Re: Moon escaping

In "nine planets" the Moon escape velocity is listed as 2.38 km/sec. And the moon is orbiting earth at 1.03 km/sec. It seem to me that it would matter which way you "leave" and this would change the Delta-v you would need to escape. Also since the Moon isn't perfect circle the Moon's speed will vary. Also I don't imagine it's taking into account the gravity of Earth. And also would the Earth/Moon orbit be a factor. How much do all these factors add up to to be? It also seem like you could go the "opposite" direction landing on the Moon, and thereby not need to deacelerate as much.

So, the question is what is the minimal delta-v needed to leave the moon in order to get back to Earth (in a spacecraft).

However, in order to get back to Earth you need to be careful that your escape from the Moon doesn't leave you moving so fast that you either escape the Earth entirely or fall into a higher orbit. So you would need to blast off from the trailing side of the Moon in order to subtract the Moon's velocity from your own; ideally, to get back to Earth you want to be at rest with respect to the Earth so its gravity can pull you in, but the best you can do, since you need to escape from the Moon, is 1.35 km/sec relative to Earth (or 2.38 - 1.03).

The escap e velocity from Earth at the Moon's distance is 1.6 km/sec, so even if you blasted off tangent to the Moon's orbit, in the opposite direction from the Moon, you would be no closer to Earth than when you started (in fact, you'd be considerably farther away since your velocity would move you to a higher orbit!)

Obviously you need to blast off in a direction which angles toward the Earth; qualitatively (I don't have the time or resources to calculate the quantitative answer) what you want is this:

1. Blast off at Lunar escape velocity relative to the Moon, but angling toward the Earth so that you are in a hyperbolic orbit (one which will whip in close to the Earth, then back out again to infinity).
2. If you've set up the geometry properly (?), you'll get to Earth with no further expenditure of energy. Won't do you much good, 'cause you'll be dead after you hit.
3. To avoid this, you could set up a situation in which you graze Earth's atmosphere for braking. Depending on how much you trust your heat shield, you may be able to brake enough to make a soft landing without burning any more fuel.
4. What the Apollo missions did was do a burn part-way back to Earth, to drop them into a lower orbit, then another burn just before hitting the atmosphere to reduce their velocity relative to Earth. The delta-v is the same as 1-3 above (though more of it comes from your fuel supply), but you do a lot less damage to yourself!