# Apollo and orbital mechanics: orbital decay if the Trans Earth Injection (TEI) burn had failed

I'm reading Jim Lovell (Apollo 8 and 13) and Jeffrey Kluger's book Apollo 13, which is a fantastic read about a long past era I only have kindergarten memories of. On page 54 there is a paragraph that reads (emphasis mine):

Also, unlike the LOI burn, during TEI there would be no free-return slingshot to send the ship home in the event that the engine failed to light. If the hydrazine, the dimethylhydrazine, and nitrogen tetroxide did not mix and burn and discharge just so, Frank Borman, Jim Lovell, and Bill Anders would become permanent satellites of Earth's lunar satellite, expiring from suffocation in about a week and then continue to circle the moon, once every two hours, for hundreds — no thousands; no, millions — of years.

Apollo 8 was in an elliptical orbit of 169.1 × 60.6 miles. I am skeptic about how long such an orbit would be stable. My skills in orbital mechanics are rudimentary at best and I know there is no atmosphere to cause orbital decay due to atmospheric drag. But I have heard about other effects causing orbits to decay over time, such as variations in the moon's gravitational field (density anomalies, mascons). This may cause lunar satellites to eventually crash into the moon. Can someone estimate how long this would be for the case of the Apollo 8 lunar orbit?

-

## migrated from skeptics.stackexchange.comMay 12 '12 at 13:10

This question came from our site for scientific skepticism.

Where have you heard that orbits about the moon could decay? I'm doubtful that variation in the gravity field could cause that. I can't think of any kind of tidal drag that could do it either. – Mike Dunlavey May 13 '12 at 2:18
@MikeDunlavey It is known that two of the Lunar Module's ascent stages, which were left in a lunar orbit, eventually crashed on the moon. See en.wikipedia.org/wiki/Apollo_Lunar_Module (LM-5 and LM-11). Other LMs were deliberately crashed on the moon, these two were left to orbital decay. – Jens May 13 '12 at 11:39
OK, I learned something. Good question. – Mike Dunlavey May 14 '12 at 0:56