Shouldn't gravity travel at light speed immediately?

If gravity travels at $c$ (light speed), why aren't objects pulled to Earth at that speed?

Since the velocity of gravity is 9.8 meters per second squared, will it eventually accelerate until it maxes out at $c$ then hold constant?

And if that is the case, then why doesn't the gravitational pull between objects and earth immediately travel at $c$ like photons?

So the acceleration of gravity is 9.8 meters per second squared only on earth.

The gravitational pull is contingent on the body off mass and the distance between the masses.

Gravity waves travel at the speed of light.

So if a gravity wave extending from one primary object of greater mass to another object of lesser mass was to move a lights speed it wouldn't affect the speed or acceleration of the secondary object. the secondary object would just react to the primary object at the speed of light, but the reaction it self is dependent upon the size and distance between them?

migrated from theoreticalphysics.stackexchange.comApr 19 '12 at 22:17

• More on speed of Gravity: physics.stackexchange.com/q/7041/2451 – Qmechanic Apr 19 '12 at 23:13
• Where you got that the velocity of gravity is 9.8 meters per second squared? Notice that velocity is measured in meters per second, not in meters per second squared. – Anixx Apr 20 '12 at 1:12

I think there's a combination of terminology and information misunderstanding going on here, so let me try and explain this at an appropriate level. First, the phrase "travel at light speed immediately" doesn't make much sense. In physics, there's not really any such thing as "immediately." "Immediately" is synonymous with "instantaneously," and there's nothing we've ever measured that we can call instantaneous communication. But, regardless of a lack of instantaneous anything, phrased this way, I hope it's clear that saying something moves instantaneously at a finite speed is nonsensical from a conceptual point of view. It's like saying something is moving at 5 m/s and 20 m/s at the same time; 5 just doesn't equal 20, no matter how you slice it.

When you talk about the velocity of gravity, you're talking about the speed at which the force carrier of gravity (or the spacetime disturbance) propagates outward. That value is c, as far as we can tell. When you start talking about 9.8 meters per second squared, you're talking about the acceleration due to gravity, which is not the same thing. How hard you push and something and how fast it moves are related, but they're not the same, right? It's the difference between velocity and acceleration.

Now, if something provides a continuous acceleration, the object that is accelerating will keep going faster and faster, approaching a velocity of c. It doesn't matter what provides the acceleration; could be gravity, could be a rocket booster with infinite fuel. The point is, the speed that gravity propagates has nothing to do with how hard it pulls on objects. Those are completely different properties that are unrelated.

Finally, the gravitational pull between all objects does respond at speed c. This includes the earth and moon. But just because gravity "gets from" the earth to the moon at a speed c, that doesn't mean it causes the moon to move toward the earth with velocity c. I hope that clears up some of the confusion.

• Also, this 9.8 $m/s^2$ is only true near the earths surface, so there is not enough time/distance to accelerate to $c$ anyhow. – Bernhard Apr 20 '12 at 5:35

9.8 m/sec/sec is not the speed of gravity, it is the acceleration due to gravity at the surface of the earth. At the surface of the moon it is a good deal less. At the surface of the sun it is a lot more.

It is true that if you could fall in a straight line, gaining 9.8 m/sec every second, after about a year you would approach the speed of light, but you would never surpass it. It would be hard to find such a building to jump out of. You could do it in space if you had a good enough rocket motor and enough fuel.

Think about sound in air. The speed of sound is about 340 meters/second, but that does not mean if the wind blows something around, it blows it at that speed. What it means is if someone claps their hands 340 meters away, you hear it one second later.

Gravity is like that. If a big piece of matter, like a planet, suddenly moves into position 30 000 kilometers away, its gravity is felt by you 1/10 second later. But that only means you feel the force at that time, not that you are traveling at that speed.