How Do We Calculate the Mass of Binary Stars Like Centauri A and B?

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SUMMARY

The discussion focuses on calculating the mass of the binary stars Centauri A and B, which have a separation of 3.45x10^12 meters and an orbital period of 2.52x10^9 seconds. The equation used, (m1 + m2) P^2 = (d1 + d2)^3, was incorrectly applied, leading to an erroneous calculation of mass. The correct approach requires careful attention to the units and proper application of Kepler's laws to determine the mass accurately.

PREREQUISITES
  • Understanding of Kepler's laws of planetary motion
  • Familiarity with gravitational physics
  • Basic algebra and unit conversion skills
  • Knowledge of binary star systems
NEXT STEPS
  • Review Kepler's Third Law of Planetary Motion
  • Study gravitational force calculations in binary star systems
  • Learn about unit conversions in astrophysics
  • Explore examples of mass calculations for other binary stars
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in the dynamics of binary star systems and gravitational calculations.

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Homework Statement



Centauri A and Centauri B are binary stars with a separation of 3.45x10^12m
and a period of 2.52x10^9s

Assuming the two stars are equally massive (which is approximately the case), determine their mass.

Homework Equations



( m1 + m2 ) P^2 = ( d1 + d2 )^3 = R^3
I used this and it doesn't work :x

The Attempt at a Solution



M1=M2
D1=D2

M(2.52x10^18)=3.45x10^36

M=3.45x10^36/2.52x10^18

= wrong :X
 
Physics news on Phys.org
[tex] {(2.52 \times 10^9)}^2 \neq 2.52 \times 10^{18}[/tex]
 

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