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I'm interested in studying where in Lunar orbit a station could be deployed. Due to mascons, Lunar orbits below about 200km will eventually decay according to this answer. Presumably, if the goal of such a station were to just be in Lunar orbit, then an orbit above 200km is preferred. However, if the goal were also to land, or conduct closer surface reconnaissance, lower orbits might be preferred.

What is the relationship between orbital altitude and delta V per day to maintain orbital stability? For simplicity I'm happy to assume a circular, equatorial orbit (although a polar orbit would make more sense for landing).

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The relationship is, unfortunately for a simple answer to this question, fundamentally chaotic. Orbits below 100 km can range from stable (over the course of years) to unstable (over the course of days).

The classic example is given by two satellites, PFS-1 and PFS-2, released on the Apollo missions. Neither had capability for stationkeeping. PFS-1 was released by Apollo 15 into a 28.5° orbit ranging from 102 km to 139 km. This changed soon after, but the satellite remained stable. The satellite broke down six months later, but was monitored for about a year after. The satellite is presumed to have since crashed (you know, eventually), but we just got bored waiting for it to do so [main src]. Contrast with PFS-2, released on Apollo 16 into a 10° orbit ranging from 90 km to 130 km. The satellite crashed just 34 days later, after a series of chaotic changes [main src].

Subsequent analysis of such effects determined that there are so-called frozen orbits (orbits where the perturbations from various effects cancel out, making the orbit stable over long periods of time). NASA identified four such orbits for the moon, at 27°, 50°, 76°, and 86°. PFS-1 had been released, accidentally but fortuitously, into an orbit very close to 27°, explaining its longevity.

Other datapoints include the Lunar Reconnaissance Orbiter (deliberately placed into a "quasi-frozen" commissioning orbit (ranging 30 km to 199 km), where it was stable for several months while it was tested, before being moving for the main mission for other purposes), Lunar Prospector (100 km circular orbit, requiring burns "every few months"), and Chandrayaan-1 (spacecraft failure in 2009, rediscovered in 2016 in a stable 150 km to 270 km orbit). Doubtless there are many other spacecraft that could be scrutinized for such salient tidbits.

The important point though, remains that whether an orbit is relatively stable or requires constant stationkeeping is highly dependent on the orbit. In general, lower orbits require more stationkeeping to compensate for mascons (around 100 km, perhaps 10s of m/s per month (?)), but plenty of low orbits exist that are quite stable (10s of m/s per year (?)). To answer such questions precisely, one would need to provide the orbit, and then simulate it accurately to inspect the stability for that particular case.

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    $\begingroup$ Thanks for the answer to a very old question! $\endgroup$ – Michael Stachowsky Apr 25 '20 at 13:09

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