Calculating the Centre of Mass in a 2-Body System

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SUMMARY

The discussion focuses on calculating the center of mass in a two-body system, specifically using Jupiter and the Sun as examples. The formula derived states that the product of Jupiter's mass and its distance from the center of mass (COM) equals the product of the Sun's mass and its distance from the COM. This relationship can be expressed mathematically as MassJupiter * DistanceJupiter-COM = MassSun * DistanceSun-COM, establishing a clear method for determining the center of mass in such systems.

PREREQUISITES
  • Understanding of Newtonian mechanics
  • Familiarity with mass and distance concepts
  • Basic algebra for solving equations
  • Knowledge of the two-body problem in physics
NEXT STEPS
  • Study the principles of the two-body problem in classical mechanics
  • Learn about gravitational interactions and their effects on orbital motion
  • Explore advanced topics in celestial mechanics
  • Investigate numerical methods for simulating two-body systems
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Students of physics, astrophysicists, and anyone interested in celestial mechanics and orbital dynamics will benefit from this discussion.

davehatton01
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A little question: as a planet (such as jupiter) orbits the sun, both the planet, and the sun orbit the same point of the centre of mass. how do you calculate where that centre of mass is?
(2 body problem only)

thanks

DH
 
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davehatton01 said:
A little question: as a planet (such as jupiter) orbits the sun, both the planet, and the sun orbit the same point of the centre of mass. how do you calculate where that centre of mass is?
(2 body problem only)



The two moment-arms should be equal, so massJuptiter * DistanceJupiter-COM = MassSun * DistanceSun-COM.
 

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