Question

How to increase the distance between earth and moon ?

v = sqrt(GM/r)

does decreasing the velocity of moon by firing thrusters in opposite direction of motion of the moon increase its distance from earth ?

Answer 1

To make things easier, rearrange the equation to solve for r. That way we can see how different variables influence the value of r:

\[r=\frac{GM}{v^2}\]
Since v^2 is inversely proportional to r, for whatever happens to v^2, the opposite must happen to r. Therefore, if you DECREASE v, you need to INCREASE r to balance this change and maintain a circular orbit. So yes, decreasing the speed would require it to be further from the Earth.

Answer 2

Take a simple example. You fire the thruster and slow the moon to zero velocity relative to earth.

What would happen?

The Earth would pull the moon crashing down. The moon's "desire" to stay in orbit is driven by its tangential velocity.

You would need to speed it up first to increase its radius of orbit.

*Then* you would need to slow it down to satisfy matt's equation for orbit.

Answer 3

Thank you both!

Does that mean decreasing the speed of moon results in a crash ?

What happens if I increase the speed of moon a little and leave.

Then would the moon escape from earth completely ?
Because the outer orbits require less speed, but the moon has a greater speed now...

Answer 4

if it slowed down, it would spiral into the earth.

if it sped up, it would begin to leave the earth.

Answer 5

have you got the answer you want to this?

it's fundamentally a very interesting question.

i'm stuffed these days for time but i would enjoy trying to answer this by equations......if our deliberations are correct, the solar system sounds like it is pretty unstable.