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

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Discussion Overview

The discussion revolves around deriving an equation for the velocity of an object falling towards Earth, expressed in terms of time rather than distance. The context involves gravitational acceleration, specifically considering the variable nature of gravitational force as the distance to the Earth changes over time.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant describes a scenario where an object in space accelerates towards Earth due to gravity, emphasizing that the acceleration should be expressed as -GM/r^2, where r decreases over time.
  • The same participant seeks assistance in identifying the necessary differential equations to derive the velocity in terms of time and distance.
  • Another participant references a previous thread that may contain a similar question, suggesting it could provide insights or solutions.
  • A later reply expresses confusion about whether the previous thread provided equations for gravitational acceleration with respect to time or if it only offered approximations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific equations needed or whether the previous thread adequately addressed the question. There is an acknowledgment of uncertainty regarding the derivation process.

Contextual Notes

The discussion highlights the complexity of modeling gravitational acceleration as a function of time, with potential limitations in understanding the mathematical steps required to solve the problem.

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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