# Gravity on the moon

## Main Question or Discussion Point

Which of them larger? The gravity of the earth to the moon or the gravity of the sun to the moon?

## Answers and Replies

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HallsofIvy
Homework Helper
I assume you mean the force of gravity the earth exerts on the moon and the force of gravity the sun exerts on the moon. You could, of course, actually calculate both forces but it seems to me that the fact that the moon orbits the earth, not the sun, says it all.

of course I mean the gravitational force ,why the moon does not orbit the sun? Is it relate to the difference of amount of gravitational force of each the sun and earth to the moon or related to the different distance of the moon from sun and earth ?

phinds
Gold Member
2019 Award
of course I mean the gravitational force ,why the moon does not orbit the sun? Is it relate to the difference of amount of gravitational force of each the sun and earth to the moon or related to the different distance of the moon from sun and earth ?
Uh ... you seem to think that the distance and force are not related. Really?

Bandersnatch
But the Moon does orbit the Sun, in very much similar way, if a bit more wobbly, as the Earth does.

D H
Staff Emeritus
You could, of course, actually calculate both forces but it seems to me that the fact that the moon orbits the earth, not the sun, says it all.
That's a trickier issue than you think. Do the calculation. The gravitational force on the Moon toward the Sun is about twice that toward the Earth.

of course I mean the gravitational force ,why the moon does not orbit the sun? Is it relate to the difference of amount of gravitational force of each the sun and earth to the moon or related to the different distance of the moon from sun and earth ?
There are two problems here. One is that you are thinking along the lines of "A orbits B" and "A orbits C" are mutually exclusive. It's not an either-or proposition. The Moon orbits the Earth and it also orbits the Sun.

The other is that gravitational force not being the right metric to decide whether a body is orbiting some other body. A much better metric is energy. Energy answers the question, "is object A gravitationally bound to object B?" Force is pretty much irrelevant.

See this wikipedia article on Hill Sphere.

Moon is closer to Earth therefore its gravitational influence on Moon is more than that of Sun.

D H
Staff Emeritus
See this wikipedia article on Hill Sphere.

Moon is closer to Earth therefore its gravitational influence on Moon is more than that of Sun.
That final statement is wrong. Consider an object orbiting the Earth at a fiftieth of an AU. That obviously qualifies as "closer to the Earth". Yet the Sun's gravitational influence is going to dominate over that of the Earth by any reasonable definition of "gravitational influence". This orbit is not stable.

What do you mean by "gravitational influence"? Certainly not force. It's a simple calculation. The gravitational force exerted by the Sun on the Moon is 2.2 times that of the Earth on the Moon. Certainly not potential energy. Now that factor of 2.2 becomes a factor of 850. So what exactly did you mean by "gravitational influence"?

I intentionally did not mention the Hill sphere because it's an advanced topic and because it does not answer the question at hand. The question at hand is "why can we say that the Moon is orbiting the Earth?" The Hill sphere doesn't address this question. What answers the question of "why can we say that the Moon is orbiting the Earth?" is mechanical energy. The Moon's mechanical energy with respect to the Earth is negative: The Moon is gravitationally bound to the Earth.

What do you mean by "gravitational influence"?
I mean resultant/dominant effect. I agree that this may not be appropriate term in physics.

The question at hand is "why can we say that the Moon is orbiting the Earth?" The Hill sphere doesn't address this question. What answers the question of "why can we say that the Moon is orbiting the Earth?" is mechanical energy. The Moon's mechanical energy with respect to the Earth is negative: The Moon is gravitationally bound to the Earth.
As you already answered OP's actual question i.e. The gravitational force on the Moon toward the Sun is about twice that toward the Earth, I read the question as "why does moon orbit the Earth instead of Sun (that attracts with twice the force)?"
The article I pointed to begins as "Hill sphere is the region in which it dominates the attraction of satellites. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere." So I thought it is good article to read.
Thank you for explaining factors that determine stable orbit.

D H
Staff Emeritus
I mean resultant/dominant effect. I agree that this may not be appropriate term in physics.
You didn't answer my question. What effect? Don't worry, it's a rhetorical question.

If you read that wikipedia article on the Hill sphere (it's a rather lousy article IMHO), you see that they define "gravitational influence" as meaning "having the same angular velocity", which to me is rather bogus. Even then, they get the Hill sphere wrong by a factor of √3.

The Hill sphere is rather arbitrarily defined as a sphere with origin at the center of the secondary body and with a radius equal to the distance to the L1 point. The wikipedia article doesn't mention that the definition is a bit arbitrary. It does mention that it helps determine if an orbit is stable. Note well: This means that whether an object is orbiting another must be defined by some other metric.

As you already answered OP's actual question i.e. The gravitational force on the Moon toward the Sun is about twice that toward the Earth, I read the question as "why does moon orbit the Earth instead of Sun (that attracts with twice the force)?"
That is exactly how I interpreted the question. The answer is not the Hill sphere. The answer is in terms total mechanical energy, or perhaps even better, escape velocity. Energy is a concept that can be grasped at the high school physics level. If the total mechanical energy is negative the object is "orbiting". At least now it is. Escape velocity is similarly within the grasp of a high school student. An object is currently orbiting some other object if the magnitude of the velocity with respect to that other body is less than escape velocity.

Almost nothing orbits forever in the N-body problem. Orbits are transient. Mercury most likely will be ejected from the solar system in a few billion years due to interactions with Jupiter and Venus. Does the fact that it won't be orbiting several billion years from now mean that it isn't orbiting now? Of course not.

The article I pointed to begins as "Hill sphere is the region in which it dominates the attraction of satellites. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere." So I thought it is good article to read.
That's wikipedia for ya. Sometimes it's very good, sometimes it's rather lousy. This is one of wikipedia's many articles of lesser quality. That's my opinion, of course.

Energy is a concept that can be grasped at the high school physics level.
Escape velocity is similarly within the grasp of a high school student.
Alright, I did not pay attention in physics class long back :)

I just searched more, and guess what I found? Why does the Moon orbit the Earth rather than the Sun?

Earth Gravitational Force greater:

$$\frac{G*M_{EARTH}}{R^2} > \frac{G*M_{SUN}}{R^2}$$