Finding Period with Double Stars

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SUMMARY

The discussion focuses on calculating the orbital period of a double star system consisting of two identical stars, each with a mass of 3.0E30 kg, separated by a distance of 2.0E11 m. The correct formula to use is derived from Newton's law of gravitation, specifically Gm / 4π² = r³ / T². The calculated orbital period is confirmed to be 7.9E7 seconds. The user initially struggled with the calculation but later found the correct answer online.

PREREQUISITES
  • Understanding of Newton's law of gravitation
  • Familiarity with orbital mechanics
  • Knowledge of the formula Gm / 4π² = r³ / T²
  • Basic algebra for isolating variables in equations
NEXT STEPS
  • Study the derivation of Kepler's laws of planetary motion
  • Learn about gravitational forces in binary star systems
  • Explore the implications of mass and distance on orbital periods
  • Investigate elliptical orbits and their characteristics
USEFUL FOR

Astronomy students, astrophysics enthusiasts, and anyone interested in the dynamics of binary star systems will benefit from this discussion.

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Homework Statement



A certain double star consists of two identical stars, each of mass 3.0E30 kg, separated by a distance of 2.0E11 m between their centres. How long does it take to complete one cycle? Give your answer in seconds.



Homework Equations



Gm / 4π^2 = r^3/ T^2 (I'm pretty sure the motion will be elliptical)


The Attempt at a Solution



I tried the above equation, and isolated for T, but I got the wrong answer. The answer is 7.9E7 seconds.
 
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