DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS , Simulation and Study of Gravity Assist Maneuvers IGNACIO SANTOS KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES 1 Simulation and Study of Gravity Assist Maneuvers Ignacio Santos Marzol Abstract—This thesis takes a closer look at the complex LIST OF ACRONYMS maneuver known as gravity assist, a popular method of AU Astronomical Unit interplanetary travel. The maneuver is used to gain or lose ESA European Space Agency momentum by flying by planets, which induces a speed and GMAT General Mission Analysis Tool direction change. A simulation model is created using the GUI Graphical User Interface JPL Jet Propulsion Laboratory General Mission Analysis Tool (GMAT), which is intended to be NAIF Navigation and Ancillary Information Facility easily reproduced and altered to match any desired gravity NASA National Aeronautics and Space Administration assist maneuver. The validity of its results is analyzed, SOI Sphere of Influence comparing them to available data from real missions. Some TCM Trajectory Correction Maneuver parameters, including speed and trajectory, are found to be TRL Technology Readiness Level extremely reliable. The model is then used as a tool to investigate the way that different parameters impact this complex I. INTRODUCTION environment, and the advantages of performing thrusting burns at different points during the maneuver are explored. According ITH the advent of space exploration, dreams of visiting to theory, thrusting at the point of closest approach to the planet W and perhaps even colonizing the planets in our Solar is thought to be the most efficient method for changing speed System began running wild. The techniques for space travel and direction of flight. However, the results from this study known at the time, however, predicted a much gloomier show that thrusting before this point can have some major future. Since the 1920s, the method considered as the state of advantages, depending on the desired outcome. The reason the art for travelling from one planet to another was the behind this is concluded to be the high sensitivity of the gravity assist maneuver to the altitude and location of the point of closest creation of Walter Hohmann, who discovered the lowest approach. energy path between any two planets [1]. This path consisted of an ellipse tangent to both orbits, and defined the minimum Sammanfattning— Detta examensarbete tittar närmare på departure velocity from Earth that a satellite would need in den komplexa manöver inom banmekanik som kallas order to reach its target. One problem became evident when gravitationsassisterad manöver, vilken är vanligt comparing these “minimum energies” to the capabilities of förekommande vid interplanetära rymduppdrag. Manövern chemical rockets available at the time. Not only were they används för att öka eller minska farkostens rörelsemängd genom att flyga förbi nära planeter, vilket ger upphov till en incapable of sending a satellite past Jupiter, but doing so förändring i fart och riktning. En simuleringsmodell är skapad would implicate excessive travel times, such as a 30-year i NASAs mjukvara GMAT med syftena att den ska vara travel to Neptune [2]. reproducerbar samt möjlig att ändra för olika But this would all change in the summer of 1961. A young gravitationsassisterade manövrar. Resultaten från mathematician by the name of Michael A. Minovitch, hired simuleringarna är validerade mot tillgängliga data från riktigt for the summer at the NASA Jet Propulsion Laboratory (JPL), rymduppdrag. Vissa parametrar, som fart och position, har en väldigt bra överenstämmelse. Modellen används sedan för att discovered a way of approaching planetary mission design noggrannare undersöka hur olika parametrar påverkar det that would revolutionize the space community, and open the komplexa beteendet vid en graviationsassisterad manöver, door to outer planets exploration [2]. He explored the genom att specifikt titta på effekterna av en pålagd dragkraft potential of using the gravitational fields of celestial bodies från motorn under den gravitationsassisterade manövern. to the advantage of the mission, as opposed to considering Teoretiskt fås mest effekt på fart och riktning om dragkraften them a nuisance to be countered with propulsion. He proved från motorn läggs på vid punkten närmast planeten. Resultaten från denna studie visar att beroende på vilken parameter man that travelling close to planets could be used to gain speed vill ändra så kan man erhålla mer effekt genom att lägga på without the use of any thrust. If planned accurately, the dragkraften innan den närmsta punkten. Förklaringen till detta resulting velocity could be directed towards a second planet, är att den gravitationsassisterade manövern är väldigt icke- where the process could be repeated. This method meant a linjär, så en tidigare pålagd dragkraft kan kraftigt förändra huge step forward in dealing with the two main challenges for farkostens bana nära planeten, så att farkosten t.ex. kommer space exploration. The propellant needed to reach the outer närmare och då påverkas mer. planets was highly reduced, allowing for a satellite to aim for Index Terms—B-Plane, Gravity assist maneuver, the nearest celestial body, and letting its gravitational field Interplanetary orbit transfer, Oberth effect, Periapsis, boost it to the subsequent ones. But the travel times were also Simulation model, Space exploration, Trajectory planning. decreased, to the point that planets could be reached in less than half the travel times that were previously obtained This report was submitted for review on November 25th, 2019. Gunnar Tibert is with the Aeronautical and Vehicle Engineering Ignacio Santos is pursuing a Master of Science degree in Aerospace Department at Kungliga Tekniska Högskolan in Stockholm, Sweden. He Engineering at Kungliga Tekniska Högskolan in Stockholm, Sweden served as the examiner for this thesis project. (email: [email protected]). 2 through the Hohmann transfer. not having any planets along the way for gravity assist. Gravity assist maneuvers, while now being commonly The first time that Minovitch’s gravity assist maneuver was used for outer solar system missions, present a challenging performed was in 1973, when the United States of America problem to most engineers. The complexity of the system launched the Mariner 10 space probe [2]. The spacecraft where all parts are moving, combined with the precision travelled to Venus using a Hohmann transfer ellipse, where it needed to perform the desired maneuver, pose a great performed a gravity assist maneuver towards Mercury. It was challenge. This project intends to find a software capable of the first spacecraft to visit the closest planet to the Sun, and recreating this maneuver, and to create a method to allow the in fact the gravity assist was used to slow down the spacecraft, reader to systematically be able to simulate simple and in order to align the new perihelion with the orbit of Mercury. complex gravity assist maneuver missions. Once the The mission was a success, and it confirmed the benefits of simulation process is achieved and validated, it is used to using the gravitational force of celestial bodies to favor space investigate the impact in trajectory deviation of several mission design by greatly decreasing the ΔV budget. factors and to find the most efficient ways of thrusting during The only other orbital probe sent to Mercury, a planetary flyby maximizing the impact on the desired MESSENGER, took place more recently, launching in 2004 trajectory modification. and entering its orbit in 2011. The mission included gravity assist maneuvers at Earth, Venus, and three of them at II. HISTORY Mercury itself, fully taking advantage of the ΔV obtained at Human technology has now been able to reach all the each one. This shows that gravity assist maneuvers are, to this planets in the Solar System, which is a magnificent feat that day, the preferred method of travelling large distances did not seem within reach one hundred years ago. The vast through Space. distances to cover, paired with the immense amounts of C. Jovian Planets energy necessary to do so, presented one of the most challenging endeavors that humanity had ever encountered. The outermost planets of the Solar System – Jupiter, Additionally, each planet presented its own set of challenges, Saturn, Uranus and Neptune – are often named Jovian as the celestial body’s properties, location, and surroundings Planets. This is due to their size, gigantic compared to Earth. were unique and, in some cases, not fully known. The The first two present a mixture of gases instead of a solid approach to exploring each of them would certainly be surface, and the latter two are composed of enormous different but, since the concept was brought up by Minovitch amounts of solid ice. This also grants them the name of Gas in 1961, gravity assist maneuvers have been a key element giants and Ice giants. In comparison with the inner planets, that space mission designers have been able to rely on. To this these are located much further apart from each other, at 5.2 day, all planets have been reached at least once with missions AU (Jupiter), 9.5 AU (Saturn), 19.2 AU (Uranus) and 30.1 involving this maneuver, and some of them have been AU (Neptune) [4]. This presents a much greater challenge for exclusively reached in this way. space exploration, due not only to the distance to be travelled by spacecraft, but also to the slow orbital period of these A. First Steps planets (i.e.: Neptune orbits the Sun once every 165 years). It is worth mentioning that, before the concept of gaining Jupiter, much like Mars and Venus, was initially reached velocity by using a celestial body’s gravitational field was with a direct trajectory in 1973 by the space probe Pioneer 10 created, other missions used similar concepts to their benefit. [5]. The Pioneer 11 however, launched in that same year, The first time that gravity was used to shape the mission would be the first probe to reach Saturn in 1979, performing trajectory was in fact two years before Minovitch’s discovery.