Kepler's Law sin[SUP]3[/SUP] i term calculation

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SUMMARY

The discussion focuses on the calculation of the expectation value in the context of Kepler's Law, specifically addressing the term involving sin3 i. It clarifies that the expectation value is derived from the solid angle multiplied by sin3 i, emphasizing that sin3 i serves as a factor relating to the unknown actual sum of masses in binary systems. The analysis assumes random distribution of binary orientations over the solid angle, necessitating the average value of sin3 i for accurate statistical evaluation.

PREREQUISITES
  • Understanding of Kepler's Laws of planetary motion
  • Familiarity with statistical analysis in astrophysics
  • Knowledge of solid angle calculations
  • Basic concepts of binary star systems
NEXT STEPS
  • Research the derivation of the average value of sin3 i over a solid angle
  • Study statistical methods for analyzing binary star systems
  • Explore the implications of random orientation distributions in astrophysics
  • Learn about the application of Kepler's Laws in modern astrophysical research
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Astronomers, astrophysicists, and students studying binary star systems and their mass calculations will benefit from this discussion.

kdlsw
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It's part c I don't understand, why the expectation value equals to solid angle * sin3 i? I mean, what role does the solid angle play? Thank you
 

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kdlsw said:
It's part c I don't understand, why the expectation value equals to solid angle * sin3 i?
It does not. sin3 i is the factor between the unknown actual sum of the masses and the quantity you can observe.

You cannot find the actual sum of masses for each binary, but you can do a statistical analysis - with the assumption that the orientations of the binaries are randomly distributed over the full solid angle. To do this, you need the average value of sin3 i over the full solid angle.
 

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