Force of gravity in terms of time, rather than distance.

AI Thread Summary
The discussion centers on calculating the velocity of an object falling towards Earth under the influence of gravity, specifically using time as a variable rather than distance. The acceleration due to gravity is expressed as -GM/r^2, where r decreases over time as the object accelerates. The participants acknowledge that solving this problem likely requires differential equations, but they are unsure which specific equations to use. There is a reference to a similar question previously answered on a physics forum, indicating that the topic has been explored before. The conversation highlights the complexity of relating gravitational acceleration to time in a precise manner.
Scottmeister
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My friends and I have a problem that seems simple enough, but has proven to be pretty hard. We need some help.

Suppose you have an object in space with no initial velocity relative to the Earth.

Now, due to the Earth's gravity, the object will begin to accelerate towards the Earth instantly.

We need to find the velocity of the object after any given time; so, we need an equation for the velocity of the object in terms of time t and the original distance r.

Please note: Acceleration due to gravity does NOT equal -9.81m/s^2 for this problem. acceleration due to gravity is -GM/r^2 and r is decreasing as t increases because the object is accelerating towards the Earth at a faster and faster rate.

Now, we realize this will probably take some differential equations to solve, but we can't find what differential equations we need to solve.

Any help at all is appreciated.

Thank you!
 
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Thank you!
 
Nabeshin said:
Basically identical question answered here:
https://www.physicsforums.com/showthread.php?t=364781

Cheers!

I read over that other thread. I couldn't quite understand though. Did you ever find equations for the acceleration of gravity with respect to time, or did you just approximate the values?
 

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