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Comparative Analysis of Chemical Propulsion Orbit Transfer Methods and Contribution of Gravity Assist for a Space Mission to Jupiter

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Comparative Analysis of Chemical Propulsion Orbit Transfer Methods and Contribution of Gravity Assist for a Space Mission to Jupiter Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 11, November-2016 Comparative Analysis of Chemical Propulsion Orbit Transfer Methods and Contribution of Gravity Assist for a Space Mission to Jupiter Naga Bharath Gundrati1 Meghana Rachamallu2 1Mechanical and Aerospace Engineering, 2Industrial and Systems Engineering, University at Buffalo, Virginia Polytechnic Institute and State University, Buffalo, USA Blacksburg, USA Abstract— The selection of an appropriate orbit transfer one planet to another. It connects the Lagrange points of the method is one of the major tasks in planning a spacecraft planets and is a result of the gravitational pull of these mission. This paper provides an analysis of three major planets. The another useful application of the planets’ chemical propulsion orbit transfer mechanisms that can be gravitational force and relative movement, is the flyby or applied to the transfer of a spacecraft from Lower Earth Orbit gravity assist. to Jupiter’s orbit; and consequentially the time is taken for the transfer, including the energy and fuel requirements. Lagrange To be able to bring all the orbit transfer methods to a points which form a gravitationally determined path to the common platform and evaluate their relevance and quantify orbit of Jupiter are calculated. The juxtaposition of all the their contribution to the overall mission is appreciated. energy and the requirements for each of the orbit transfer This paper compares the different types of orbit method and Interplanetary Transfer Network are presented. transfers to come out with the optimal method for The Hyperbolic Excess and Capture velocities required to interplanetary transfer to Jupiter based on the different types escape the Gravitational force of Earth and get drawn into an of mission requirement. orbit about a particular altitude above Jupiter respectively are calculated. Finally, the velocity boost from the gravitational II. INITIAL SETTING force of Mars, due to a flyby is also computed and the effect of orientation angle on the velocity gain is shown. We consider a spacecraft mission involving traversing from earth to reach Jupiter. To achieve this, we make a few Keywords— Gravity assist, Hohmann transfer, assumptions to set a background for the comparison. interplanetary transfer network, Jupiter, orbit transfer. A. Assumptions I. INTRODUCTION 1) Circular Orbits There are no circular orbits in the solar system. The The primary motivation behind this particular topic is orbits of every planet have some eccentricity. But in an effort the spacecraft mission by NASA called the Juno. The orbital to simplify the calculations we assumed all the planets to transfer is an integral part of orbital mechanics dealing with have circular orbits. Although orbit transfer mechanisms can the trajectory of the spacecraft involving orbital maneuvers, also be applied to the transfer between elliptical orbits and plane changes, and interplanetary transfers. circular and elliptical orbits, our focus is only on the transfer There are chiefly three types of chemical propulsion between two circular orbits. orbit transfer methods which are unique in their approach 2) Two-body problem trajectories, the Delta-V and time required to reach the final To focus on the orbit transfer mechanisms alone we orbit. The orbital transfer chosen for a satellite is a eliminate the external stimuli such as the effect of the other compromise between the mission requirements, the celestial bodies, space debris etc. This is accomplished by capabilities of the rocket used to launch the satellite and treating the orbit transfer as a two-body problem. This orbital mechanics. In addition to the orbit transfer, the Delta- effectively simplifies our approach and prevents the V required for the spacecraft to escape the gravitational pull consideration of the gravitation forces of the other planets of the source planet and to hook on to the destination orbit and space objects. are overlooked. In the effort to be more accurate for the total fuel required and time required for the mission it is essential 3) The velocity changes due to propulsion are to calculate the hyperbolic escape and capture velocities as considered to occur instantaneously. well. 4) Origin of the launch Often in the space travel, the presence and motion of The spacecraft is launched from a location at the equator astronomical bodies are exploited to provide a and is parked in the Lower Earth orbit (LEO). The lower predetermined path or to gain velocity to aid in the travel of earth orbit (LEO) is the orbit where the spacecraft is usually the spacecraft to the desired planned or an orbit quickly. The parked for assembly and other purposes. It is assumed to be Interplanetary Transport Network is a low energy transfer at an altitude of 350 km from the earth. alternative which requires little to no energy to traverse from IJERTV5IS110077 www.ijert.org 102 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 11, November-2016 5) Inclination of the orbits The hyperbolic escape velocity is computed to be The spacecraft from LEO is transferred to the Jupiter’s 13.57 km/s and the corresponding Delta-V required to orbit which is at an inclination of 1.03 degrees. gain the velocity beyond the escape velocity of earth is 6) Symbols and Notations 2.39 km/s. TABLE 1 Symbols and Notations 2) Hyperbolic Capture Velocity 푣푒푠푐 Escape vf Final The subsequent step after the orbit transfer is to velocity Orbital Velocity capture the spacecraft into the Jupiter’s orbit. This µ Gravitational vt Velocity at requires an additional velocity for the spacecraft to constant Transfer r Radius of the τ Time taken intersect the planets orbit at a certain elevation which is planet for the transfer taken as 500 km for calculation purposes. 2 ∆푣푒 Hyperbolic et Eccentricity ∆푣 = √푣 2 + 푣 − 푣 (3) escape velocity of transfer ellipse 푐 푒푛푐 푒푠푐 푒푠푐 ∆푣푐 Hyperbolic ϕ Flight path capture velocity angle This results in a hyperbolic capture velocity to be 푣푒푛푐 Encounter E Eccentric 60.77 km/s which is higher than the escape velocity of velocity anomaly Jupiter by 1.42 km/s. 훥푣푛푐 Delta-V for y Ratio of inclination mass of planet and sun 푣 Initial orbital z Ratio of the velocity distance from to C. Inclination Change sun and planet inc Inclination a Semi-major in degrees axis The LEO is out of plane with the Jupiter’s zero degrees m Mass of fuel e Eccentricity orbit by 1.03 degrees. To change the orbital plane of the Isp Specific rp Closest spacecraft the velocity vector is adjusted thereby inclination impulse point of approach to the planet of the spacecraft is remodeled [2]. 2 푛푐 푔표 9.8m/s vp Velocity at ∆푣푛푐 = 2푣 sin ( ) (4) the closest point 2 to the planet rp Initial orbital f True Utilizing the law of cosines, the thrust in a direction radius anomaly perpendicular to the orbital plane of the spacecraft is rf Final orbital vB Velocity of determined. radius the flyby body at Semi-major h Momentum axis of the transfer The Delta-V is computed to be 0.53 km/s. orbit vi Initial orbital v∞ Speed of D. Fuel Consumption velocity approach from infinity The Delta-V budget and the minor changes in it are B. Entry and Exit Velocities better understood if their repercussions on the fuel mass that The Delta-V calculated for the orbit transfer does not needs to be carried are studied. The specific impulse of the incorporate the velocity change required to overcome the fuel is assumed to be 500 secs; this value reflects the amount gravitational force of the corresponding planets. If the of thrust produced when a unit of propellant is consumed [3]. spacecraft is put into a transfer orbit alone it would keep The dry mass of the spacecraft i.e. excluding the fuel mass shuttling between the two planet orbits because the orbital is assumed to be 500 kg. period of the spacecraft does not equal to either of the planets ∆푣 orbital periods. 푚 = 푑푟푦 푚푎푠푠(푒퐼푠푝∗푔표 − 1) (5) 1) Hyperbolic Escape Velocity III. HOHMANN TRANSFER The concept of escape velocity is such that the spacecraft just barely escapes the gravitational field of the Hohmann transfer is credited to be the fundamental planet. It is essential that we provide a certain amount of orbit transfer for the interplanetary space missions. energy for the spacecraft to not only escape the gravity of Hohmann transfer works on the assumption that the source Earth but have a finite constant value [1]. Hence we choose and the destination orbits are circular. the LEO as our burn-out point where we intend to initiate the orbit transfer. The Hohmann transfer strategy uses an elliptical 2휇 trajectory between the initial orbit and the final orbit. This 푣 = √ (1) 푒푠푐 푟 transfer mechanism is known to be one of the low energy transfer, involving two burns. The two burns take place one 2 2 at the perigee and the final burn at the apogee of the transfer ∆푣푒 = √푣푒푛푐 + 푣푒푠푐 − 푣푒푠푐 (2) [4]. IJERTV5IS110077 www.ijert.org 103 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Published by : International Journal of Engineering Research & Technology (IJERT) http://www.ijert.org ISSN: 2278-0181 Vol. 5 Issue 11, November-2016 휇 2휇 휇 푣 = √ (6) 푣푡2 = √( ) − ( ) (19) 푟푖 푏 푟푡 푎푡2 휇 2휇 휇 푣푓 = √ (7) 푣푡2 = √( ) − ( ) (20) 푟푓 푏 푟푡 푎푡2 2휇 휇 2휇 휇 푣푡푎 = √( ) − ( ) (8) 푣푡2푐 = √( ) − ( ) (21) 푟푖 푎푡 푟푓 푎푡2 2휇 휇 휇 푣푓 = (22) 푣푡푏 = √( ) − ( ) (9) √푟 푟푓 푎푡 푓 ∆푣푎 = 푣푡푎 − 푣 (10) ∆푣푎 = 푣푡1푎 − 푣 (23) ∆푣푏 = 푣푓 − 푣푡푏 (11) ∆푣푏 = 푣푡2푏 − 푣푡1푏 (24) | | | | ∆푣 = ∆푣푎 − ∆푣푏 (12) ∆푣푐 = 푣푓 − 푣푡2푐푏 (25) 푎 3 ∆푣 = |∆푣 | + |∆푣 | + |∆푣 | (26) 휏 = 휋√ 푡 (13) 푎 푏 푐 푡 휇 푎 3 푎 3 휏 = 휋√ 푡1 + 휋√ 푡2 (27) The Delta-V required for both the burn including an 푡 휇 휇 inclination change prior to the transfer is 14.97 km/s.
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