Kepler's Third Law and Motion of Two Point Masses

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SUMMARY

The discussion centers on the application of Kepler's Third Law and the equations from the paper 'Gravitational Radiation and the Motion of Two Point Masses' by Peters (1964) to a binary star system with equal solar masses. The calculated separation of the stars is approximately 10 solar radii, with an orbital period of about 4.5 days and a lifetime for decay of 3x1012 years. The user encounters discrepancies in their calculations for the decay lifetime and orbital period, specifically with the constants and formulas provided in their lecture notes.

PREREQUISITES
  • Understanding of Kepler's Third Law of planetary motion
  • Familiarity with gravitational physics and binary star systems
  • Knowledge of physical constants such as G (gravitational constant) and c (speed of light)
  • Ability to perform unit conversions between solar masses, solar radii, and astronomical units
NEXT STEPS
  • Review the derivation of Kepler's Third Law in the context of binary star systems
  • Examine the calculations for B using the correct units and constants
  • Investigate the implications of gravitational radiation on orbital decay
  • Explore the relationship between orbital period and separation in binary systems using numerical simulations
USEFUL FOR

Astronomy students, astrophysicists, and researchers studying binary star systems and gravitational radiation will benefit from this discussion.

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I'm trying to work through some equations in the paper 'Gravitational Radiation and the Motion of Two Point Masses' (Peters, 1964) but I can't get out the right values

1. Homework Statement

For a binary star system with each mass = 1 solar mass, the equations give the results:
Separation ~ 10 solar radii
Period ~ 4.5 days
Lifetime for decay ~ 3x1012 years

Homework Equations


T = a4/4B
B = (64/5)G3m1m2(m1+m2)/c5

The Attempt at a Solution


Using solar mass = 1.989 x 1030kg,
solar radius = 695700 km
G = 6.67408 x 10-11 m3kg-1s-2
c = 3 x 108 ms-1

I get B = (1/(3 x 108)5)(64/5)(6.67408 x 10-11)3 x 2 x 1.989 x1030 x 103 = 6.229 x 10-42

T = (10 x (695700 x 1000))4/4B = ~1.12 x 1051 s, which isn't at all near 3 x 1012 years :( Help?
 
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Oh, also regarding Kepler's third law. My lecture notes give it as

(G/4pi2)(m1 + m2) t2=a3

where t is orbital period in years, masses are in solar units, and a is in au. This formula also isn't working for me yet?
 

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