# Gravitational Force Between; Sun and Earth, Moon and Earth

by NewtonJR.215
Tags: earth, force, gravitational, moon
 P: 10 1. The problem statement, all variables and given/known data "Calculate the gravitational force between: A) The sun and the earth B)The moon and the earth" 2. Relevant equations F= M/r2 3. The attempt at a solution A)The sun and the earth Earth: mass 5.97*10^24 kg Radius 6,380,000 meters Sun: mass 1.99*10^30 Radius 696,000,000 Distance Between Sun &Earth: 1.5*10^11 meters (149,668,992,000 meters) (5.97*10^24)/1.5*10^11 =3.98*10^13 B) The moon and the earth Moon: mass 7.35 *10^22 kg Radius 1,740,000 meters Earth: mass 5.97*10^24 kg Radius: 6,380,000 meters Distance between moon and earth: 384,000,000 meters 5.97*10^24/384,000,000 = 1.55*10^16 **I'm not sure if i'm doing this correctly. I'm not sure if I should use the mass of the sun/moon also or just the earth's mass. Also not sure if i should use the distance between the planets... Thanks for looking it over! 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
Mentor
P: 40,691
 Quote by NewtonJR.215 2. Relevant equations F= M/r2
The gravitational force between two astronomical bodies depends on both their masses and the distance between them:

$$F = \frac{G M_1 M_2}{R^2}$$

(Look up Newton's law of universal gravity.)
P: 10
 Quote by Doc Al The gravitational force between two planets (or planet and moon) depends on both their masses and the distance between them: $$F = \frac{G M_1 M_2}{R^2}$$ (Look up Newton's law of universal gravity.)
So for sun and earth... 6.67*10^-11(5.97*10^24)(1.99*10^30)/ r2

I'm not sure what the radius would be. I thought it would be the distance between the sun and the earth. Which radius would I use, that of the earth or that of the sun?

For the moon and earth...6.67*10^-11(5.97*10^24)(7.35*10^22)/r2

Once again, not sure which radius I would use.

Mentor
P: 40,691

## Gravitational Force Between; Sun and Earth, Moon and Earth

The "R" in the formula for gravity that I gave stands for the distance between the two bodies, not the radius.
P: 10
 Quote by Doc Al The "R" in the formula for gravity that I gave stands for the distance between the two bodies, not the radius.
Oh. Thanks for the response.

So for sun and earth use: 1.5*10^11^2 .... or 149,668,992,000^2

and for moon and earth use: 384,000,000^2

....? thanks again doc.
Mentor
P: 40,691
 Quote by NewtonJR.215 Oh. Thanks for the response. So for sun and earth use: 1.5*10^11^2 .... or 149,668,992,000^2
It doesn't much matter, but 9 significant figures is overkill. But let the calculator do the work. Generally, I advise you to use the most accurate numbers given and only round off your final answer.
 and for moon and earth use: 384,000,000^2
That's fine.
 P: 10 I made it a much smoother number. Thanks for the help Doc. This Problem is SOLVED.
 Mentor P: 40,691 Excellent. Mark it Solved: How to mark problems SOLVED
 P: 6 Sorry for posting on a nearly year old thread and I'm not expecting responses from the original posters but for anybody out there, I've got a question I'm curious about. I googled "gravitational force earth moon" and all I could find is this thread, I was actually looking for the exact figures for the force. Anyways, I thought in the equation (Gm1m2)/(R^2), the R is the distance between the centers of the masses. In other words, the radius of the moon, plus the radius of the earth, plus the average distance between the moon and earth, so not just the average distance between the moon and earth alone. Please correct me if I'm wrong because it will affect my numbers.
Mentor
P: 40,691
 Quote by billyx3 In other words, the radius of the moon, plus the radius of the earth, plus the average distance between the moon and earth, so not just the average distance between the moon and earth alone.
Generally, when figures are given for the average distance between moon and earth they are talking about center to center distance. For example, see: Wiki: Moon.
 P: 6 thank you very much, this clears up a lot for me
 P: 1 I came across this site while following up a funky proposition I found here: which states that the sun's pull on the moon, during a new moon, is almost 3X that of the earth and asks why the moon doesn't just take off When I pound the numbers through G*m1*m2/d² I get min/max numbers of 1.77E20 to 2.3E20 N for Earth<->Moon and min/max numbers of 4.42E20 to 4.49E20 N for Sun<->Moon I've checked the numbers a few times, and used the calculator at http://www.ajdesigner.com/phpgravity...tion_force.php and get the same results. Either I'm making some mistake in the math, or What Ralph Rene claims is a very interesting question... kk
Mentor
P: 40,691
 Quote by kootzie I came across this site while following up a funky proposition I found here: which states that the sun's pull on the moon, during a new moon, is almost 3X that of the earth and asks why the moon doesn't just take off
Careful what you read on crackpot sites. I didn't check your calculations, but the force of the sun on the moon is greater than the earth on the moon. So what? Both moon and earth are in orbit around the sun.

A more interesting question would be: What's the difference in the strength of the sun's gravitational field at the moon's various locations versus the earth's location. (Answer: Not much!)
 P: 1 I came up with 3.5428*10^22N. Other sites have answers that approximate this value.
P: 2
 Quote by Doc Al A more interesting question would be: What's the difference in the strength of the sun's gravitational field at the moon's various locations versus the earth's location. (Answer: Not much!)
Good day new poster here, I was wondering how we would calculate this question? Well my question specifically would be can we calculate the gravitational forces exerted by the moon to a point on the Earth on an hourly basis?
HW Helper
P: 2,324
 Quote by kootzie I came across this site while following up a funky proposition I found here: which states that the sun's pull on the moon, during a new moon, is almost 3X that of the earth and asks why the moon doesn't just take off When I pound the numbers through G*m1*m2/d² I get min/max numbers of 1.77E20 to 2.3E20 N for Earth<->Moon and min/max numbers of 4.42E20 to 4.49E20 N for Sun<->Moon I've checked the numbers a few times, and used the calculator at http://www.ajdesigner.com/phpgravity...tion_force.php and get the same results. Either I'm making some mistake in the math, or What Ralph Rene claims is a very interesting question... kk
Think about an astronaut in the ISS. Earth exerts a much greater force than the ISS on the astronaut, but he doesn't fall to the Earth. Why? Because both he and the ISS ARE falling towards the Earth; they're both in orbit, so the Earth imparts the same acceleration to both objects.
HW Helper
P: 2,324
 Quote by koko86 Good day new poster here, I was wondering how we would calculate this question? Well my question specifically would be can we calculate the gravitational forces exerted by the moon to a point on the Earth on an hourly basis?
What do you mean "a point on the Earth"? Gravity only acts on objects with mass; a geometrical point is not a massive object. That said, you can certainly calculate the Moon's gravitational field. Currently-available astronomical data is more than precise enough to reveal hour-by-hour differences.
 P: 2 By point I mean would the gravitational force being exerted by the Moon on a body of water say in Sydney (Australia) be slightly different to the amount being exerted in say Tokyo Japan, assuming they share the same timezone but have very different coordinates.

 Related Discussions Classical Physics 23 General Physics 10 Introductory Physics Homework 1 Introductory Physics Homework 15 General Physics 7