# Would flying westwards on the Moon be more efficient than east?

I understand that flying in either direction on a planet that has an atmosphere doesn't effect flight times, but on a body such as the moon, would it improve flight times?

Yes, your suborbital hop stays fixed in an inertial frame of reference, and the Moon rotate slowly underneath you.

It is not that important though, as the rotation rate of the surface of the Moon is only $4.6m/s$, relatively small compared to the orbital velocity of $1720m/s$

Actually, a similar but even weaker effect exists on Earth too, only eastwards instead. With the same velocity relative to the air, you are then moving at a higher fraction of orbital velocity, and it is then easier to counteract gravity.

The most efficient way of performing a flight on the Moon is a suborbital ellipse, with foci in the centre of the Moon, and directly between the two endpoints:

• I am wondering if I'm the first to invent that technique. I had been searching for years and then one of Mark Adler's stack exchange answers about suborbital hops had the phrase "minimum ΔV ballistic trajectory". That jogged my memory that Conway and Prussing used the phrase "minimum energy ellipse" in their chapter on Lambert space triangles. Rereading that chapter, this pretty geometry then became obvious. Feb 14, 2016 at 16:47
• @HopDavid I found your blog post a while ago, and I just had to check the math. Beautiful! That diagram is always with me. Feb 14, 2016 at 17:09
• 9.36m/s (2*4.67) of savings on Moon/s equator, times cosine of latitude, for other latitudes. If that's a problem in your delta-v budget, you should really rethink the whole mission.
– SF.
Feb 14, 2016 at 19:41