed locations on Earth. This presented issues with loss of communications when the space asset and ground station were not in view of each other. During the manned

Moon missions, another issue was the result of the Moon coming in between the Apollo

Command Module (CM) and the Earth, a process called occulting, when it went to the far or

“dark” side. Communication was also lost between the LM due to occulting of the CM by the

Moon along with the Earth rotation moving the ground station out of line of sight.

The Deep Space Network (DSN) is comprised of antenna complexes located throughout the world roughly 120 degrees apart longitudinally. Located at Goldstone, California; Madrid,

Spain; and Canberra, Australia, communications are handed off to the next ground station prior to loss of signal (LOS) as the Earth rotates. (Jet Propulsion Laboratory n.d.) The DSN was created by NASA to support all deep space missions and eliminating the need for mission specific ground stations and provides for the command and control, tracking, and monitoring of deep space mission assets (Jet Propulsion Laboratory n.d.).

The DSN uses Earth based ground stations that are very large to receive the faint signals from the various spacecraft, probes, landers, and rovers as well as providing high power transmitters for sending signals to deep space. Even today, communications from landers and rovers on Mars, probes to the outer planets, and even Voyager 1 and 2 communicate to the DSN.

Communications with the DSN is often interrupted due to orbits taking the satellite to the far side

16 of the astronomical body, rotation of the body on which the lander or rover is on, and occulting bodies coming in between the Earth and the device.

The DSN uses antennas that range from 34 meters to 70 meters in diameter for the receiving and transmitting of commands, telemetry, voice, and data of to and from spacecraft, probes, satellites, rovers, and landers. Due to the weak signals, very large antennas and sensitive receivers must be used to detect the faint incoming communications. Very high power transmitters are used to send to the device that may be at very long distances (Jet Propulsion

Laboratory n.d.).

Other space networks include the Near Earth Network (NEN) which is used for missions to

Low Earth Orbit (LEO), Geosynchronous Earth Orbit (GEO), and Moon and provides telemetry, command and control, tracking, data and communications. The Space Network (SN) provides tracking and communications to near-Earth spacecraft from ground stations throughout the world. TDRS is comprised of nine satellites, with the first one being launched in 1985 and the latest 2015, that provide near-continuous communications relay between space-based and Earth- based systems (NASA 2016). TDRS provides continuous communications and data transfers between earth orbiting satellites, spacecraft, and the international space station.

2.2 Moon and Beyond

As missions to the Moon and beyond are planned and executed, deploying of communications networks in space become more vital to their success. Reliance on reach back to

Earth, as a direct connection, will not be practical, cost effective, or even reliable (Bhasin, et al.

2006). The U.S. Administration, February 2004, in its “Vision for Space Exploration” stated that lunar communications would be crucial and there is a need for the development of a communications architecture (Department of Aeronautics & Astronautics University of

17 Washington n.d.). To support future manned and unmanned missions to the Moon, such as long- term human exploration and human and robotic missions to areas not visible to Earth, NASA’s

Space Operations Mission Directorate (SOMD) established the Space Communication

Architecture Working Group (SCAWG). The SCAWG was chartered with the goal of developing an architecture that would support surface-to-surface and surface to Earth communications. Their work was focused in 4 areas: relay constellation orbital design, new satellite designs, existing satellite design usage, and cost of the different options (Bhasin, et al.

2006, 2-3).

2.2.1 Moon Constellation

The Luna POLARIS mission is one architecture proposed that defines a lunar communications network of satellites, or constellation, which would enable manned and unmanned missions to communicate between the Moon and Earth from anywhere on the lunar surface or in orbit. Current communications with the Moon missions are limited to the DSN and operate using line of sight transmissions. This limitation in communication resigns missions to the areas that are visible from Earth (Department of Aeronautics & Astronautics University of

Washington n.d.).

To provide a continuous, two-way communications network from the Earth to the Moon, the Luna POLARIS mission would be based on an eight-satellite constellation. These eight satellites would be placed in orbits that provide for two satellites covering 90% of the surface and one satellite covering 100% of the surface at all times. This constellation would use two orbital planes based on frozen orbits in which four satellites are in each plane. These orbits would have a low eccentricity orbit to facilitate cross-links between satellites. The Luna

POLARIS architecture and orbital placement is designed to provide a high bandwidth

18 communications link that will service simultaneously multiple lunar users (Department of

Aeronautics & Astronautics University of Washington n.d.).

A constellation of eight satellites using four satellites and two orbital planes was recommended. It met the requirement of 90% availability with a 2.4% coverage area with a single satellite, resulting in a 97.6% multi-satellite coverage of the Moon. The period of time,

4.25 hours, for single satellite coverage was also acceptable though provided no redundancy.

(Department of Aeronautics & Astronautics University of Washington n.d., 5)

2.3 Mars

NASA has committed to the exploration of Mars with current ongoing and future missions.

The success of missions such as: Mars Pathfinder, Mars Global Surveyor, Mars Odyssey,

Opportunity, Phoenix, Curiosity, and MAVEN have returned valuable scientific data which has and continues to increase our knowledge of Mars. To add to these and other ongoing missions,

NASA is planning new missions such as: InSight, Red Dragon, and Mars 2020 over the next two decades with launches approximately every 26 months to coincide with alignment of Earth and

Mars and culminating in manned missions (Ely, et al. n.d.) (NASA n.d.).

The increased NASA missions, missions from other nations, longevity of missions, and critical nature of manned missions will increase the demand for communication services in the

Martian vicinity and between Earth and Mars. To meet this increased demand, implementation of a Mars satellite constellation would provide a partial solution. This constellation of satellites would provide in-situ relay between on-orbit and ground based users along with store and forward capabilities for transmission between Earth and Mars. Acting as part of the DSN, additional communications capabilities could be provided to augment, extend, and off-load current requirements. A Mars satellite constellation would also be an enabling technology that

19 could be taken advantage of in future mission designs and planning. Such a satellite constellation would have the following purpose: relay commands, data, and telemetry between Earth and

Mars; provide location services to on-orbit and ground based systems; and act as a communications relay for in-situ missions (Ely, et al. n.d.).

2.3.1 Mars Constellation

Understanding what the Martian communications usage will be over the next couple of decades will facilitate the design of the satellite constellation in regards to coverage and reliability. Due to the cost of injecting satellites into a Mars orbit, minimizing the number of satellites required to provide the desired coverage, while taking into account the reliability of the network, most be considered. There are performance considerations for the Mars network that will need to be considered in the design trade to meet the communications needs of Mars ground and orbit users along with Earth based users. Usage of selected metrics will identify the design trades to meet the requirements of the communications network. Table 1 provides a list of performance goal for a Mars communications network (Ely, et al. n.d.).

Table 1: In designing a Mars network constellation there are high-level performance goals that need to be considered.

Mars network constellation performance goals Global Martian coverage. Large volume communication support. Maximize communication and navigation performance across Martian surface. Minimize communication and navigation performance variations across Martian surface. Provide maximum utility during buildup of the constellation. Provide redundant coverage in the event of the loss of any single satellite. Minimize coverage variability due to long-term orbit perturbations. Minimize orbital maintenance as measured in operations time/cost and expended Delta V.

When designing the constellation and determining key parameters such as orbital altitude, consideration needs to be made regarding the user’s needs. It is foreseeable that this constellation may need to not only provide communications, but also provide navigational support similar to

20 the Global Positioning System (GPS) around Earth. Maximizing the performance of competing design goals becomes a challenge with trade-offs in payload, power, orbits, and other parameters.

Surfaced-based users utilizing low-power transmitters and small aperture antennas will require satellites be in view for long periods of time and minimal range whereas navigational systems will require multiple satellites to be in view (Ely, et al. n.d.).

A recommended constellation named 4retro111 is comprised of two satellites in a one orbit plus four satellites in a separate orbit meets the requirements defined in Table 1. This constellation of 6 total satellites uses the retrograde orbits, the same altitudes, but different inclinations to provided continuous coverage of Mars with minimal overlap at the poles. Other positives are the provision for redundancy in the constellation, which again meets the design objectives. (Ely, et al. n.d., 4, 12)

Earth based navigational constellations in providing positional and timing data require at least four satellites, 4-fold coverage, to be in view. Projected Mars constellations will not be able to provide this type of coverage due to the smaller number of satellites, such as 4, 5, 6 or 8, and lower orbital altitudes. Using higher orbital altitudes may provide the solution when a limited number of satellites are available, but communications delay may become a concern (Ely, et al. n.d., 2-3).

The Mars Network is a NASA project that is researching communications and navigational infrastructures in support of Mars missions to determine the orbital arrangement and parameters, and the minimum required satellites. These constellations could be comprised of satellites whose primary mission is data collection with an additional communications payload as a secondary function to satellites dedicated to communications. Compared to Earth orbiting constellations, the number of satellites will be small and there may be discontinuous coverage.

21 These so-called sparse configurations may not be able to provide navigational support in the familiar sense, but communications should be able to be maintained with a single satellite. (T. A.

Ely 2001, 1, 4, 6-7)

2.4 Lagrange Points

In the Earth-Sun system there exists points in space, called Lagrange points, where a low mass satellite can be at equilibrium to the gravitational attraction of high mass bodies. These equilibrium points are solutions to the Restricted Three Body Problem (RTBP) and assume a

Keplerian, or circular, orbit around their center of mass. Missions such as SOHO, MAP, and

Genesis have taken advantage of these Lagrange points and future missions are being planned.

There are some known solutions to the General Three Body Problem (GTBP) and RTBP, in particular the solution called L4 and L5, forms an equilateral triangle with two massive bodies and the small mass satellite which has an angular velocity that is determined by the length of the sides of the triangle and the masses. (Canalias, Marcote and Masdemont n.d., 5-6).

Continued and increased interest in the advantages of the Lagrange points, along with advances in understanding of theoretical, analytical, and numerical aspects, has advanced mission designs to these points. One of the solutions to the General Three Body Problem (GTBP), and the RTBP is when the two large bodies and one small body form an equilateral triangle.

With proper ratios of the distances between small and large bodies, location of the center of masses, and rotating coordinates a solution can be found that keep the bodies aligned. These solutions are known as the Lagrange points, Figure 1 (Canalias, Marcote and Masdemont n.d., 5-

6).

Figure 1: Diagram illustrating the configuration of the Earth-Sun Lagrange points. S is the Sun, E is the Earth, L1 – L5 are the Lagrange points. L4 and L5 are stable, equilibrium points in space requiring minimal station keeping due and allow signals to be routed around the Sun.

2.5 Inner-Planetary Network Connectivity, Performance, Reliability

The Mars communications network will be comprised of a Martian constellation of non- geostationary satellites, inter-planetary relay satellites, and the DSN. This configuration will require analysis of several key aspects such as: link budget, link load, latency, traffic, multipath

(Donner, Fissling and Hermenier 2009), routing, store and forward (Cruz-Sanchez, Franck and

Beylot 2010) and others.

All communications suffer from propagation loss due to the distance the signal has to travel. This loss is directly proportional to the square of the distance and the wavelength of the transmitted signal. To support missions at large distances, the use of high power transmitters along with very large antennas are required to overcome the loss due to the signal propagation

(Fossa, Jr 1998, 7).

Understanding of the performance of the network will be important to determine the most efficient way to route data. This can be accomplished through understanding the end-to-end delays. The end-to-end delay is built-up from the various delays that will be inherent in the

23 network such as: access delay, uplink delay, cross delay, downlink delay, sat delay, and number of satellites (Fossa, Jr 1998, 40) (Pratt, et al. 1999, 8). Reliability and survivability will have to be designed into the network. Utilizing a graph that represents the nodes and connections in the network the redundancy can be analyzed and the critical nodes and connections can be determined. This analysis will provide the measure of the network to route data between nodes with links or nodes removed (Fossa, Jr 1998, 21-22).

2.6 Summary

There has been and continues to be research conducted in providing communications in support of missions to the inner-solar systems. While the literature provides details on constellations to support coverage of the planet or Moon, there is no information regarding the network segment between the planet or Moon and the Earth. The Moon is close enough that a few second delay may not be the best scenario but is acceptable, even in a critical situation. Near real-time communications is still viable. When dealing with greater distances, say to Mars, the focus has been on constellations neglecting the space in between.

24 3 APPROACH TO ANALYSIS

3.1 Introduction

Literature research concluded that the architecture for a complete Earth-Mars continuous satellite communications network has not been published. While there has been no published paper on continuous communications architectures, research has and is being conducted on

Lunar and Mars constellations. The Lunar and Mars constellations rely on the DSN for communications with Earth and have the same issues of loss of signal, occulting. For this research a review of published literature related to satellite constellations, satellite communications, and orbital mechanics was conducted and provided information required for the creation of models.

To understand what is expected to be the primary cause of loss of signal, occulting, two satellite configurations will be used, polar and geostationary. The General Mission Analysis Tool

(GMAT), an open source application from NASA and is available for download at https://sourceforge.net/projects/gmat/files/GMAT/GMAT-R2012a/, will be used to model the occulting period for the Earth-Mars network to determine severity of the problem. Since the study of satellite constellations for the Earth, Moon, and Mars has been published, a comparison of several satellite constellation configurations will be performed.

Models will be created of the communications network to include inter-planetary relay satellites at the Sun-Earth Lagrange points L4 and L5. Modeling of the communications path between the satellites will look at free-space transmission loss, bandwidth, latency, alignment and other factors to support Earth-Mars communications. To identify single points of failure in the network, a network analysis will be performed to verify redundancy and survivability.

25 3.2 Modeling Occulting of Mars

As missions to inner-solar system increase the need for continuous communications will have to be addressed. The issue of occultation becomes even more of an issue as manned missions reach beyond the moon to Mars. The time, or latency, of transmission ranges between 3 and 22 minutes in one direction to Mars depending on where Earth and Mars are in their orbits around the Sun. As mentioned in the Introduction, this latency will not be addressed by current technology but can be improved upon by providing continuous and deterministic capabilities.

Exacerbating the latency issue will be the loss and reacquisition of signal. Current missions beyond Earth orbit have to deal with the loss and regaining of communications with the DSN due to objects coming between the Earth and spacecraft or rotation of the planet in the case of landers and rovers. For unmanned and robotic missions this has been the norm. Even the manned missions to the Moon, lost signal as the Apollo spacecraft went around the far side.

The loss of signal and subsequent reacquisition (access time) of the communications signal for the unmanned and manned Moon missions did not present a major issue. When dealing with the loss and reacquisition of communication signals for manned missions to Mars and other planets, even a best case six minutes round-trip could mean the loss of life. By providing a continuous communications network that includes multiple paths the risks due to loss and reacquisition of communications will be mitigated, only the latency will remain.

For Mars missions there are possible periods of occultation with multiple large objects:

Sun, Moon, Venus, Mercury, Mars, Phobos, and Deimos. Though these may not be regular occurrences, they still pose a potential risk to missions. What then is occultation? Occulting occurs when an astronomical object such as a planet, moon, or asteroid comes in between Earth and the remote spacecraft. An example of occulting occurred when the Apollo spacecraft went

26 around the Moon to the “dark side” and the Moon blocked the signal. Current satellites and probes in orbit around Mars experience this when they go behind the planet and landers and rovers on Mars exhibit this as Mars rotates on its axis.

One example of signal loss between Mars and Earth occurs due to the Sun blocking the communication signals. As Earth and Mars orbit the Sun, there are periods of time when the Sun comes between them and creates a zone of signal loss or shadow and no signal can be received.

Worst case for this shadow occurs when the Earth and Mars are opposite and directly in line with the Sun, Figure 2. Also to be considered is not only a shadow cast, but also the Earth and Mars are moving in their respective orbits causing the shadow to move and effecting the time in the shadow.

Earth

Zone of Signal Loss

Sol

Mars

Figure 2: Area Zone of Signal Loss caused by occultation of Mars by the Sun (not to scale). Periodic signal loss will occur as the Sun comes between the Earth and Mars. This is a temporary concern as the planets continue in their orbits.

27 Taking into account the orbital eccentricity of Earth and Mars, this zone of signal loss becomes greater when either Earth or Mars are at perihelion due to the angle formed with Sun,

Figure 3. When one planet is at aphelion and the other planet is at perihelion the distance traveled through the shadow cast from perihelion to aphelion is greatest. This research will be based on the relationship where Mars is at perihelion to the Sun and Earth is at aphelion to the

Sun.

Figure 3: The shadow cast or Zone of Signal Loss increases as the distance to Sun decreases. When Mars is at its perihelion the distance that Earth will travel through will increase. The placement of relay satellites at points in space that allow for the routing of the communications signals around the occulting body would mitigate this issue of signal loss. Using the Earth-Sun Lagrange points L4 and L5, which are formed at 60 degrees from the line from the center of Earth to center of Sun and forming an equilateral triangle, would provide alternate paths for communications along with providing redundancy in case of a failure in the primary

Earth-Mars communications path, Figure 4. The L4 and L5 satellites would be at the same distance from the Earth to the Sun, or approximately 150 x 106 km and would have the advantage of the low station keeping requirements of these Lagrange points.

28 Earth

Zone of Signal Loss L4 L5

Sol

Mars

Figure 4: The position of relay satellites at Earth-Sun Lagrange points L4 and L5 provides for routing of the communications around the Sun and unobstructed path to Mars. (Not To Scale)

Mathematical modeling of the duration of the occultation and communications path will be conducted using the data in Table 2, Figure 5, and the following equations. To determine the length of time in days that Mars will be occulted by the Sun from Earth’s perspective, the angle �, needs to be determined using Equation 1 where hSun is the distance to the Sun at perihelion and rSun is the radius of the Sun, 695700 km.

� = ��!! !!"# (1) !!"#

29 Mars rSun q hSun dE lshadow Earth

Figure 5: In determining the length of shadow, Zone of Signal Loss, Earth travels through, several parameters need to be used as indicated in the diagram. Relativistic effects of the strong gravitational effect of the Sun are not considered. The length of the shadow (zone of signal loss) along the Earth orbit is determined by Equation 2, where lshadow is the approximate length of shadow along the orbital path, dE is the distance between Earth (aphelion) and Mars (perihelion) for worst case scenario.

�!!!"#$ = 2(tan � ∗ �!) (2)

Total days of occultation is determined by Equation 3 where tdays is the time in days of occulting period, vhigh is the higher of the two orbital velocities, vlow is the lowest.

!!!!"#$ �!"#$ = (3) !!!"!!!!"# ∗ !"#$$!"#$%&!

Due to the orbits of Mercury and Venus being inside of Earth’s, their orbital velocities are higher than the Earth’s. The shadow cast will overtake the Earth in its orbit. In the case of Earth and

Mars, the orbit of Mars is outside of Earth’s resulting in Mars have a lower orbital velocity and

Earth will overtake the shadow.

Table 2: Occultation distances and times can be calculated for the Earth-Mars system using the values in this table. The values for Mercury and Venus are provide for comparison, while Mars is used throughout as an exemplar. Distance to Earth is determined by the Earth at aphelion and the other planet at perihelion to the Sun in a direct path through the Sun.

Planet Distance Mars Orbital to Earth Perihelion velocity (106 km) (106 Km) (Km/s) dE hSun v

30 Planet Distance Mars Orbital to Earth Perihelion velocity (106 km) (106 Km) (Km/s) Mercury 198.100 46.000 47.360 Venus 259.580 107.480 35.020 Earth ------29.780 Mars 358.720 206.620 24.070

Verification of the occultation period will be performed using GMAT and modification of a provided tutorial for contact detection of a single satellite orbiting Mars. Changes will be made to the initial date of the simulation and duration. A date of 1 May 2016 00:00:00.000 UTC will be used along with a 3700 day simulation period reflecting a 10-year cycle. This period was selected as a representative timeframe and a possible window to establish the Earth-Mars network. A simulation of the occulting bodies will include Mars, Deimos, Phobos, Mercury,

Venus, Moon, Sun, and all. The targets on Earth will include the three Deep Space Network ground stations located at Canberra, Australia; Madrid, Spain; and Goldstone, California.

3.3 Mars Constellation Modeling

Constellations for the Mars portion of the communications network will be analyzed using available published configurations that have been proposed for the Martian and Lunar environments. Preference will be given to minimal configurations as these will be easily deployed and implemented using just a single mission. A comparison of parameters to include number of satellites required, altitude, orbital period, coverage, dwell time, redundancy, and theoretical verses actual.

Included in the analysis will be two Earth constellations, Iridium and GPS. These will be used as a comparison of currently operating constellations and their characteristics to provide global coverage. Also, a theoretical constellation patented by John E. Draim, utilizing four satellites to provide global coverage in a tetrahedral constellation will be included. A benefit of

31 this constellation is the high orbital altitude that provides line-of-sight to the each satellite and long dwell time over a hemisphere. (J. E. Draim 1989)

3.4 Earth-Mars Network Modeling

The Earth-Mars communications network as depicted in Figure 6, shows the relationship of Earth, Mars, and the L4 and L5 relays. With the placement of the relays at L4 and l5, the signal can be affectively routed around the occulting body. While this eliminates the loss of signal, significant delay or latency is introduced into the system. With one-way times between

Earth and Mars between 3 and 22 minutes, would the added latency be of significance or would the benefit of continuous communications outweigh this negative?

To understand the issue of the latency, one has to remember that photons only travel at the speed of light, approximately 3.0 x108 meters per second in space, the cosmic speed limit. Radio and light signals propagating through space must adhere to this speed limit. Transmitting to and from Earth experiences a delay, but is not of appreciable duration to create problems and with

TDRS acting as relays, continuous contact with ground stations can be maintained. Even at the distance of Moon, the transmission one-way is under 2 seconds, again an acceptable level of latency. When one looks at the distance to Mars, the speed limit of light becomes a major factor.

Looking at Figure 6, the addition of the L4 and L5 paths will increase the distance and time the signal has to travel.

32 Earth

Zone of Signal Loss L4 L5

Sol

Mars

Figure 6: Diagram showing the communications path using the relay satellites at Earth- Sun L4 and L5. Communications will be routed through either or both of the relay satellites when the Sun occults Mars. There will be an increase in latency due to the added distance to the path. (Not To Scale)

Modeling of the Earth-Mars network will utilize, Figure 7, which depicts the main systems in the communications network, and Equation 5, which provides the delay or latency of a data packet where Taccess is the access delay, Tuplink, Tcross, and Tdownlink are the delay for the links,

Tsat is the average processing and queuing delay, and N is the number of satellites in the path

(Pratt, et al. 1999, 8).

�!"#$%& = �!""#$$ + �!"#$%& + � − 1 �!"#$$ + ��!"# + �!"#$%&$' (5)

There are three primary areas of analysis. First, the latency between elements in the network need to be determined. Two, the transfer time from one network to another needs to be modeled. Three, the point in the Earth-Mars orbital dance when relay through L4 or L5 becomes

33 too costly in terms of latency. An additional area to understand would be what benefit, if any, there may be in using multiple paths at one time, either for higher throughput or guaranteed delivery.

L4 Relay

E a r rs t a h

M t to o 4 L L 4

Mars

Direct Path to Mars Lander

Comm sat DSN

L5 h Earth

to t

m o

rs L 5

L5 Relay

Figure 7: The Earth-Mars communications network is depicted in this diagram. Transmission from the Earth have multiple paths that can be used. Normal communications will use a direct path until occulted, then an alternate path through the L4, L5 relay. The multiple paths provide redundancy, guaranteed delivery, and priority based transmissions. (Not To Scale)

At certain points in the orbit of Earth and Mars, Mars comes closer than the L4, L5 points and relay through them would add extra and unnecessarily latency. The relay satellites at L4, L5 provide redundant paths around the sun. Only at the point where the Earth, Sun, and Mars are directly inline will the L4, L5 paths be equal. Throughout half of Mars’ orbital period, either L4 or L5 will have the shortest path the Mars. Relaying through L4 or L5 does not come in to play until the distance between Earth and Mars is greater than ~150 x106 km away. An analysis of the appropriate distance for direct Earth communications switchover will be performed.

If latency were not enough to be concerned with, degrading of the signal, or propagation loss, due to dispersion along the path traveled occurs. The propagation loss occurs at an

34 exponential rate and is determined by the wavelength of the signal and the distance traveled. The signal degrading will be worse at higher frequencies and is a factor that should be considered in the design and selection of antennas, transmitters, receivers, and the transmission medium. After determining the configuration of satellites, the losses due to free-space and alignment will be evaluated to determine viability of the network (Roddy 2006).

The last components of the network include the Earth ground stations and Mars constellation. Currently, the DSN utilizes very large antennas and high power transmitters and

Mars orbital and surface systems are significantly small and low in power. Using a Mars constellation where larger antennas and higher power transmitters can be placed in orbit and L4 and L5 to amplify and relay transmissions will allow for smaller ground stations on Earth and could increase the number of ground stations.

3.4.1 Network Performance, Survivability

In a continuous communications network between Earth-Mars occultation by Sun, Moon,

Mars, Deimos, Phobos, Mercury, and Venus will be a major influencer. Occultations will require that relay satellites will have to be placed to go around the Sun. This will increase the path and thus the latency and time of the transmissions, but a continuous network will be maintained. The worst-case time of the occultation will be used as the determining factor for positioning the relay satellites. One factor that will not be explored is the issue of the effect of the Sun’s gravity on the transmission. The network will therefore ignore this effect, but needs to be considered if implemented.

Two relay satellites will be configured and modeled at L4 and L5 (T. A. Ely 2001) points along the Earth orbital path. This path may not be a straight line and not the shortest, what is important is that a continuous network is maintained between Earth-Mars.

35 Network latency in one direction will be modeled with the equation 5 where c is the

8 speed of light which is approximately 3.0 x 10 meters per second and d1 is the distance between

Earth and the astronomical body or satellite.

� = !! (6) !"# !

Table 3 provides the distances to be used to determine the latency in one direction. Both the minimum and maximum distances are provided in order to compare the minimum and maximum latency. Looking at Mars, which is the exemplar for this paper, the distance varies from 55.7 x 106 km to 401.3 x 106 km, an increase of 620.47 percent.

Table 3: Distances to Earth for large inner-solar system objects used in determining the signal path delay. In their respective orbits, as the planets approach Earth the distance decreases dramatically.

Astronomical Distance (d1) Percentage (%) body (106 Km) change in distance Min Max Moon 0.36 0.41 13.89 Mercury 77.30 221.90 187.06 Venus 38.20 261.00 583.25 Mars 55.70 401.30 620.47 Sun/L4/L5 147.09 152.10 3.41

The primary delay is mainly along the long distance path between Earth and Mars so constellation and Mars to orbit times will not included. At certain points in the orbit of Earth and

Mars, Mars comes closer than the L4, L5 points and relay through them would add extra and unnecessarily latency. Relaying through L4 or L5 does not come in to play until the distance between Earth and Mars is greater then ~150 x106 km away. At this point the time delay between

Earth and Mars would be equal. The relay satellites at L4, L5 provide redundant paths around the sun. Only at the point where the Earth, Sun, and Mars are directly inline will the paths be equal.

Throughout half its orbital period either L4 or L5 will have the shortest path the Mars. The L4,

36 L5 relay satellites still provide a redundant path in the event of an occulting body.An analysis of the appropriate distance for direct Earth communications switch-over will be performed.

The last components of the network include the Earth ground stations. Currently the DSN utilizes very large antennas. The usage of these large aperture antennas is to collect and focus the extremely weak signals received from deep space. As an electro-magnetic wave travels through space the signal loss due to wave propagation is directly proportional to the square of the path distance as described in Equation 7 where � is the wavelength, d is the path distance, and Ls is the path loss. To compensate for this loss, either high power transmitters or large aperture antennas are used (Fossa, Jr 1998, 7). Using L4 and L5 to relay transmissions may allow for smaller ground stations on Earth. These smaller units could increase the number of GS.

! � = !!" (7) ! !

To compensate for this loss, consideration of the transmitting and receiving antennas and electronics need to be considered. Whereas on Earth large aperture antennas and the accompanying electronics can be constructed, deployed, maintained, and upgraded easily, placing satellites in space and the distances involved becomes a complex and difficult project.

An analysis will be conducted using published data as to the availability of deployable antennas with large apertures and good gain along with the power requirements to reduce the signal loss due to wave propagation.

37 Earth

~150 x106 Km ~500 seconds

L4 L5

~401 x 106 Km ~1336 seconds

~349 x 106 Km ~1163 seconds

Mars

Figure 8: The direct path between Earth and Mars provides a shorter distance and less signal delay than the L4/L5 path between Earth and Mars. The Earth-L4/L5 path is a constant while the Mars-L4/L5 path varies in relationship to Earth as Mars orbits the Sun. The values shown indicate the worst case distances and times.

An analysis of the signal loss along path to Earth will be compared to new path with L4,

L5 using Equation 7 and Figure 8. A link analysis will be performed using a graph of nodes and links, Error! Reference source not found.Figure 9, to ascertain the survivability of the network and critical nodes (Fossa, Jr 1998, 21-22). The Earth-Mars communications network will be providing multiple paths for communications to flow, which will enhance the survivability, but may have a greater latency.

38 Mars Inter-planetary Relay Earth Segment Segment Segment

MC DSN

Figure 9: The network diagram depicted is provides a graphical representation of the paths of the Earth-Mars satellite network and is used to link analysis and single points of failure. MC refers to the Mars constellation, L4/L5 are the relays at the Earth-Sun Lagrange points L4 and L5, and DSN represents the Earth based network. There are three paths to be modeled. 3.5 Summary

Even with the distances involved in an Earth-Mars network preventing any communication

at a real-time rate, a continuous network can be established. The primary concern of occulting

can be overcome by deploying relay satellites at the Earth-Sun L4 and L5 points. This

arrangement will also provide redundant paths for communications enhancing survivability. A

modeling of the Earth-Mars communications system will look at occulting of various bodies,

the network path between Earth and Mars, latency of the network, routing and switching

between the paths, and survivability and reliability.

39 4 DATA ANALYSIS

4.1 Introduction

Using the models and initial data form Chapter 3, and analysis of the Earth-Mars network was conducted. These analyses confirm that a communications network providing a continuous communications between Earth and Mars, and by substitution any of the inner-planets, is possible. Utilizing the Earth-Sun L4 and L5 Lagrange points provides a stable position in space for the deployment of the relay satellites. The L4 and L5 points due add additional latency to the signal path, but provide a method of routing the signals around the Sun during occulting periods.

4.2 Occulting of Mars

Utilizing Figure 5, Equation 1 and Table 2 the angle, �, formed between the line from the center of Mars to center of the Sun, hsun, and the line from center of Mars to the corona of the

Sun, rsun, is recorded in Table 4 along with values for Mercury and Venus for comparison. This angle, � along with Equation 2 and the distance from Mars to Earth, dE, provides the length of the zone of signal loss, lshadow, along the orbit of Earth. Comparing the angle, �, and the shadow, lshadow, cast, when the planet is at perihelion to the Sun, the larger the angle and longer the shadow that Earth has to travel through.

Using Table 2, Equation 3 and Figure 5, the time for Earth to traverse this zone is recorded in Table 4. The fact that the two planets are moving in their respective orbits is taken into account by the difference in their orbital velocities in Equation 3. Staying with the exemplar of Earth and Mars, the period that Earth travels through the zone of signal loss is approximately five days showing a worst-case timeframe. One factor not taken into account during this analysis is the inclination of Mars to the elliptic. This inclination for Mars of 1.85o will have an effect on the duration of the time traveling through the shadow.

40 Table 4: Distances and times along the orbit of Earth that signal loss will occur from the occulting caused by the Sun. The perihelion is used as it forms the largest Zone of Signal Loss and duration that Earth will travel through the zone.

Planet Distance Mars Angle Shadow Orbital Time of to Earth Perihelion (degrees) (106 Km) velocity occultation (106 km) (106 Km) (Km/s) (Days) dE hSun � lshadow v tDays Mercury 198.100 46.000 0.866 8.134 47.360 5.355 Venus 259.580 107.480 0.371 3.522 35.020 7.780 Earth ------29.780 --- Mars 358.720 206.620 0.193 2.445 24.070 4.957

To validate the magnitude of the occulting issue and subsequent signal loss, GMAT was used to simulate a ten-year period from March 1, 2016 to June 17, 2026. A polar orbit satellite, with an inclination of 89 degrees, and orbital time of 2 hours and a geostationary satellite to provide a use case that would simulate a communications satellite or lander, were used in the simulation. The accumulated time of signal loss due to occulting is shown in Table 5 for the main bodies related to this loss. The maximum times are recorded also to show relevant signal loss that could occur.

Table 5: Cumulative and maximum occulting times of Mars. Mars can be seen to have the most accumulative time whereas the Sun creates the longest single duration of signal loss due to occulting.

Occulting Body Cumulative occultation Maximum occultation (minutes/days) (minutes/days) Deimos - - - - Phobos - - - - Mars 1948900.22 1353.403 46.333 0.032 Mercury 0 0 0 0 Venus 0 0 0 0 Moon 456.276 0.317 174.505 0.121 Sun 2416.461 1.678 2322.881 1.613

Occulting of Mars by the Sun was shown to have a maximum of approximately two days and compares favorably to the value in Table 4. The difference arises in the algorithms used by

41 GMAT that takes into account more parameters during its simulation. Looking at Table 5, it can be seen that Mars itself is the largest contributor to signal loss resulting from the orbit of satellites and the rotation of Mars itself. Over the ten-year period simulated, Mercury and Venus played no part in occulting of Mars, however the Moon did have somewhat of an impact.

Figure 10 shows a time span from 1 May 2016 to 17 June 2026 that Mars is occulting the simulated satellites. As can be seen, over a ten year period occultation and the resulting loss of signal will be a constant issue. To support constant communications when manned missions go to Mars, this is one area that needs to be focused on.

Figure 10: Cumulative occulting by Mars for a period of ten years. The X-axis is the date and Y-axis indicates whether signal loss occurred (1) or was received (0). This graph indicates that Mars will be the primary cause of signal loss. When Mars is simulated by itself, Figure 11 shows a focused view of the occulting caused by Mars again indicating that it is a primary source of occulting. As satellites orbit Mars, they will periodically travel to the side opposite and away from Earth putting Mars in between which will block all signal transmission and reception between Earth and Mars. Simulations shows that the maximum signal loss is on the order of 46 minutes in duration but occurs multiple

42 times throughout the day as referenced from Earth ground stations. As an example, 29 August

2018 the Canberra, Australia ground station will incur a signal loss of 42 minutes at five different times. After handing off to Madrid, signal loss will occur another three times. For this particular day, a total of 5.51 hours of signal loss will have occurred. This does not include the time required to reacquire the signal or the potential data loss that may occurred.

In the case of geosynchronous orbiting satellites, landers, and rovers which will appear more as stationary points in relation to Mars, as Mars rotates they will travel to the opposite side and away from Earth placing Mars in between and thus blocking the signal to and from Earth.

Depending on the orbit altitude and rotation of Mars, this could be as long as half a Martian day or just over twelve hours.

Loss of Signal Due To Occulting by Mars

0 8/1/18 0:00 8/11/18 0:00 8/21/18 0:00 8/31/18 0:00

Loss of Signal

Figure 11: A one month focused view of occulting caused by Mars reveals continuous periods of signal loss (1) interspersed throughout. Repeating patterns can be seen within the graph. Signal loss on this order can be overcome by a Mars constellation.

Besides the occulting caused by Mars, GMAT simulations of the Sun and Moon present other scenarios when a body comes in between Earth and Mars. GMAT data shows that a maximum continuous outage caused by the Sun occurs on 17 November 2023 at 7:53 UTC,

Figure 12 and Figure 13, which lasts for 2322.881 minutes or 1.61 days. Though this is a less

43 frequent occurrence than what is caused by Mars, it is the longest period of signal loss and the length of time could be a major concern, especially during manned missions.

Figure 12: Occulting caused by the Sun over the ten-year period is not a common phenomenon due to the orbital dance and inclination of Mars. The Sun creates the longest duration of signal loss (1) during the occulting on 17 November 2023. The duration between 2 and 24 August 2018 is an anomalous indication that was not investigated.

Figure 13: Focused view of Sun occulting period shows that from 17 to 19 November 2023, signal loss (1) occurs for 1.61 days. This is a significant period of time of lost communications especially during manned missions.

44 Figure 14 and Figure 15 shows the occulting caused by the Moon over the ten-year period. The Moon occults Mars more frequently than the Sun, but the durations are significantly less with the maximum of 0.12 days occurring 8 December 2022 at 6:06 UTC. Due to the frequency of occulting periods, the Moon could present a significant issue for manned missions to Mars.

Figure 14: Occulting caused by the Moon over the ten-year period is not a common phenomenon due to the orbital dance and inclination of Mars. The Moon creates multiple signal loss (1) scenarios, the longest occurs on 8 December 2022 for approximately 3 hours. The duration between 2 and 24 August 2018 is an anomalous indication that was not investigated.

Figure 15: Focused view of Moon occulting period shows that within a two month time frame, signal loss (1) occurs three separate time with the longest being almost 3. This is a significant period of time of lost communications especially during manned missions.

45 4.3 Mars Constellations

Several constellations were investigated from published works and outlined in Table 6.

These particular constellations showed that they could provide full coverage around Mars, but currently none have been built and deployed except Iridium and GPS. Because of the distance and cost to deploy satellites to Mars, a minimum configuration needs to be considered. The design of the Moon constellations can be updated to support the Martian orbital requirements and support full coverage using four, six, or eight satellites. Geostationary satellites will not provide the required total Martian coverage, especially at the poles and were not considered.

Geostationary satellites may be a future addition to augment the constellation and provide additional capabilities and capacity.

The use of constellations such as Iridium and GPS would provide the best scenarios for a constellation for Mars, but due to the complexity and number of satellites, the logistics and costs preclude them at this time for consideration. The 4retro111, Luna POLARIS, Draim are viable options for the Mars environment. Cost should be moderate and could take advantage of planned missions and “piggyback” the satellite payload. Specific missions for deploying the constellation could be designed to deploy all satellites at one time depending the design of the satellites, especially size and weight.

Table 6: Comparison of satellite constellations using a minimal quantity of required satellites to provide full coverage of the Martian surface.

Constellation type of Name Satellites Orbital Benefits/Risks Planes 4retro111 6 6 Designed for Mars, Global (Ely, et al. n.d.) coverage, acquisition of satellites could be problematic, retrograde orbits, high inclination orbit to cover the poles, low inclination to cover equatorial region, low 800 km altitude, no inter-satellite communications, short dwell time

46 Constellation type of Name Satellites Orbital Benefits/Risks Planes Luna POLARIS 8 2 Designed for the Moon, high (Department of Aeronautics orbital altitude, inter-satellite & Astronautics University of communication, moderate dwell Washington n.d.) time Draim 4 4 Minimalist configuration, high (J. E. Draim 1989) orbital altitude provides full view of satellites, long dwell time of >24 hours per hemisphere, no redundancy, unique orbital design GPS 27 6 Global coverage, fault resilient, (National Coordination Office large constellation, very high cost for Space-Based Positioning, Navigation, and Timing 2016) IRIDIUM 66 11 Global coverage, mesh network, (Iridium Communications, fault resilient, extremely large Inc. 2012) constellation, very high cost

4.4 Network Performance, Survivability

An understanding of the basic performance of the communications network is important in the design of the Earth-Mars satellite communications network. Using the speed of light, c, of

8 3.0 x 10 meters per second, the one-way theoretical transmission time, Tsec, can be determined using Equation 6, Table 3. The minimum and maximum values are recorded in Table 7 for the distance and the one-way transmission times or the latency. Both the minimum and maximum distances are provided in order to compare the minimum and maximum latency. Looking at

Mars, which is the exemplar for this paper, the latency varies from 185.67 seconds to 1337.67 seconds, a difference of 720.46 percent.

Table 7: Time for one-way transmission based on the distances to Earth from various large inner-solar system objects. At its closest, Earth-Mars is approximately 3 minutes, but extends to 22 minutes. L4/L5 exhibits a relative constant in the time for a one-way transmission.

Astronomical Distance (d1) Time (Tsec) body (106 Km) for one-way (Sec) Min Max Min Max Moon 0.36 0.41 1.19 1.36

47 Astronomical Distance (d1) Time (Tsec) body (106 Km) for one-way (Sec) Min Max Min Max Mercury 77.30 221.90 257.67 739.67 Venus 38.20 261.00 127.33 870.00 Mars 55.70 401.30 185.67 1337.67 Sun/L4/L5 147.09 152.10 490.30 507.00

The communications delay or latency is primarily from the long distance between Earth and Mars so constellation switching and Mars to orbit delay times are not included. The Earth-

Mars baseline delay of 185.8 seconds, minimum, to 1337.7 seconds, maximum will be used for comparison. For comparison, the maximum Tsec for the Moon is 1.36 seconds as opposed to

1337.67 seconds for Mars. This is approximately 98358 percent or almost 1000 times increase in the transmission time. The delays from ground to space and constellation switching and routing are not a factor in the delay times.

Relay satellites placed at the Earth-Sun L4 and L5 Lagrange points will exhibit changes in their distance relative to the Earth and the Sun due to the change in their orbits around the Sun.

These changes represent approximately a one percent change in the distance. This equates to an increase of approximately one percent, or 17 seconds, in the delay time as seen in Table 7.

Using Figure 8 as a reference showing the path that a signal takes and the distance travelled through the L4 or L5 relay satellites, approximately 500 seconds will be added to the transmission time. For the purposes of this analysis 500 seconds will be used as a constant since there is an approximate one percent difference between minimum and maximum values due to perturbations in their orbits at the Lagrange points. The distance from L4 or L5 to Mars, is determined to have a maximum value of 349.1 x 106 km and a maximum time delay of 1163.7 seconds. Combining the two paths gives a total distance of 499.1 x 106 km and approximately

48 1663.7 seconds of delay maximum. Relaying through L4 or L5 does not come in to play until the distance between Earth and Mars is greater then ~150 x106 km away. The graph in Figure 16 shows that when the total distance between Earth and Mars through the L4 or L5 points is approximately 485 x 106 km, the added delay becomes less of a concern.

Delay verses distance

505.0 500.0 495.0 km) 6 490.0 485.0 480.0 475.0 470.0 465.0 Distance (x 10 460.0 455.0 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 Percent (%)

Delay verses distance

Figure 16: The transmission delay time percentage increases through L4 or L5 as the distance to Mars increases. As the total distance approaches the maximum distance the signal travels through the L4/L5 relays, the delay becomes acceptable. At certain points in the orbit of Earth and Mars, Mars comes closer than the L4, L5 points and relay through them would add extra and unnecessarily latency. When the distance to Mars from Earth is less than approximately 275 x 106 km, the benefit of relaying communications through the L4 or L5 diminishes rapidly when the latency is only considered. The L4 and L5 relay satellites still provide a redundant path in the event of an occulting body.

Utilizing relay satellites at the L4 and L5 Lagrange points provides alternate paths for the communications to travel between Earth and Mars, as shown in Figure 9. As can be seen, the loss of up to two paths will allow communications to continue. This redundancy also allows for multiple paths for the communications to travel providing a higher aggregate throughput,

49 neglecting the inherent delay, along with alternate paths to carry different data across or guaranteed delivery.

The last components of the network include the Earth ground stations. Currently the DSN utilizes very large antennas that range from 34 to 70 meters in diameter, using L4 and L5 to relay transmissions will allow for smaller ground stations on Earth. Since the distance to L4 and L5 will be fixed for all intents and purposes, the use of smaller antennas would be possible due to the reduced and constant signal loss along the transmission path and these smaller units could increase the number of available.

Using Equation 5 and Equation 7, along with Figure 8, a look at signal loss along different paths were compared indicating that signal loss in free space relatively consistent, Figure 17, for the maximums and when L4 or L5 is included. Compared to the Mars Minimum there is additional loss due to the added distance from Mars to L4 or L5. This can be compensated for easily with the proper selection of wavelengths and satellite antenna design both with the Mars constellation and the L4/L5 relay satellites.

1E+49 1E+47 Mars Minimum 1E+45 Mars Maximum 1E+43 L4/L5 to Mars Minimum 1E+41 1E+39 L4/L5 to Mars Maximum 1E+37 L4/L5 to Earth 1E+35 Mars, L4/L5, Earth Minimum Signal Loss (dB) 1E+33 1.00E-03 1.00E-06 1.00E-09 1.00E-12 Mars, L4/L5, Earth Maximum Wavelength (m)

Figure 17: Graph of signal loss for a range of wavelengths indicates that compared to direct to Mars minimum, the Mars, L4/L5, Earth minimum will incur additional signal loss with the primary loss is in the L4/L5 to Mars path.

50 NASA and other space agencies have decades of experience and knowledge in the design, building, launching, deployment, and mission planning of satellites and probes that receive and transmit at great distances. This experience will be critical in the architecture of the inner-solar system communications network. Satellites that make up the Mars constellation for instance would be based on a design that incorporates Earth orbiting communications satellites and space probes. These satellites around Mars for example, would use phased-array antennas for orbit to ground and orbit to orbit communications. Steerable and deployable mesh antennas of up to 18 meters in diameter would be used for communications to the Earth-Sun L4 and L5 points and the DSN.

Satellites at the Earth-Sun Lagrange points L4 and L5 would be based upon the experience and knowledge in the designs used interplanetary missions. Using dual deployable mesh antennas of sizes up to 50 meters could be possible. One antenna would be continually pointed towards Earth reducing the necessity for alignment. The other would be steerable and track Mars.

Power for the satellites will be generated by solar arrays in the case of both the Mars environment and the Earth-Sun L4 and L5 points. The design and deployment of the satellites would need to consider the large diameter antennas to prevent blocking of the solar panels.

4.5 Summary

The largest impact to communications beside the distance, is the phenomenon of occultation, Mars is seen as the primary body that will obscure communications between Earth and Mars and can be overcome by placing a constellation of satellites in orbit. Throughout the

10-year analysis period, the Moon and the Sun provided additional times of occulting and could be a major issue due to their length.

51 The analysis of Earth-Mars continuous satellite communications network shows that utilizing the Earth-Sun Lagrange points L4 and L5 it is possible for continuous data transfer.

Added latency from the increased path length will increase the transmission time, but the network adds redundancy and survivability, plus alternate paths. A link budget analysis shows that the primary delay is in the Earth to Mars Earth to Mars portion of the network.

Analysis showed further that as Mars and Earth are closer together, the relay through L4 or

L5 becomes non-prudent except in the case of redundancy for survivability and alternate data paths for guaranteed delivery.

Several constellation configurations using a minimal set of satellites have been investigated that provide global coverage for the Moon and Mars. These constellations have not been proven in an operational environment, so are unproven. Constellations can take advantage of a hybrid approach to the design of the satellites by utilizing the experience and knowledge in current

Earth based systems and space probes. The Earth-Sun Lagrange L4 and L5 relay satellites would also benefit from this knowledge along with large deployable mesh antennas. This stated, the technology already exists to design, build, and deploy satellites to meet the network requirements.

52 5 DISCUSSION and CONCLUSION

5.1 Introduction

A continuous satellite communications network using the Earth-Sun Lagrange L4 and L5 points along with a satellite constellation orbiting an astronomical body such as Mars is possible.

The distances between Earth and the body prohibit real-time communications and the phenomenon of occulting will place a body in between Earth and the satellite or lander. Utilizing

L4 and L5 provides a method of routing around the object maintaining communications. The use of these Lagrange points will increase the latency by a constant 500 seconds, which is manageable, and as the total distance of the network reaches approximately 485 x 106 km, the percentage increase becomes more acceptable. There are several advantages of using these points such as alternate paths for communications, redundancy and survivability in case of up to two paths loss, guaranteed delivery, and priority selection.

5.2 Restatement of Research Goal

5.3 Research Motivation

As the missions to the inner-planets, Mercury, Venus, Mars, and other bodies such as asteroids continue and increase, along with current missions, the need to communicate with

Earth on a continuous basis will become paramount to the mission success. There are certain aspects of any deep space communications network that will not be overcome due to the limits of

53 our known physical universe, namely the speed at which a photon travels in space, which is approximately 3.0 x 108 meters per second. On Earth and in near-Earth orbit, this limitation is typically not an issue, but as the distance increases to beyond the Moon, the latency, becomes a major issue for real-time or near real-time communications. A communications network between

Earth and the various probes, satellites, landers and rovers can be developed and deployed that can provide a continuous communications network even with latency of tens of minutes.

5.4 Conclusions

Research continues to be conducted regarding communications in support of missions to the inner-solar systems. Review of literature provided details on constellations to support coverage of the planets, particularly Mars, or the Moon. The literature did not provide information regarding the network segment between the planet or Moon and the Earth. A few second delay may not be the best scenario but is acceptable, even in critical situation, in communicating to the Moon with near real-time communications being possible. At greater distances, say to Mars, no consideration has been given to a network for continuous communication.

The distances involved in an Earth-Mars network prevent real-time communication, but a high latency continuous communications network is possible. One concern that such a network overcomes is occulting. Deploying relay satellites at the Earth-Sun L4 and L5 points will allow routing around the object. Also this network will provide redundant paths for communications enhancing survivability.

The analysis of Earth-Mars continuous satellite communications network shows that utilizing the Earth-Sun Lagrange points L4 and L5 is possible for continuous data transfer.

Added latency from the increased path length will increase the transmission time, but the

54 network adds redundancy and survivability plus alternate paths. A link budget analysis shows that the primary delay is in the Earth to Mars portion of the network. Analysis showed further that as Mars and Earth are closer together, the relay through L4 or L5 becomes non-prudent except in the case of redundancy for survivability and alternate data paths for guaranteed delivery.

5.5 Significant Results of Research

The analysis performed on the occulting of Mars revealed that the Sun is not the primary concern in causing signal loss. Within the 10-year period of simulation, Sun occulted Mars only once and Moon six times. Simulation results of the Sun recorded the maximum signal loss period at just less than two days. Though this is not a long time, it could be significant in regards to manned missions. The major source of occulting came from Mars itself as either satellite or lander and rovers went to the back or dark side.

As the distance increased in the Earth to L4 or L5 to Mars network, it was seen that the percentage difference in the latency becoming less. At approximately 485 x 106 km, this difference was deemed acceptable for alternate paths for communication purposes.

Using current satellite and probe technology, experience, and knowledge the design, building, and deployment of a Mars constellation is possible. Deployment seems to be the only challenge due to the long distance and cost of placing satellites at Mars. Again, current technology, knowledge and experience will allow the placement of relay satellites at the Earth

L4 and L5.

5.6 Recommendations for Future Research

There are several areas that will require additional research. One area of research would be the Earth-Sun Lagrange L4 and L5 points. Concern regarding these points and the accumulation

55 of space debris could hinder satellite placement. Research should be conducted in the form of simulation of the gravitational effects of Earth and Sun and the true stability of L4 and L5.

Observations of L4 and L5 also need to be performed to quantify the amount of debris present and possible future.

Research in the placement of relay satellites in places other than L4 and L5 should be performed. Location of relays closer to Earth will reduce the added latency incurred by L4 and

L5. Using station keeping and reaction control techniques that could have a life span of ten years or longer will allow placement within a million kilometers or less. Reducing the latency to a few minutes or even seconds would make the relay a valid option. This research would also look at the optimum placement to relay throughout the inner-solar system.

Lastly, continued research in the constellation design should be performed to determine the optimum size and configuration. Included in this research would be the satellites that would make up the constellation and the relay satellites at the Earth-Sun Lagrange points L4 and L5 or other intermediate locations.

56 APPENDIX A

A.1 GMAT Occulting Model Configuration Parameters

To model the occulting phenomenon caused by various astronomical bodies, the following model was used with Mars as an exemplar. Mars was chosen due to the current focus on possible manned missions in the late 2020’s to early 2030’s. Also, GMAT already had supplied models and examples for Mars, making the development of the model easier.

% Occulting of spacecraft by Mars, Phobos, Deimos, Mercury, Venus, Luna, Sol %------%------Solar System User-Modified Values %------GMAT SolarSystem.EphemerisSource = 'SPICE'; GMAT SolarSystem.SPKFilename = '../data/planetary_ephem/spk/de421.bsp'; %------%------User-Modified Default Celestial Bodies %------GMAT Earth.EquatorialRadius = 6378.1366; GMAT Earth.Flattening = 0.00335281310845547;

GMAT Mars.OrbitSpiceKernelName = {'../data/planetary_ephem/spk/mar063.bsp'}; %------%------User-Defined Celestial Bodies %------Create Moon Phobos; GMAT Phobos.NAIFId = 401; GMAT Phobos.SpiceFrameId = 'IAU_PHOBOS'; GMAT Phobos.OrbitSpiceKernelName = {'mar063.bsp'}; GMAT Phobos.OrbitColor = Tan; GMAT Phobos.TargetColor = DarkGray; GMAT Phobos.EquatorialRadius = 13.5; GMAT Phobos.Flattening = 0.3185185185185186; GMAT Phobos.Mu = 0.0007093399; GMAT Phobos.PosVelSource = 'SPICE'; GMAT Phobos.CentralBody = 'Mars'; GMAT Phobos.RotationDataSource = 'IAUSimplified'; GMAT Phobos.OrientationEpoch = 21545; GMAT Phobos.SpinAxisRAConstant = 0; GMAT Phobos.SpinAxisRARate = -0.641; GMAT Phobos.SpinAxisDECConstant = 90; GMAT Phobos.SpinAxisDECRate = -0.5570000000000001;

57 GMAT Phobos.RotationConstant = 190.147; GMAT Phobos.RotationRate = 360.9856235; GMAT Phobos.TextureMapFileName = 'GenericCelestialBody.jpg'; GMAT Phobos.3DModelFile = ''; GMAT Phobos.3DModelOffsetX = 0; GMAT Phobos.3DModelOffsetY = 0; GMAT Phobos.3DModelOffsetZ = 0; GMAT Phobos.3DModelRotationX = 0; GMAT Phobos.3DModelRotationY = 0; GMAT Phobos.3DModelRotationZ = 0; GMAT Phobos.3DModelScale = 10; Create Moon Deimos; GMAT Deimos.NAIFId = 402; GMAT Deimos.SpiceFrameId = 'IAU_DEIMOS'; GMAT Deimos.OrbitSpiceKernelName = {'mar063.bsp'}; GMAT Deimos.OrbitColor = Tan; GMAT Deimos.TargetColor = DarkGray; GMAT Deimos.EquatorialRadius = 7.5; GMAT Deimos.Flattening = 0.3066666666666666; GMAT Deimos.Mu = 0.0001588174; GMAT Deimos.PosVelSource = 'SPICE'; GMAT Deimos.CentralBody = 'Mars'; GMAT Deimos.RotationDataSource = 'IAUSimplified'; GMAT Deimos.OrientationEpoch = 21545; GMAT Deimos.SpinAxisRAConstant = 0; GMAT Deimos.SpinAxisRARate = -0.641; GMAT Deimos.SpinAxisDECConstant = 90; GMAT Deimos.SpinAxisDECRate = -0.5570000000000001; GMAT Deimos.RotationConstant = 190.147; GMAT Deimos.RotationRate = 360.9856235; GMAT Deimos.TextureMapFileName = 'GenericCelestialBody.jpg'; GMAT Deimos.3DModelFile = ''; GMAT Deimos.3DModelOffsetX = 0; GMAT Deimos.3DModelOffsetY = 0; GMAT Deimos.3DModelOffsetZ = 0; GMAT Deimos.3DModelRotationX = 0; GMAT Deimos.3DModelRotationY = 0; GMAT Deimos.3DModelRotationZ = 0; GMAT Deimos.3DModelScale = 10; %------%------Spacecraft %------Create Spacecraft sat; GMAT sat.DateFormat = UTCGregorian; GMAT sat.Epoch = '01 May 2016 00:00:00.000'; GMAT sat.CoordinateSystem = MarsMJ2000Eq;

58 GMAT sat.DisplayStateType = Cartesian; GMAT sat.X = -1436.997966885567; GMAT sat.Y = 2336.077717512846; GMAT sat.Z = 2477.8214161098; GMAT sat.VX = -2.978497667195256; GMAT sat.VY = -1.638005864673215; GMAT sat.VZ = -0.183638513743837; GMAT sat.DryMass = 850; GMAT sat.Cd = 2.2; GMAT sat.Cr = 1.8; GMAT sat.DragArea = 15; GMAT sat.SRPArea = 1; GMAT sat.NAIFId = -10002001; GMAT sat.NAIFIdReferenceFrame = -9002001; GMAT sat.OrbitColor = Red; GMAT sat.TargetColor = Teal; GMAT sat.Id = 'SatId'; GMAT sat.Attitude = CoordinateSystemFixed; GMAT sat.SPADSRPScaleFactor = 1; GMAT sat.ModelFile = '/Users/rspangler/Applications/Geospatial/GMAT/R2015a/data/vehicle/models/aura.3ds'; GMAT sat.ModelOffsetX = 0; GMAT sat.ModelOffsetY = 0; GMAT sat.ModelOffsetZ = 0; GMAT sat.ModelRotationX = 0; GMAT sat.ModelRotationY = 0; GMAT sat.ModelRotationZ = 0; GMAT sat.ModelScale = 1; GMAT sat.AttitudeDisplayStateType = 'Quaternion'; GMAT sat.AttitudeRateDisplayStateType = 'AngularVelocity'; GMAT sat.AttitudeCoordinateSystem = EarthMJ2000Eq; GMAT sat.EulerAngleSequence = '321'; %------%------GroundStations %------Create GroundStation Goldstone; GMAT Goldstone.OrbitColor = Thistle; GMAT Goldstone.TargetColor = DarkGray; GMAT Goldstone.CentralBody = Earth; GMAT Goldstone.StateType = Spherical; GMAT Goldstone.HorizonReference = Ellipsoid; GMAT Goldstone.Location1 = 35.42573800000001; GMAT Goldstone.Location2 = 243.110531; GMAT Goldstone.Location3 = 1.009999999998399; GMAT Goldstone.Id = 'Goldstone'; GMAT Goldstone.MinimumElevationAngle = 7;

59 Create GroundStation Madrid; GMAT Madrid.OrbitColor = Thistle; GMAT Madrid.TargetColor = DarkGray; GMAT Madrid.CentralBody = Earth; GMAT Madrid.StateType = Spherical; GMAT Madrid.HorizonReference = Ellipsoid; GMAT Madrid.Location1 = 40.431147; GMAT Madrid.Location2 = 355.752044; GMAT Madrid.Location3 = 0.789; GMAT Madrid.Id = 'Madrid'; GMAT Madrid.MinimumElevationAngle = 7; Create GroundStation Cabera; GMAT Cabera.OrbitColor = Thistle; GMAT Cabera.TargetColor = DarkGray; GMAT Cabera.CentralBody = Earth; GMAT Cabera.StateType = Spherical; GMAT Cabera.HorizonReference = Ellipsoid; GMAT Cabera.Location1 = -35.402477; GMAT Cabera.Location2 = 148.981401; GMAT Cabera.Location3 = 0.648; GMAT Cabera.Id = 'Cabera'; GMAT Cabera.MinimumElevationAngle = 7; %------%------ForceModels %------Create ForceModel fm; GMAT fm.CentralBody = Mars; GMAT fm.PrimaryBodies = {Mars}; GMAT fm.Drag = None; GMAT fm.SRP = Off; GMAT fm.RelativisticCorrection = Off; GMAT fm.ErrorControl = RSSStep; GMAT fm.GravityField.Mars.Degree = 0; GMAT fm.GravityField.Mars.Order = 0; GMAT fm.GravityField.Mars.PotentialFile = 'Mars50c.cof'; %------%------Propagators %------Create Propagator prop; GMAT prop.FM = fm; GMAT prop.Type = RungeKutta89; GMAT prop.InitialStepSize = 60; GMAT prop.Accuracy = 9.999999999999999e-12; GMAT prop.MinStep = 0.001; GMAT prop.MaxStep = 2700; GMAT prop.MaxStepAttempts = 50;

60 GMAT prop.StopIfAccuracyIsViolated = true; %------%------Coordinate Systems %------Create CoordinateSystem MarsMJ2000Eq; GMAT MarsMJ2000Eq.Origin = Mars; GMAT MarsMJ2000Eq.Axes = MJ2000Eq; %------%------EventLocators %------Create ContactLocator cl; GMAT cl.Target = sat; GMAT cl.Filename = '/Users/rspangler/Applications/Geospatial/GMAT/R2015a/Thesis/Martian_contact_Sun.report'; % Replace the following body with one of Sun, Mercury, Venus, Luna, Mars, Phobos, Deimos % or all of them GMAT cl.OccultingBodies = {Sun}; GMAT cl.InputEpochFormat = 'TAIModJulian'; GMAT cl.InitialEpoch = '21545'; GMAT cl.StepSize = 100; GMAT cl.FinalEpoch = '21545.138'; GMAT cl.UseLightTimeDelay = true; GMAT cl.UseStellarAberration = true; GMAT cl.WriteReport = true; GMAT cl.RunMode = Automatic; GMAT cl.UseEntireInterval = true; GMAT cl.Observers = {Cabera, Goldstone, Madrid}; GMAT cl.LightTimeDirection = Transmit; %------%------Mission Sequence %------BeginMissionSequence; Propagate prop(sat) {sat.ElapsedDays = 3700};

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