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

[kdlsw]

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

 

[mfb]

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.