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 teroxide did not mix an d 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. This may cause satellites to eventually crash into the moon. Can someone estimate how long this would be for the case of the Apollo 8 lunar orbit?