Centre of Mass of two Gravitating bodies from rest

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SUMMARY

The discussion focuses on demonstrating that the center of mass of two point particles, with masses m1 and m2, remains stationary when released from rest from an infinite distance. The key insight is the application of the conservation of total momentum, which confirms that the center of mass does not change its position despite the gravitational interaction. This principle simplifies the analysis by eliminating the need for time-dependent calculations.

PREREQUISITES
  • Understanding of classical mechanics principles
  • Familiarity with the concept of center of mass
  • Knowledge of conservation laws, specifically conservation of momentum
  • Basic grasp of gravitational forces between point masses
NEXT STEPS
  • Study the mathematical formulation of center of mass for multiple bodies
  • Explore conservation of momentum in various physical systems
  • Investigate gravitational interactions and their effects on motion
  • Learn about the implications of releasing bodies from different initial conditions
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in gravitational dynamics and the behavior of point masses in motion.

Phillips101
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Hi

How would I show that the centre of mass of two point particles, one of mass m1 and the other m2, when released from rest from infinite simultaneously, stays in the same place?

I feel this is a very simple question, I just can't seem to get it right. Everything I've tried still involves time in it...

Thanks for any help!
 
Physics news on Phys.org
Have you tried conservation of (total) momentum?
 
D'oh. I was right, it was very simple. Thanks for that!
 

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