Determine frozen orbits around the Moon around Poles

[MatthewGrim]

This issue will try to replicate results for frozen orbit families and determine if there is a high altitude orbit that is appropriate for use for SPS applications in polar orbits.

Brandhorst's chapter from the Book Moon, by V. Badescu, suggests that there is but does not give a reference.

Lunar Frozen Orbits by Folta nd Quinn suggests otherwise for high altitude orbits.

I need to review some literature and try to understand the fundamentals of their models so I can understand their assumptions.

[MatthewGrim]

Review of Orbits

The high inclination orbits are LLO and not appropriate.

The Ely orbits are at 51 degrees, more elliptical and a potential alternative to the basic simulations we've so far used.

The Prograde circular orbits are higher inclination and in the range of those we've used in our simulations. This might even be the best option I need to do more research.

[MatthewGrim]

This overview paper of staging orbits related to the links above is my best lead beyond the papers on frozen orbits.

[MatthewGrim]

For FO and PCO, the following references were given:

Elipe, A., and M. Lara. “Frozen Orbits About the Moon,” Journal of Guidance, Control, and Dynamics, Vol, 26, No. 2, March-April 2003. [16] Folta, D. and D. Quinn. “Lunar Frozen Orbits,” 8 -Manuscript Draft- October 21, 2015, 4:12pm AIAA/AAS Astrodynamics Specialist Conference and Exhibit, AIAA 2006-6759, August 2006, Keystone, CO. [17] Ely, T. and E. Lieb. “Constellations of Elliptical Inclined Lunar Orbits Providing Polar and Global Coverage,” AAS/AIAA Astrodynamics Specialist Conference and Exhibit, AAS 05-343, August 2005, Lake Tahoe, CA.

None of these support PCOs which make me think they are a red herring for the Moon. The others are all papers I have read, which make me think I should just proceed with my original plan and validate the Ely and Quinn orbits with HPOP.

[MatthewGrim]

Validate Figure 2 of Ely and Lieb

Figure 2 shows the behaviour of several frozen orbits computed numerically with Earth gravity included. I am currently in the process of replicating these results to see if we can find comparable orbits with the theory they propose.

[MatthewGrim]

The two results are similar to the plots in the paper. I have similar results for the first two years of the circular orbit case as well.

[MatthewGrim]

An close approximation to the orbit used in our polar simulations is given below.

The orbit fails after 1.5 years - presumably because the perigee altitude is too low. If we need to be this close, then we need a slightly lower eccentricity. 300km altitude is still where the lunar perturbations are significant.

[MatthewGrim]

A second approximation that I set to have an altitude above 800km with e=0.45 survives, but gets dangerously close to the moon at one point...

[MatthewGrim]

So the Ely orbit that is cited is stable. The question is whether I can get a better orbit for targets at the 45 degree angle that approximates polar?

[MatthewGrim]

How do I best make use of the data sets that we already have for the polar orbits

What I need to do is to find similar frozen orbits to these polar cases, most importantly with the same eccentricity as this will affect the access time to the target most.

The apogee radius is also important as any tilt from the lunar Z axis will mean the satellite will have less line of sight access to one side of the Moon over the other.