Calculating Energy, Angular Momentum & Period for Binary Stars in ZMF

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SUMMARY

The discussion focuses on calculating the total energy, angular momentum, and period of a binary star system in the Zero Momentum Frame (ZMF) before a stellar explosion. The two stars have masses m1=mo and m2=2mo, and are in circular orbit around their common center of mass. Key calculations involve determining the individual energies of the stars, summing them for total energy, and recognizing that angular momentum is not zero due to the system's orbital motion. The period can be derived using Kepler's laws, considering the new mass distribution post-explosion.

PREREQUISITES
  • Understanding of binary star systems and their dynamics
  • Familiarity with the concept of the Zero Momentum Frame (ZMF)
  • Knowledge of gravitational potential energy and kinetic energy equations
  • Basic principles of angular momentum in orbital mechanics
NEXT STEPS
  • Study the equations for gravitational potential energy in binary star systems
  • Learn about angular momentum conservation in orbital mechanics
  • Explore Kepler's laws to calculate orbital periods
  • Investigate the effects of mass loss in binary star systems post-explosion
USEFUL FOR

Astronomy students, astrophysicists, and educators interested in binary star dynamics and energy calculations in astrophysical systems.

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Homework Statement



Two individual stars in a binary system (m1=mo, m2=2mo) are in circular orbit about their common centre of mass and are separated by a distance ro. At some stage, the more massive star explodes - resulting in the two stars having equal mass after the explosion

(a)Calculate the total energy, angular momentum and period of the binary star as viewed in the ZMF before the collision.

Homework Equations





The Attempt at a Solution



Not sure how to do this...For energy, do I find the energy of each inidividually and add? How about for angular momentum? Surely that is just zero in total because the two are equal and opposite?
thanks
 
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