Gravitational Forces: Ratio of Earth & Sun on Moon

[312213]

Homework Statement

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.)

Homework Equations

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

The Attempt at a Solution

F=G(m_Earthm_Moon)/d²
F=6.67×10^-11((6×10²⁴)(7.3×10²²))/3.9×10⁸²
F=192074950690335305719.92110453649
F=1.9e+20N

F=G(m_Sunm_Moon)/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.
What is wrong about this and where?

 

[LowlyPion]

Homework Statement

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.)

Homework Equations

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

The Attempt at a Solution

F=G(m_Earthm_Moon)/d²
F=6.67×10^-11((6×10²⁴)(7.3×10²²))/3.9×10⁸²
F=192074950690335305719.92110453649
F=1.9e+20N

F=G(m_Sunm_Moon)/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.
What is wrong about this and where?

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.

 

[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.

 

[LowlyPion]

The moon is 3.9 × 10⁵ km from Earth's center {Re} and 1.5 × 10⁸ km {Rs} from the sun's center. If the masses of the moon, Earth, and sun are 7.3 × 10²² kg, 6.0 × 10²⁴ kg {Me}, and 2.0 × 10³⁰ kg {Ms}, 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.)

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.

 

[tiny-tim]

Hi 312213!

Well, that method should work …

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

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

Try again!

 

[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.

 

[berkeman]

Merged two duplicate threads into this one...