Orbital Mechanics of Spacecraft

Recently, the Parker Solar Probe made history by being the fastest man-made rocket ever. Rocket scientist Jeremy McCauley provides an inside peek at this fascinating launch toward our sun.

Thank God He both created the heavens with orbits and chose to make them in a way we can analyze. Because of the way He has designed the heavens, we can use mathematics to produce orbital mechanics.  Orbital mechanics is a wonderful application of mathematics directly to a physical application. Gravitational orbits are well defined and consistent, based upon ellipses with the planet or sun as one of the two focal points. The trick comes in switching from one orbit to another. This is done by looking at the intersection between the ellipse you are in and the one into which you want to move and figuring the difference between the speed and direction (velocity vector) between the two. There is always some set of thrust maneuvers that allow you to switch between those two, whether in a sustained burn or sets of short pulses. 

For space flight, the challenge then becomes not whether you can switch orbits, but how can you do it most efficiently. In space, there are no gas stations so you only have as much fuel as you can fit on your spacecraft. The more you use early in the flight, the less you have for later and the earlier you will have to shut down or deorbit your satellite. Since I build mostly scientific satellites, this means losing the chance to get more scientific data and possibly missing an event that provides particular insight. 

What is most impressive about the current state of orbital mechanics is the number of tools and the increase in ability that has come to plan maneuvers. We have, over the past decade, flown fleets of five spacecraft in separate orbits that line up in specific positions for scientific observation on a regular cadence (THEMIS). We have flown earth-bound spacecraft repurposed to moon-based observations (ARTEMIS). To do that requires many orbital changes, but with some detailed planning and a stop at L2 (a parking orbit between Earth and the Moon that will soon be occupied by the James Webb Space Telescope) the extremely valuable diminishing fuel resources were able to accomplish the move. 

More recently in the news has been the launch of NASA’s Parker Solar Probe which will take many years and seven Venus flybys to reach its final orbit. Each of these orbital paths, close planetary encounters and the maneuvers associated with them were carefully planned to provide the best science return from the most stable position with the most chance of success, all while saving fuel to provide the long life we hope for from such an observatory. As of today, the inside story showed a better than expected orbital insertion which will provide more fuel for work down the road; hopefully, it will enable a useful life extended far beyond the initial science mission as we go to explore within the Sun’s corona for the first time.

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