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Circulating Transportation Orbits Between Earth and Mars

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Circulating Transportation Orbits Between Earth and Mars CIRCULATING TRANSPORTATION ORBITS BETWEEN EARTH AND MRS 1 2 Alan L. Friedlander and John C. Niehoff . Science Applications International Corporation Schaumburg, Illinois 3 Dennis V. Byrnes and James M. Longuski . Jet Propulsion Laboratory Pasadena, Cal iforni a Abstract supplies in support of a sustained Manned Mars Sur- This paper describes the basic characteristics face Base sometime during the second quarter of the of circulating (cyclical ) orbit design as applied next century. to round-trip transportation of crew and materials between Earth and Mars in support of a sustained A circulating orbit may be defined as a multi- manned Mars Surface Base. The two main types of ple-arc trajectory between two or more planets non-stopover circulating trajectories are the so- which: (1) does not stop at the terminals but called VISIT orbits and the Up/Down Escalator rather involves gravity-assist swingbys of each orbits. Access to the large transportation facili- planet; (2) is repeatable or periodic in some ties placed in these orbits is by way of taxi vehi- sense; and (3) is continuous, i.e., the process can cles using hyperbolic rendezvous techniques during be carried on indefinitely. Different types of the successive encounters with Earth and Mars. circulating orbits between Earth and Mars were Specific examples of real trajectory data are pre- identified in the 1960s 1iterat~re.l'*'~'~ Re- sented in explanation of flight times, encounter examination of this interesting problem during the frequency, hyperbol ic velocities, closest approach past year has produced new solution^.^'^'^ Some distances, and AV maneuver requirements in both involve only these two bodies while others incor- interplanetary and planetocentric space. porate Venus encounters in the scenario. Some have more or less desirable characteristics as measured by flight times, frequency of encounters, hyper- I. Introduction bol ic approach velocities, closest approach dis- tances, and the amount of midcourse propulsive 4 V The concepts and principles of planetary needed to adjust and maintain the orbit contin- swingby or "gravity-assist" are now we1 1-esta- uously . blished in both theory and practice. A number of planetary science missions a1 ready flown have Circulating orbits share one potential advan- utilized gravity-assist swingbys of Venus and tage for manned transportation between Earth and Mercury (Mariner lo), the Moon ( ISEE-3/ICE), and Mars. They allow a large orbiting facility (herein the giant outer planets (Voyager). This energy- called a "CASTLE") providing all power, living and saving technique can be expected to see increased work space, life support, gravity environment, and use in future automated and manned interplanetary solar storm shelter to be "once-launched", thereby travel. The potentia1 application of interest in obviating the need to carry these massive elements this paper is the transportation of crew and repeated1y through large planetocentric A V maneu- vers. Transportation to and from these CASTLES is carried out by small er Space Taxis using hyperbol ic System Analyst, Member AIAA and AAS rendezvous techniques. Department Manager, Member AIAA Consultant, Member AIAA and AAS This paper will describe the basic character- Member of Technical Staff, Member AIAA istics of circulating orbit design and specific ex- amples of real trajectory data that have been gen- This work was performed by SAIC and JPL under JPL erated in a recent study of this problem.8 The two Contract No. 957404 and NASA Contract No's. NAS7- 918 and NASW-3622. main types of circulating orbits having desirable This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. characteristics are the so-called VISIT orbits and that the connecting heliocentric orbit be nearly the Up/Down Escalator orbits. Each of these candi- tangent to the planetary orbits, i.e., the peri- date orbits will first be discussed in terms of helion of the transfer orbit must be near 1.0 AU their design principles in the approximate model and the aphelion near 1.52 AU. The orbit which world of circul ar and cop1 anar pl anetary motion. satisfies this exactly in the circular coplanar With this background, quantitative results are then model has a semi-major axis of 1.26 AU and a period presented and compared for the multi-orbit propaga- (P) of 1.415 years. If, in addition, it is re- tions in the actual case of eccentric and inclined quired that the. transfer orbit be resonant with planet orbits. Also covered are orbital analysis both Earth and Mars, that is: topics related to the use of the circulating trans- nP = m portation mode, e.g., Taxi vehicle maneuver re- and (1) jP = kPM quirements in launching to (orbit injection) and where n, m, j, and k are small integers, then there separating from (orbit capture) the circulating are only two possibilties. The first possibility facilities. The reader is referred to a companion (denoted VISIT-1) has a period of 1.25 years and a paper in the Conference Proceedings which describes semi-major axis of 1.16 AU. This orbit completes the overall mass performance analysis of circu- four revolutions about the Sun while Earth com- 1ating orbits compared to traditional, minimum- pletes five. It a1 so completes three revolutions energy stopover trajectories in support of a 9 about the Sun while Mars completes two. Hence, the sustained manned Mars Base. 4:5 resonance with Earth and 3:2 resonance with Mars means that Earth encounters will occur once every five years and Mars encounters once every 11. Prelude to Circulating Orbit Design 3.75 years. The second possibility (denoted Earth and Mars revolve about the Sun with VISIT-2) has a period of 1.5 years and a semi-major orbit periods of 1.0 year and 1.8808 years, axis of 1.31 AU. This orbit completes two revolu- respectively. Earth travels in the ecliptic plane tions about the Sun while Earth completes three. with an orbit eccentricity of 0.0168 while Mars It also completes five revolutions about the Sun travels in a plane inclined by 1.85' to the ecl ip- while Mars completes four. The 2:3 resonance with tic with an eccentricity of 0.0934. As a help in Earth and 5:4 resonance with Mars means that Earth understanding the properties of circulating orbits, encounters occur once every three years while Mars ignore for the moment the non-circular, non-co- encounters occur once every 7.5 years. In the cir- planar motion of the real world. Additionally, cular coplanar world the VISIT-1 orbit must have a approximate the period of Mars (PM) by 1.875 years, perihelion of less than 1.0 AU and the VISIT-2 so that every 15 years Earth makes 15 revolutions orbit must have an aphelion of greater than 1.52 AU about the Sun while Mars makes exactly eight revol- since their periods are respectively less than and utions. Since the re1ative geometry between Earth greater than the value of 1.415 computed above. In and Mars repeats with the synodic period of 1517 = the real world, the eccentricity of Mars' orbit 2.1429 years, trajectories connecting them will makes the VISIT-1 orbit ideal for encountering Mars re-occur with this period also. The inertial geo- near its perihelion and the VISIT-2 orbit ideal for metry repeats every 15 years. These relationships encountering Mars near its aphelion. These orbits have important ImpllcatSons in the design and are illustrated in Figure 1. repeatability of circulating orbits between these planets. Due to the resonant characteristics of the VISIT orbits with their Earth and Mars encounters The VISIT type of circulating orbit, first they remain fixed in inertial space in the circular proposed by ~iehoff~'~,evolved from consideration coplanar world. The implication of this is that of a class of trajectories which might display low the planetary encounters must have only a negligi- relative velocities at both Earth and Mars ter- ble effect on the transfer trajectory, but this minals. In order for this to occur it is necessary implies in turn that the encounters while close on a heliocentric scale must be distant on a planeto- the requirement of encountering Earth and Mars. centric scale. This leaves only the eccentricity, e, to be deter- mined. The UpIDown Escal ator type of circul at ing orbit, first proposed by ~ldrin~,evolved from the From Figure 2, it is seen that the magnitude desire to have more frequent and regular encounters of the true anomaly at Earth encounter, 0, is with both Earth and Mars. Since encounter loca- exactly one ha1 f of the required advance of peri- tions on a 1517 synodic period orbit rotate 117 of helion, 101 = A 9/2. Thus, Earth is encountered at a circle per revolution, there exists a synodic a true anomaly of 25.7" and the flyby changes the precession of the line of apsides equal to 51.4' true anomaly to -25.7'. The net effect is to ro- per orbit which must be accommodated by either tate the orbit by 51.4O. The value of true anomaly propulsive maneuvers (which are not desirable) or, at Earth encounter specifies the final orbital to the extent possible, by gravity-assist swingbys element, e, through the conic equation: 2 of the planets (primarily Earth since it is more r = a(1-e )/(l+ecosQ) (2) massive). Given this effective trajectory shaping, where both Earth and Mars will be encountered sequen- r = 1 AU tially every 2-1/7 years. The encounter speeds at a = (15/7)~/~-=1.662 AU both planets (but principally Mars), however, will 0 = -25.7 degrees be significantly higher than those of VISIT orbits Solving the quadratic equation in e gives e = because the 2-117 year period transfer orbit has an 0.416.
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