When is the force of gravity 0?

[Alameen Damer]

Homework Statement

Homework Equations

Fg=Gm1m2/r^2
g=Gm/r^2

The Attempt at a Solution

I am having trouble finding a way to start. I can't set the g to 0 because that would not let me solve for radius.

 

[RUber]

The net Gravity is zero when the two forces are in equilibrium. Set gravity from Earth equal to gravity from moon and solve for r.

 

[Alameen Damer]

Do i make it so the forces of gravity equal to 0 or the accelerations of gravity equal to 0

 

[DaveC426913]

Do i make it so the forces of gravity equal to 0 or the accelerations of gravity equal to 0

It's late, and I'm not overthinking this but I do believe that the answer is: yes!

F=ma, but you will find that m will drop out of the equation (since it does not matter how massive the rocket is).

 

[Alameen Damer]

Ok so the forces of gravity must cancel out:

FgE=FgM

9.8m=gMm

gM must equal 9.8

9.8=Gm1/r^2
r=root(Gm1/9.8)
r=709685

Shouldn't that be the answer? As at that distance the g of the moon equals 9.8?

 

[haruspex]

Ok so the forces of gravity must cancel out:

FgE=FgM

9.8m=gMm

gM must equal 9.8

9.8=Gm1/r^2
r=root(Gm1/9.8)
r=709685

Shouldn't that be the answer? As at that distance the g of the moon equals 9.8?

But what will the acceleration due to Earth's gravity be there?
(Besides, that's less than the moon's radius.)

 

[MalachiK]

If I were going to solve this problem then I'd start by drawing a diagram with the Earth and the Moon separated by the orbital radius of the moon that is given in the question. Next, I'd mark a point somewhere between the Earth and the Moon were the pull towards the Earth is the same as the pull towards the moon. We don't know where this point is yet, but we know that it is some distance r₁ from the Earth and some other distance r₂ from the Moon.

Then I'd pretend that I was putting a small mass, m, at that point. We already have a formula to calculate the force on the small mass due to the Earth. The same formula works for the force pulling towards the Moon. All we have to do is write down an equation (don't put in any numbers yet!) setting these two forces equal to each other. You might notice that some terms can be canceled out.

We can also write down another equation. What would you get if you added together r₁ and r₂?

Since we have two equations you might want to think about how we can now solve for the two unknown quantities r₁ and r₂. If you can remember solving simultaneous equations in a maths class then this will be useful.

 

[RUber]

If you let R be the distance between the centers of the Earth and moon, then the only unknown for distance is r, the distance from Earth's center. The distance from the moon's center is necessarily R-r.