# Gravitational Forces

1. Apr 1, 2009

### 312213

1. The problem statement, all variables and given/known data
The moon is 3.9 × 105 km from Earth's center and 1.5 × 108 km from the sun's center. If the masses of the moon, Earth, and sun are 7.3 × 1022 kg, 6.0 × 1024 kg, and 2.0 × 1030 kg, respectively, find the ratio of the gravitational forces exerted by Earth and the sun on the moon. (Use G = 6.670 × 10-11 Nm2/kg2.)

2. Relevant equations
F=G(m1m2)/d²
Where F is the force, G is gravity constant, m1 and m2 are masses, and d is distance.

3. The attempt at a solution
F=G(mEarthmMoon)/d²
F=6.67×10-11((6×1024)(7.3×1022))/3.9×108²
F=192074950690335305719.92110453649
F=1.9e+20N

F=G(mSunmMoon)/d²
F=6.67×10-11((2×1030)(7.3×1022))/1.5×1011²
F=432808888888888888888.88888888889
F=4.3e+20N

1.9e+20N / 4.3e+20 = 2.2
and I tried its inverse, 0.44

Neither of these are correct.
I am probably missing something from the question.

Last edited: Apr 1, 2009
2. Apr 1, 2009

### LowlyPion

First of all lose the precision. It only makes it difficult to see what's going on.

Second of all since they want a ratio. Take it right upfront and recognize that you can express it more simply as:

Fe/Fs = Me*ds2/Ms*de2

Makes calculation a little easier.

3. Apr 1, 2009

### 312213

Me*ds2/Ms*de2
(6×1024*1.5×1011²)/(2×1030*3.9×108²)
0.44

Imputing this as an answer results in an incorrect.

I'm not really sure what the question is asking for, since what I did seems to be correct, as far as I can tell.

4. Apr 1, 2009

### LowlyPion

Earth to Sun Ratio = (6.0 x 1024 kg) * (1.5 × 108 km)2 / 2.0 × 1030 kg * (3.9 × 105 km)2 = .4438

Sun to Earth ratio = 2.253

The numbers look right.

5. Apr 2, 2009

### tiny-tim

Hi 312213!

Well, that method should work …

but why are you putting G and mmoon into the figures?

This is a dimensions problem, and all you need is the ratios.

Try again!

6. Apr 2, 2009

### 312213

Well this was just the first way I took it. As ratios, the numbers are the same.

Fe/Fs = Me*ds2/Ms*de2

Me*ds2/Ms*de2
(6×1024*1.5×1011²)/(2×1030*3.9×108²)
0.44

Still 0.44.
I think the question is looking at something else. Or wrong altogether.

7. Apr 2, 2009

### Staff: Mentor

Merged two duplicate threads into this one...