# Can objects accelerate due to their own gravity?

Gravity is at least primarily based on mass, more mass = more gravity. Planets and stars are spherical because gravity is great enough to compress them into spherical shapes, but (at least as I understand it) even stars are not perfect spheres. As well, most planets are not made of just one element or molecule, so there is also different amounts of matter in different areas of the planet. Smaller objects might be able to be purely one element or molecule, but are usually too small to become spherical due to gravity. Because of this, mass is not perfectly distributed evenly, and so neither is gravity. This can and has been calculated on earth. 9.8 M/s is just the rounded average. Wikipedia's article notes the gravity varies from 9.76 to 9.83 M/s on the surface depending on location.

Since Gravity is not exactly the same all around, then calculating the net force half the planet exerts, and then comparing it to the other half, the forces should not be exact opposites of each other for almost every single plane you choose (With very few exceptions, though probably at least one thanks to the Intermediate Value Theorem). While on earth the mass distribution can change slightly, its so big its probably going to be negligible, while on asteroids, they mostly will not change ever without external forces. Overall, once a net force is found, it would in most instances exist for at least a very long time.

1) Can this net force actually exist due to the planets gravity?

2) If it does exist, Could this force cause the object to move? If not, Why does it not exist, or what cancels it out?

If necessary, Assume there would be some way to tell that it is moving and/or accelerating.

• What do you call net force? The force exerted on which object? – user1583209 Jan 3 '17 at 21:04
• @user1583209 I dont get what you mean. Net force is the accumulation of all forces involved. There is no other explanation, is there? As for which object, I'm talking about parts of an object affecting the Whole of the object. A mountains affect on the planet. – Ryan Jan 3 '17 at 21:16
• @Ryan Net force on what object? Force doesn't exist as a separate entity except in science fiction movies and books. A force is the result of an interaction of two separately existing entities, and they come in pairs (Newton's 3rd Law). – Bill N Jan 3 '17 at 22:21
• @BillN Since when did I say any of that. I never referenced anything smaller than a mountain, and mountains are an accumulation of trillions upon trillions of entities called atoms. Together, they create a net Force on the planet they are located on, a part of the planet is exerting a force on the planet as a whole. All things we can call objects are made up of numerous atoms, and all of them are just the sum of the entities that are their parts. – Ryan Jan 3 '17 at 22:46
• Well, good luck in your studies, then. – Pirx Jan 4 '17 at 1:18

1) The force one part of a planet exerts on another part does exist.

2) This force cannot cause the planets' center of mass to move because it is not the NET force acting on the planet, which should be, by Newton's third law, zero, assuming you ignore the force due to other objects in the Universe.

• Because the gravitational effects of every piece of the planet can be represented as a single point mass at the center of gravity of the planet. – kolosy Jan 3 '17 at 21:32
• @Ryan: As written in the answer by Newton's third law the net force is zero. Imagine for instance a system of just two (point) masses, A (larger mass) and B (smaller mass) making up the "planet". The absolute value of the force that A exerts on B is as large as the one that B exerts on A and given by Newton's law of gravitation: $F_{AB}=F_{BA}=G\frac{m_Am_B}{r^2}$. The two forces have opposite direction so the total force on the planet is zero. Also take Archimedes: "Give me a place to stand on, and I can move the earth." You don't have a place to stand on... – user1583209 Jan 3 '17 at 21:34
• @veletluna -- What's wrong is my bad eyesight. I completely misread what you wrote, so I'm deleting my comment. – David Hammen Jan 4 '17 at 1:07

Can this net force actually exist due to the planets gravity ?

If it does exist, Could this force cause the object to move? If not, Why does it not exist, or what cancels it out?

In a way it can, but perhaps not the way you mean.

An object can collapse due to gravitational forces. Other forces can ultimately prevent an object's complete collapse, but not always.

During a collapse you could consider the different parts as being accelerated inward.

Now if the mass is not symmetrically distributed, I think you are asking if this causes a net motion of the planet, and there is no net motion because the center of the planet is defined to be it's center of mass. The way the mathematics works out the net force on the center of mass will be zero.

Remember that each part "feels" the same force, but in opposite directions.

Someone suggested this :

The force one part of a planet exerts on another part does exist.

This is not correct.

Every part of a planet exerts forces on all the other parts.

We generally do not work with gravity in that way, because we have theorems that say we can make use of less complex mathematics for many purposes.

• Re The force one part of a planet exerts on another part does exist. That is correct. It's what pulls out-of-round pre-planetary objects into nice roundish planetary objects. It's what makes terrestrial planets differentiate into a metallic core surrounded by a rocky mantle. However, no matter how you slice a planet up, the net gravitational force that all those disparate parts exert on one another add up to zero. – David Hammen Jan 4 '17 at 1:11

The net force exerted by any portion of an asteroid on the remainder of the asteroid is zero. Otherwise there would be a relative acceleration between the two components.

Choose a portion, A, of the asteriod. It pulls on the other portion, B. Due to Newton's Third Law, B pulls back on A with the same force that A pulls on B. So while A tries to pull the asteroid in one direction by pulling on B, B pulls the asteroid in the opposite direction by pulling on A. These forces are equal and opposite regardless of the relative size of A versus B.

If gravity were the sole force acting, A and B would each have net forces acting on them and would accelerate toward each other. But this is prevented by another force, compression. Due to the electromagnetic repulsion of the particles making up the asteroid, A and B are kept apart. The compressive force A exerts on B is exactly equal, and opposite, to the gravitational force A exerts on B. So the net force on A is zero, gravity balanced by compression. Likewise for B.

This holds true even with a horseshoe-shaped asteroid. As gravity pulles the ends of the horseshoe together, this gravitational force is balanced by forces of tension within the arms of the horseshoe.

Can this net force actually exist due to the planets gravity?

No, it can't.

Let's suppose it does. Break the planet down into a number of different parts. The net internal gravitational force on the planet as a whole is the sum of the gravitational forces those various parts exert on one another: $$\vec F_\text{self grav,net} = \sum_i \sum_{j\ne i} \vec F_{\text{grav}_{i,j}}$$ where - $F_{\text{grav}_{i,j}}$ is the gravitational force exerted on part number $i$ by part number $j$, - The outer sum is over all of the different parts of our arbitrary breakdown of the planet, and - The inner sum is over all of those parts except for part $i$ itself.

Gravitation obeys Newton's third law, which means $\vec F_{\text{grav}_{j,i}} = -\vec F_{\text{grav}_{i,j}}$, which in turn means that $\vec F_\text{self grav,net} = 0$.

If the body is spinning, and it collapses to a smaller size under gravity, it is going to spin faster, due to conservation of angular momentum.

But it is not going to gain any net linear movement.

For a moment, suppose the body you are thinking about, starts moving in one direction as a whole. That means it gained some momentum in that direction. This violates law of linear momentum. Where is the balancing momentum?

Think like this - suppose you are in space (and can survive there). To simulate the scenario of your imagination, you have all the freedom to move your body parts any way you want. Now do you think you can swim linear in space by moving your body parts? You can not!

In order to gain any momentum in a direction, you have to throw equal momentum in opposite direction. That means the "body as a whole" can not linearly move at all in space by itself in any direction - due to gravity, or by any other means. (excluding things like em drive)