Do two masses gravitate to their centre of mass

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SUMMARY

Two masses falling towards each other under gravitational attraction will meet at their center of mass, assuming negligible external gravitational forces. An observer located at the center of mass will find it stationary during the in-fall, confirming that both masses will reach the collision point simultaneously. This principle applies to point masses, while non-point masses will meet where their surfaces touch. The discussion clarifies the dynamics of gravitational attraction and the behavior of mass in relation to its center of mass.

PREREQUISITES
  • Understanding of gravitational attraction
  • Familiarity with the concept of center of mass
  • Basic knowledge of point mass vs. non-point mass dynamics
  • Concept of collision points in physics
NEXT STEPS
  • Study the mathematical derivation of gravitational attraction between two masses
  • Explore the implications of center of mass in multi-body systems
  • Learn about collision dynamics in non-point mass scenarios
  • Investigate the effects of external forces on center of mass stability
USEFUL FOR

Physics students, educators, and anyone interested in understanding gravitational dynamics and the behavior of masses in motion.

jja
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Given two masses falling towards each other under gravitational attraction, do they meet at their joint center of mass, assuming other gravitational forces are negligible?
 
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answering own question

On reflection, to a (massless :-) observer at the center of mass of the two in-falling masses, the center of mass must remain stationary during the in-fall (because there is no force to move it), therefore the two masses must meet at the center of mass. This means the time for each mass to reach the collision point must be equal (which may make it easier to calculate the time it takes for them to arrive at the collision point?) Is this correct?
 
If you have two point masses, they will meet at their center of mass by construction.

If they are not point masses, they will meet where their surfaces touch.
 

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