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i.e. why the fractional distribution of binary stars is df = sini * di, where i is the inclination angle?

Where does the sin i come from? Why is not not uniformly distributed across angles?

Thanks.

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- Thread starter Miviato
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In summary, the probability of the inclination angle of a binary system being less than i_0 is 1-cos(i_0). Sin i comes from the fact that the fractional distribution of binary stars is df = sini * di, where i is the inclination angle. The reason not uniformly distributed across angles is because the sin i is a function of the distance between the stars and the inclination angle.f

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i.e. why the fractional distribution of binary stars is df = sini * di, where i is the inclination angle?

Where does the sin i come from? Why is not not uniformly distributed across angles?

Thanks.

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Thanks!

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Clearly, I'm going to have to do a little reading and correct myI don't quite see how it answers my question --

"inclination angle." Didn't mean to drag your question off on a "tangent," with a hasty leap --- thought I'd found another application of some of the neat little tricks Gamow collected.probability of the inclination angle of a binary system being less than i_0 is 1-cos(i_0)

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1 degree of latitude from equator to 1 degree latitude is a band around Earth 1 degree wide but 360 degrees long - all around the length of equator. 1 degree of latitude from latitude 89 to pole at latitude 90 is a small circle, with radius 1 degree, but accordingly only a tiny circumference.

I understand that the values of inclination are counted so that inclination 0 is the viewer looking at one pole (latitude 90, the pole where the orbit is counterclockwise), so very improbable, inclination 90 is the viewer looking at the plane/equator of orbit (latitude 0, most probable) and inclination 180 is the viewer looking at the other pole (latitude also 90, the pole where the orbit is clockwise), so also very improbable.

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