Calculating Gravities for Math to the Moon

[nution]

I have a question for someone who may know a bit more about the calculations involved in this process. Let's say for instance you are standing on Earth and somehow fly off the ground and go straight to the moon. Throughout the flight you will be experiencing different forces of gravity pulling you to the Earth and then eventually towards the moon on your flight.

How can I calculate the various effects of the different gravities on an object at a given point along this trajectory? Also, how could I determine the point where the moons gravity will actually take over and the Earth will loose its grip of you.

Also, is there actually a single point in space that you could "sit" that the pull of Earth's gravity and the pull of the moons gravity have you in a sort of "limbo" where each pulls at the same force, thus canceling each other out?

 

[Pengwuino]

Yes, there is a spot you can sit where you would be under equal gravitational influences from the Earth and Moon. However, the spot moves since if you have two bodies moving, that spot is going to move as well.

The calculation is just a two-body gravitational field problem. Not that "just" implies it's easy.

 

[Filip Larsen]

is there actually a single point in space that you could "sit" that the pull of Earth's gravity and the pull of the moons gravity have you in a sort of "limbo" where each pulls at the same force, thus canceling each other out?

There is (almost) such a point and it is called the first Lagrangian point or L1 [1]. The reason for the "almost" is because L1 is not a stable equilibrium point, meaning that L1 for Earth-Moon in the actual Solar system, an object would slowly drift away from L1. However, the space around L1 is still quite interesting if you want "station-keeping" with minimal use of fuel.


[1] http://en.wikipedia.org/wiki/Lagrangian_point