This answer to Would we have spotted the ascent stage of Apollo 11's Eagle if it was still in orbit around the Moon? and discussion under it suggests that as a check of the orbital propagation calculations for the Apollo 11 ascent stage which show it may have been in a survivable orbit, the author should have repeated their calculations for the PFS objects as a check on their methods.

note: PFS = Particles and Fields Subsatellite 1, 2

The calculation is described below. Here, I would like to ask:

Question: Are the initial conditions for the Apollo PFS objects' orbits known (or knowable) as well as they were for the Apollo 11 ascent module? Could these calculations have been repeated for them to verify this GMAT-based methodology?

From the paper in arXiv

  1. Methodology

The simulator used is the General Mission Analysis Tool (GMAT) which was developed by NASA and is freely available online (NASA, 2019). This environment has been certified by NASA for use in mission planning. GMAT allows for the substitution of gravity models, and can natively load and interpret GRAIL models, which are also freely available. Lunar gravity is modeled using spherical harmonics, and GRAIL models are available with harmonic degree and order as high as 1200. The simulations reported here used the “gggrx 1200a sha.tab” model. The computation required to propagate a simulation increases roughly as the square of the harmonic degree/order, and this places a practical limit on the fidelity of the model that can be used. Simulations described here were run with degree/order of the models set to 200, and in this case a simulation of ten years of spacecraft time completes in about 8 hours. Trial runs with degree and order as high as 1000 showed very similar results relative to “standard” runs at 200, suggesting that the major conclusions of this work would stand up even if significantly greater computation had been dedicated to the task. The simulation results also have been verified by a third party using a lunar orbit simulation tool that is completely independent of GMAT.


The PFS- satellites were inserted into a lunar orbit in order to map, amongst other things, its gravitational field. So you would expect their orbit to be accurately known and monitored. The Apollo 16 mission report gives the following orbital parameters in Sect. 5-5

PFS-1 : Perilune 105 km, Apolune 144 km, Inclination -28 deg

PFS-2: Perilune 97 km, Apolune 120 km, Inclination -11 deg

These two NASA pages (PFS-1 , PFS-2 give slightly different values though

PFS-1: Perilune 102 km, Apolune 139, Inclination -28.5 deg

PFS-2: Perilune 90 km, Apolune 130 km, Inclination -10 deg

According to the information in theses NASA documents PFS-2 crashed after 425 revolutions on the far side of the moon. PFS-1 was still in orbit when ground support was terminated after about 1.5 years but is supposed to have crashed some time after that.

The orbital elements used in the cited work for simulating the orbit of the Eagle ascent stage after being jettisoned from Apollo 11 are actually apparently those of the command module as calculated from the orbit data in the Apollo 11 mission report (Table 7-II) (the lunar module was not really of any interest anymore at this point, so it probably was not systematically tracked after that). This resulted in the following orbital elements they tried for their simulations for the lunar module

enter image description here

The eccentricity of the orbit for these three cases is practically the same: 0.0037, 0.0038, 0.0035 for the nominal, maximum and minimum case respectively.

However, in the Apollo 11 Flight Journal they mention these figures explicitly for the lunar module shortly after 'Ignition of Trans-Earth Injection burn' (about 5 and 7 hours after jettison of the LM)

just before 135:47:24 mission time: Perilune 100.7 km, Apolune 118.7 km

just before 137:30:12 mission time: Perilune 100.7 km Apolune 119.3 km

(they are saying '-cynthion' instead of '-lune' there)

This results in eccentricities 0.0049 and 0.0050 respectively, so substantially higher than assumed for the simulations based on the command module orbit at the time of separation.

So the author may want to revise the orbital parameters in this sense, and also apply the simulation to the PFS-2 satellite in order to remove any ambiguities here and make his results more conclusive.

  • $\begingroup$ Im not suggesting a different mechanism for expansion. I only ask what would be visible if all particles expand if there are no forces between them. No basic forces that is. If only gravity (curved spacetime) is present. Sorry for commenting here. I will soon delete. I think its an intersting issue. I cant comment on the astronomy site. $\endgroup$ Aug 2 at 18:14

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