# The sun exerts a greater gravitational force on the mars compared to the moon right?

#### LoveKnowledge

Just wanted to make sure..

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#### Redbelly98

Staff Emeritus
Homework Helper
Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

The answer isn't obvious. Mars is more massive, but is farther away from the sun. You'd have to compare using Newton's gravitational equation.

#### seto6

Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

just like redbelly said just put in the values in the Newton's gravitational equation..

#### brainstorm

Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

Why wouldn't/isn't the sun's gravitational pull on the moon noticeable in its orbital shape? I would think it should be much farther from the Earth when closer to the sun and much closer to the Earth when on the side away from the sun. Does Earth's pull on the moon somehow neutralize the sun's effects on it?

#### Pengwuino

Gold Member
Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

Why wouldn't/isn't the sun's gravitational pull on the moon noticeable in its orbital shape? I would think it should be much farther from the Earth when closer to the sun and much closer to the Earth when on the side away from the sun. Does Earth's pull on the moon somehow neutralize the sun's effects on it?
The distance from the Earth to the Moon is orders of magnitude less than the distance from the Moon to the Sun. Though, the mass of the Earth is orders of magnitude less than the Sun, but you can do the calculation and the Earth should certainly dominate as far as who wins the gravitational tug of war.

#### Dale

Mentor
Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

Why wouldn't/isn't the sun's gravitational pull on the moon noticeable in its orbital shape? I would think it should be much farther from the Earth when closer to the sun and much closer to the Earth when on the side away from the sun. Does Earth's pull on the moon somehow neutralize the sun's effects on it?
The Earth's pull does not in any way neutralize the sun's effect on the moon. In fact, the sun's pull on the moon is about double the earth's pull on the moon. The sun's pull on the moon can vary between 4.2E20 N and 4.5E20 N if everything lines up just right. The earth's pull on the moon can vary between 1.8E20 N and 2.2E20 N. So even the earth's strongest pull is about half of the sun's weakest pull on the moon.

The distance from the Earth to the Moon is orders of magnitude less than the distance from the Moon to the Sun. Though, the mass of the Earth is orders of magnitude less than the Sun, but you can do the calculation and the Earth should certainly dominate as far as who wins the gravitational tug of war.
The semimajor axis of the earth is about 3 orders of magnitude larger than the semimajor axis of the moon. The mass of the sun is about 6 orders of magnitude larger than the mass of the earth. Since the radius is squared in Newton's law of gravitation the effects of the sun's larger mass and the earth's closer distance are both about 6 orders of magnitude. The sun actually wins the gravitational tug of war, but by less than an order of magnitude.

#### Dale

Mentor
Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

You are correct, the moon does go around the sun rather than the earth. The earth just adds a wobble to the moon's path around the sun.

#### D H

Staff Emeritus
Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

by this calcn the moon should go around the sun rather the earth - is there something i am missing here ?
By that I assume you mean that the since the gravitational force exerted by the Sun on the Moon is about twice that exerted by the Earth then the Moon should escape the gravitational influence of the Earth.

Since the Moon has been orbiting the Earth for 4+ billion years, that obviously is not the case. So yes, you are missing something.

One obvious way to look at the Moon's orbit about the Earth (better stated: the orbit of the Earth and Moon about their common center of mass) is to examine the Moon's behavior from the perspective of an Earth-centered reference frame. This is an accelerating reference frame due to the presence of the Sun and Moon. Strictly speaking, Newton's laws don't apply in such a frame, but with the addition of inertial force terms Newton's laws can be used to examine the Moon from the perspective of an Earth-centered observer.

Gravitation makes the Earth and Moon accelerate toward one another and toward the Sun. From our Earth-centered perspective, the apparent gravitational acceleration of the Moon toward the Sun is that given by Newton's law of gravitation less the gravitational acceleration of the Earth toward the Sun,

$$\vec a_{\text{sun}} = \frac{GM_{\text{sun}}}{||\vec r_{\text{sun}}-\vec r_{\text{moon}}||^3} (\vec r_{\text{sun}}+\vec r_{\text{moon}}) - \frac{GM_{\text{sun}}}{||\vec r_{\text{sun}}||^3} \vec r_{\text{sun}}$$

This acceleration is greatest for a new moon at apogee, about 3.2×10-5 m/s2.

The acceleration of the Moon toward the Earth due to their mutual gravitational attraction to one another is

$$\vec a_{\text{earth}} = -\,\frac {G(M_{\text{earth}}+M_{\text{moon}})}{||\vec r_{\text{moon}}||^3} \vec r_{\text{moon}}$$

This acceleration is smallest when the Moon is at apogee, about 2.5×10-3 m/s2. From this perspective, the gravitational acceleration toward the Sun is a smallish perturbation of the much larger mutual gravitational acceleration of the Earth and Moon toward one another.

#### D H

Staff Emeritus
Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

Why wouldn't/isn't the sun's gravitational pull on the moon noticeable in its orbital shape?
The Sun certainly does effect the Moon's orbit, but no so much its shape as other effects. Even the ancients (Ptolemy) noticed some of the effects. The Moon, for example, appears to speed up at new Moon and slow down at full Moon. This is the eviction, and Ptolemy saw this. There are lots of other effects, some rather small. The eviction is the largest effect.

#### brainstorm

Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

You are correct, the moon does go around the sun rather than the earth. The earth just adds a wobble to the moon's path around the sun.
That's interesting. Doesn't that mean that the Earth must be decelerating or accelerating in its path around the sun depending on where the moon is in its orbit?

Also, from the other posts it really sounds like the moon should be much closer to Earth when it's on the side opposite the sun. About how much distance in the two points of orbit is there?

Here's another related question: if the moon would be annihilated as it is orbiting on the sun-side of the Earth, would that cause the Earth to move away from the sun? If so, how far would it go? What about if that happened while it were on the side away from the sun? Would Earth fall into the sun then?

#### D H

Staff Emeritus
Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

Also, from the other posts it really sounds like the moon should be much closer to Earth when it's on the side opposite the sun.
That is not what happens. There certainly is an effect, however. If the Sun and other planets were not present and if the Earth truly was spherical the Moon would follow an elliptical path. The line from the Moon at perigee to the Moon at apogee would be unchanging. What the Sun does is to make that line of apsides precess. It takes just under nine years for the Moon's line of apsides to complete one revolution.

Here's another related question: if the moon would be annihilated as it is orbiting on the sun-side of the Earth, would that cause the Earth to move away from the sun? If so, how far would it go? What about if that happened while it were on the side away from the sun? Would Earth fall into the sun then?
The effect would be to change the Earth's perihelion and apihelion by a rather small amount, and opposite the sense that you have concluded.

#### LoveKnowledge

Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

Wow what interesting replies. I just want to thank all of you! What a great forum :)

#### brainstorm

Re: the sun exerts a greater gravitational force on the mars compared to the moon rig

The effect would be to change the Earth's perihelion and apihelion by a rather small amount, and opposite the sense that you have concluded.
I was thinking in terms of an astronaut throwing a wrench to produce thrust to project themselves in the opposite direction. The Earth letting go of the moon wouldn't have a similar effect?

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