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PAstudent
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Homework Statement
Homework Equations
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The Attempt at a Solution
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Orbital Period Calculation for Binary Star Systems
- Thread starter PAstudent
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SUMMARY
The discussion focuses on calculating the orbital period of binary star systems using the formula T² = (4π²/GM)r³, where M represents the mass of the attracting body. Participants clarify that the distance of each star from the center of mass (c.o.m.) is not simply L/2, but rather depends on the positions of adjacent stars. The correct interpretation of M is crucial, as it should denote the mass of the attracting body rather than the mass of each orbiting star.
PREREQUISITES- Understanding of Newton's Law of Gravitation
- Familiarity with the concept of center of mass in a binary system
- Knowledge of orbital mechanics and Kepler's laws
- Basic algebra for manipulating equations
- Study the derivation of Kepler's Third Law for binary star systems
- Learn about the calculation of center of mass in multi-body systems
- Explore gravitational interactions in astrophysics
- Investigate the use of simulation tools for modeling binary star orbits
Astronomy students, astrophysicists, and educators involved in teaching orbital mechanics and binary star systems.
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SteamKing
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The distance of each star from the c.o.m. of the system is not L/2. Each star in the group is located L/2 from the two stars immediately adjacent.PAstudent said:
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Herman Trivilino
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You start with the formula ##T^2=\Big( \frac{4 \pi^2}{GM} \Big)r^3## where ##M## is the mass of the attracting body.
But in your solution you use ##M## for the mass of each orbiting sun.
But in your solution you use ##M## for the mass of each orbiting sun.
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