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December 16th, 2007, 05:15 PM   #1
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Circular Motion

1. Suppose a spacecraft was in between the Earth and the Moon. At what distance from the Earth would the Moon's gravity balance Earth's gravity?
2. What would be the acceleration due to gravity on the surface of the Sun? (The Sun has a radius of about 700000 km.)

These problems are hard for me, and I have an final exam on Tuesday, so if anyone will help me out on these problems, it'll be much helpful to me.


Thanks,

J.
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December 16th, 2007, 05:38 PM   #2
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Re: Circular Motion

For both problems all the physics you need is that the gravitational force between two objects of mass M and m at distance d is GMm/d^2, where G is the gravitational constant.

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Originally Posted by johnny
1. Suppose a spacecraft was in between the Earth and the Moon. At what distance from the Earth would the Moon's gravity balance Earth's gravity?
Let G be the gravitational constant, E be Earth's mass, M be the moon's mass, d the distance from the craft to the earth's center, d' the distance from the craft to the moon's center, and s be the spacecraft's mass.

GEs/d^2 = GMs/d'^2
Ed'^2 = Md^2

Let D = d + d' be the distance from the earth's center to the moon's center. Then
E(D-d)^2 = Md^2
(D-d)^2 = Md^2/E
D^2-2dD+d^2 = Md^2/E
(1 - M/E)d^2 - 2Dd + D^2 = 0
You can use the quadratic formula to get d.

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Originally Posted by johnny
2. What would be the acceleration due to gravity on the surface of the Sun? (The Sun has a radius of about 700000 km.)
The force would be F = GMm/r^2, and the acceleration would be F / m = GM/r^2. You are given the radius, so just plug in the gravitational constant and mass M of the sun from somewhere and you're done.
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December 16th, 2007, 05:55 PM   #3
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Thanks for the help. I'm having a final this coming tuesday, so are there any more equations or anything that I should brush up on besides the two examples that I've just gave?
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December 16th, 2007, 06:36 PM   #4
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I don't know. I've not taken any physics since my freshman year of undergrad. Most formulas are pretty easy at that level -- dimensional analysis gives you just about everything you need.
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