Is Gravitational Interaction Affected by Different Shapes of Bodies?

Click For Summary

Discussion Overview

The discussion centers on the gravitational interaction between bodies of various shapes, specifically whether one can treat the mass of non-symmetrical bodies as concentrated at their centers for the purpose of calculating gravitational forces. The scope includes theoretical considerations and counterexamples related to gravitational force calculations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant wonders if gravitational interaction can be simplified by assuming mass is located at the center of non-symmetrical bodies, similar to the case with spherical symmetry.
  • Another participant asserts that this assumption is not valid in general, indicating that the gravitational force cannot be computed as if the bodies were punctual for all shapes.
  • A later reply presents a counterexample involving three point masses arranged linearly, demonstrating that the actual gravitational interaction differs from the simplified assumption about centers of mass.

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity of simplifying gravitational interactions by treating mass as concentrated at the center for non-symmetrical bodies. The discussion remains unresolved, with differing views on the applicability of this assumption.

Contextual Notes

The discussion highlights limitations in the assumptions made about mass distribution and gravitational interaction, particularly for non-symmetrical bodies. The reliance on specific configurations and the need for more complex calculations are noted but not resolved.

paweld
Messages
253
Reaction score
0
I wonder about gravitational interaction between two bodies of any shape (not necessarly symmetrical).
I would like to predict the motion of their centers of mas if they don't interact with any other bodies. Can I assume that mass of each body is located only in the center and compute the gravitational force as if the bodies were punctual? (In fact I should compute double vector integral over volume of each body.)

I know that it's true in case of bodies with spherical symmetry (one can prove this using e.g. Gauss theorem). Is it always true for all shapes of bodies.
 
Physics news on Phys.org
paweld said:
Can I assume that mass of each body is located only in the center and compute the gravitational force as if the bodies were punctual?
No.
I know that it's true in case of bodies with spherical symmetry (one can prove this using e.g. Gauss theorem). Is it always true for all shapes of bodies.
No, it's not true in general.
 
Thanks.

I've just devised a simple counterexample.
Consider three points of equal masses m lying on the line in the distance a from each other.
One body consists of two points lying side by side and other of one point. The real interaction between bodies is up to multiplicative constant 1/a^2 +1/(2a)^2 while according to my assumption about the center of masses it would be 2/(3/2 a)^2.
 
Good!
 

Similar threads

Undergrad A "continous" gravitational field formula r=0 to infinity
  • · Replies 16 ·
Replies
16
Views
1K
Undergrad Doubts about the relativistic description of electrical interactions
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Capture by Gravitational Radiation in 2-Body System?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate N-Body inputs from Keplerian Orbits
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad What is the nature of the force causing deviation from a circular orbit in GR?
  • · Replies 29 ·
Replies
29
Views
3K
Undergrad Gravity inside an exponential mass disk
  • · Replies 16 ·
Replies
16
Views
2K
Graduate Gravitational Redshift in Newtonian Equivalence Principle?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Statistical physics in 2D world: How to simulate gas and its interaction with objects? (game design)
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Understanding Physical Processes: EM, Gravitational, Mechanical & Entropic
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Synchronizing clocks at different locations to measure speed of light
  • · Replies 58 ·
2
Replies
58
Views
6K