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

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SUMMARY

The discussion focuses on deriving gravitational potential energy (GPE) when a test mass is moved from infinity to a distance r from a massive body, specifically Earth. The user initially calculates a positive GPE by integrating the force over the distance, leading to confusion regarding the sign of the potential energy. The correct interpretation reveals that the work done against the gravitational force results in a negative potential energy, as the system's energy at infinity is defined as zero. Thus, the derivation confirms that gravitational potential energy is negative when considering the work done in bringing mass from infinity to r.

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  • Understanding of gravitational force and its mathematical representation
  • Familiarity with integration techniques in physics
  • Knowledge of the concept of work-energy principle
  • Basic grasp of potential energy definitions in classical mechanics
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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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