Similar masses gravitating stably together

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SUMMARY

The discussion centers on the N-body problem, specifically exploring the maximum number N of equivalent masses M that can stably gravitate within a radius R. It clarifies that the focus is on the ability of these masses to move in a stable orbit around their common center of mass, rather than strictly circular orbits. The conversation emphasizes that for N greater than 2, the orbits may not be circular but can remain confined stably to a distance R from the center of mass. The relationship between N, M, and R is critical in determining the stability of these gravitational interactions.

PREREQUISITES
  • Understanding of the N-body problem in astrophysics
  • Knowledge of gravitational dynamics and orbital mechanics
  • Familiarity with concepts of center of mass and stable orbits
  • Basic mathematical skills for analyzing functions of N and M
NEXT STEPS
  • Research the mathematical formulations of the N-body problem
  • Study gravitational interactions and stability criteria in multi-body systems
  • Explore simulations of N-body systems using tools like MATLAB or Python
  • Investigate the implications of mass distribution on orbital stability
USEFUL FOR

Astronomers, physicists, and students of astrophysics who are interested in gravitational dynamics and the behavior of multiple bodies in space.

Loren Booda
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What is the greatest number N of equivalent masses M which can mutually gravitate over time within a radius R?
 
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"Mutually gravitate over time with radius R"? Do you mean stably move in a circular orbit (about their common center of mass) with radius R?
 
HallsofIvy said:
"Mutually gravitate over time with radius R"? Do you mean stably move in a circular orbit (about their common center of mass) with radius R?

As an example, consider the N-body problem where N>2, M=M0=constant, and R is a function of N (and possibly M0). The orbits are not circular, but might be confined "stably" to a distance R from the center of mass.

N>2 equal masses co-orbit perpetually within what minimum limit R(N)?
 

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