Gravitational Potential Energy: A Basic Explanation

Click For Summary
SUMMARY

The definition of gravitational potential energy (GPE) is established as the negative of the line integral of force, specifically represented as PE = -∫ F·dr. This formulation arises from the work-energy theorem, which necessitates the negative sign to maintain consistency. In gravitational fields, particularly from a point source, the potential energy is quantified as PE = -GmM/r, where G is the gravitational constant, m is the mass of the object, and M is the mass of the point source. Using infinity as a reference point is crucial, as it ensures that the potential energy approaches zero at infinite distances.

PREREQUISITES
  • Understanding of line integrals in vector calculus
  • Familiarity with the work-energy theorem
  • Knowledge of gravitational forces and constants (e.g., G)
  • Basic principles of potential energy in physics
NEXT STEPS
  • Study the mathematical derivation of line integrals in vector fields
  • Explore the work-energy theorem in various physical contexts
  • Investigate gravitational potential energy calculations for different mass distributions
  • Learn about the implications of using different reference points in potential energy calculations
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding the mathematical foundations of gravitational potential energy.

ian2012
Messages
77
Reaction score
0
A very basic question:

Why is the definition of gravitational potential energy, bringing an object from infinity (or any point of reference) to zero, the negative of the line integral of F.dr ? I am assuming since potential energy in an attractive field , which is defined to be negative, the integral was fixed to lead to this result... or is there a more mathematical reason?
 
Physics news on Phys.org
Hi ian2012! :smile:

potential energy (gravitational electric or whatever) is defined as minus the work done …

and work done = integral of force "dot" displacement …

so PE = -W = -∫ F.dr :wink:

(and it has to be minus so that the work-energy theorem works)
 
thank you for your post
 
ian2012 said:
Object infinity zero
In the case of gravity from a point source, potential energy = -G m M / r. Because of this, using infinity as a reference point makes since, becaue - G m M / ∞ = 0, and all GPE's at finite distances from a gravitational point source would be negative.
 

Similar threads

Graduate Gravitational potential energy -- Why is it always negative?
  • · Replies 10 ·
Replies
10
Views
3K
High School Conceptually understanding change in potential energy with 0 net work
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Gravitational potential energy
  • · Replies 46 ·
2
Replies
46
Views
5K
Undergrad Confusion over the "centrifugal potential energy"
  • · Replies 10 ·
Replies
10
Views
7K
Undergrad What is the zero point for Potential Energy and how to find it from integral limits?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How to interpret this definition of potential energy?
  • · Replies 10 ·
Replies
10
Views
2K
High School How does an object gain potential energy?
  • · Replies 54 ·
2
Replies
54
Views
6K
Undergrad How to relate the gravitational potential energy zero to the axes?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad System, potential energy, and nonconservative forces
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Change of coordinates in a potential energy field
  • · Replies 2 ·
Replies
2
Views
2K