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Physics, Astronomy & Cosmology / Re: Would a Hohmann Transfer be more fuel efficient to attain lunar orbit?
« on: 20/02/2018 22:49:50 »
OK, hardcore orbital mechanics follows, you have been warned.
First, it's not true that Hohmann is necessary minimal (bielliptic transfers can be lower delta-v). To be accurate you can't even use a Hohmann transfer to get to the moon, because a Hohmann transfer only works between two circular orbits around a single central gravitating body. But with the moon there, there's a second body. It turns out though that that's a good thing.
The Apollo transfer uses less fuel than a Hohmann transfer would because it uses Oberth effect:
https://en.wikipedia.org/wiki/Oberth_effect
In other words as the vehicle falls into the lunar gravitational field it speeds up. But rockets work better at high speed/lower altitude, so it can do a small burn at the closest point and enter an orbit around the moon. That also means that the closer the orbit is to the moon when you do the braking burn, the more efficient the trip is. If you did a normal Hohmann at lunar orbital radius, but away from the moon, the vehicle would be at very high altitude above the Earth and the vehicle would be moving very slowly, and so during the circularising burn (to oversimplify slightly) the exhaust would end up moving very fast, and waste lots of energy and fuel.
First, it's not true that Hohmann is necessary minimal (bielliptic transfers can be lower delta-v). To be accurate you can't even use a Hohmann transfer to get to the moon, because a Hohmann transfer only works between two circular orbits around a single central gravitating body. But with the moon there, there's a second body. It turns out though that that's a good thing.
The Apollo transfer uses less fuel than a Hohmann transfer would because it uses Oberth effect:
https://en.wikipedia.org/wiki/Oberth_effect
In other words as the vehicle falls into the lunar gravitational field it speeds up. But rockets work better at high speed/lower altitude, so it can do a small burn at the closest point and enter an orbit around the moon. That also means that the closer the orbit is to the moon when you do the braking burn, the more efficient the trip is. If you did a normal Hohmann at lunar orbital radius, but away from the moon, the vehicle would be at very high altitude above the Earth and the vehicle would be moving very slowly, and so during the circularising burn (to oversimplify slightly) the exhaust would end up moving very fast, and waste lots of energy and fuel.