Can Non-Constant Gravity Affect Velocity and Acceleration Equations?

[gill12]

I am trying to devise an equation to describe distance, velocity, and acceleration with non-constant acceleration due to gravity changing with respect to distance. For instance, at 100,000 meters the gravitational acceleration is let's say X, yet at 1,000 meters the gravitational acceleration is 10,000X. This gives different distance, velocity, and acceleration equations. Can anyone help me? Thanks in advance!

 

[gill12]

I am trying to calculate the distance, velocity, acceleration, and time of a free falling object. Yet, my velocity after a certain amount of time and/or sufficient acceleration will exceed c, 299792458 m/s. I am looking for a transform for any of these 4 parameters that will describe the object relativistically. Basically, what transform do I use and what do I use it on so that my velocity, v, does not exceed c, but only approaches it as time goes to infinity?

 

[pervect]

You might want to look at http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

Note that this is a rocket with a constant proper acceleration of 1g. There isn't any way for a rocket to have a constant coordinate acceleration of 1g in flat space-time.

A somewhat related question is the issue of falling into a black hole. This may or may not be closer to what you are interested in, but it is complicated by the presence of curved space-time and its associated metric coefficients.

This gets involved, but has been discussed (if that's what you're interested in), see for instance the following posts (and the associated threads).

https://www.physicsforums.com/showpost.php?p=1209950&postcount=70
https://www.physicsforums.com/showpost.php?p=602558&postcount=29