Deriving gravitational potential energy (by bringing mass from infinity to r)

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Discussion Overview

The discussion revolves around the derivation of gravitational potential energy (gpe) when considering a test mass being moved from infinity to a distance r from a mass, particularly focusing on the signs and the integration process involved in this derivation.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses confusion regarding the derivation of gpe, noting that their integration leads to a positive value for gravitational potential energy when moving from infinity to r.
  • Another participant clarifies that integrating the force times displacement (F*dr) gives the work done, and since the energy at infinity is considered zero, a positive result implies that potential energy must be negative to satisfy the energy conservation equation (Ep + Ek = 0).
  • A third participant requests a detailed derivation, indicating that the explanation provided does not resolve their question.
  • Another participant questions the choice of force F and its direction, suggesting that understanding the correct force and its orientation is crucial for the derivation.

Areas of Agreement / Disagreement

Participants do not reach a consensus. There are competing views regarding the signs in the derivation and the interpretation of the results, with some seeking clarification while others assert their understanding.

Contextual Notes

There are unresolved aspects regarding the assumptions made about the force and the direction in which it acts, as well as the integration process itself.

Miraj Kayastha
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I understand the derivation of gravitational potential energy when an object is moved away from Earth but when I try to derive the formula for gpe by considering a test mass moving from infinity to r then I end up with a positive gravitational potential energy. Because integrating F.dr from infinity to r is equal to (magnitude of F) times (dr) times (cos 0) and I get a positive gravitational potential energy?

Can somebody show me the derivation of gpe considering a mass brought from infinity to r with detailed explanation (especially the signs)?
 
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Integrating F*dr from infinity to r gives you the work done. In the infinity the energy of system was 0. The work done gives you the change in kinetic energy. Since you got positive result, Ep + Ek = 0, therefor potential energy must be negative.
So everything is OK
 
I did not get my answer from that. I need the derivation
 
Miraj Kayastha said:
Because integrating F.dr from infinity to r is equal to (magnitude of F) times (dr) times (cos 0) and I get a positive gravitational potential energy?
What are you taking as your force F? What direction does it have?
 

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