Gravity and Acceleration

I seem to be missing something very basic to the relationship between gravity and mass. If gravity is equivalent to acceleration, what is the basis for the acceleration that generates the gravitational force of an object such as the earth? What is accelerating? Am I even thinking about this in the right way?

Staff Emeritus
what is the basis for the acceleration that generates the gravitational force of an object

I don't understand the question. However, in case this is the question, gravity causes acceleration. Acceleration does not cause gravity.

jbriggs444
Homework Helper
I seem to be missing something very basic to the relationship between gravity and mass. If gravity is equivalent to acceleration, what is the basis for the acceleration that generates the gravitational force of an object such as the earth? What is accelerating? Am I even thinking about this in the right way?

If you adopt an inertial free fall frame (the rest frame of an apple falling from a tree, for instance) then the tree and the surface of the earth are accelerating outward while the apple remains at rest.

The tricky part is accounting for the idea that every part of surface of the earth is accelerating outward but those parts are not getting any farther apart from one another. That is where curved space-time comes in. The equivalence between gravity and acceleration is a local equivalence. The fact that the pieces of the earth are not getting farther apart is a feature of more global geometry. When you tie all of the local inertial frames together into a global manifold, you have to do some twisting to make them fit together. That's curved space-time.

stevendaryl
Staff Emeritus
I seem to be missing something very basic to the relationship between gravity and mass. If gravity is equivalent to acceleration, what is the basis for the acceleration that generates the gravitational force of an object such as the earth? What is accelerating? Am I even thinking about this in the right way?

It's not quite right to say that gravity is equivalent to acceleration. Let me see if I can better explain what the relationship is.

If you are in outer space, far from any significant source of gravitation, then you will find that there is a natural motion to objects, expressed by Newton's first law of motion: An object at rest tends to remain at rest. An object in motion tends to remain in motion, traveling in the same direction at the same speed. These natural motions of objects are sometimes called "freefall paths". To make an object depart from its freefall motion requires acting on it with a force. You have to push or pull the object. If the object is you, say sitting in the chair of a rocket, then you will feel your seat press into your body---it's the force of your seat on you that causes you to have a motion that is different from freefall.

Now, when you are close to a source of gravitation, such as the Earth, the effect of that gravitating body, according to Einstein's theory of gravity, is to warp the freefall paths. Instead of the freefall path being straight lines when you graph your spatial position as a function of time, they are curved into orbits---circular, elliptical, hyperbolic, etc. But in the same way as when you are far away from any gravitational forces, your natural motion is to follow the freefall paths, and it takes a force acting on you in order to make you depart from a freefall path.

If you start from rest on the surface of the Earth, the natural freefall path is one directed toward the center of the Earth. To prevent you from following this path, you have to have a force acting on you. So sitting in a chair, the seat presses up against you preventing you from following the natural freefall path.

The kind of equivalence that Einstein's equivalence principle talks about is not the equivalence of gravity and acceleration. Instead,
1. Being in freefall near a gravitating body is equivalent to being in freefall in empty space. In both cases, you don't feel anything---it just feels like you're floating.
2. Being forced to depart from a freefall path near a gravitating body is equivalent to being forced to depart from a freefall path in empty space. In both cases, you feel a seat pressing up on you, causing you to accelerate away from where you would naturally go, if you were allowed to follow a freefall path.

Jimmy and Ibix
Thanks to the three of you for taking the time to respond to my question. They were exactly at the level that I was hoping for and greatly enhanced my understanding of this aspect of relativity.

PeterDonis