# Gravity to surface and speed of stars

1. Jul 31, 2012

### Kristiandhd

the law of gravity states that objects accelerate at a constant speed, but i'm wondering that if you take into consideration that time travels slower the closer you are to the surface of the earth. doesn't that imply that although it seems to us that it is constant acceleration that, it is actually accelerating at a faster rate as it falls.

maybe this would also explain why stars on the outside of a spiral galaxy seems to us to travel faster when they shouldn't be. when in reality it is that time travels faster the farther you get from matter because less space is being altered.

so it is space pushing us into the mass, and gravity depends on the amount of matter distorting space. and space is pushing from all direction creating they semi circular from of celestial bodies to try and reach its equilibrium where space isn't being affected by matter?

2. Jul 31, 2012

### Nessdude14

The constant acceleration of 9.81 m/s2 on the surface of earth is only an approximation. Newton's law of gravitation doesn't state that the acceleration is constant, but it is actually given by:
F=G(m1m2)/r2
This equation shows that the closer you are to a mass (a planet, for example), the stronger the gravitational pull.

That's classical physics, however. The effects of time dilation that you mention would have an extremely small effect on your observed acceleration, but it's such a small effect that it's insignificant on earth. Relativistic effects such as time dilation become significant only when dealing with extremely large quantities of space, time or mass. In the case of spiral galaxies, cosmologists are aware of the need to account for this relativistic behavior, and the behavior of the galaxies still differs from what we expect.

Last edited: Jul 31, 2012
3. Jul 31, 2012

### Staff: Mentor

Those stars are quicker by a factor of roughly 2-3. If you would compress all mass in the milky way to a black hole, it would have a radius of ~1 light year, but the relevant stars have a distance of >20,000 light years. This gives a factor of about 1.00005 for the relative "speed of time". Several orders of magnitude away from the observed effect. In addition, I am not sure if the sign fits at all.