Average value of sin(i) in radial velocities (exoplanets)

[cahill8]

When a stars radial velocity is measured in search for a planet, the planet imparts a radial velocity shift proportional to [itex]m\sin i\text{ where }i[/itex] is the orbital inclination of the planet with respect to our line of sight and [itex]m[/itex] is the planet mass. I've heard that even though the inclinations are generally unknown, the true masses can be approximated for a large sample by multiplying [itex]m\sin i[/itex] values by 1.33. I'm wondering where this value comes from?

Assuming a uniform distribution of [itex]i[/itex], [itex]\int^\pi_0 \sin i di/\pi[/itex] gives a value of [itex]2/\pi[/itex] implying that the [itex]m\sin i[/itex] should be multiplied by [itex]\pi/2[/itex] (1.57, opposed to the 1.33 I've seen). Does anyone have a derivation or reference for this number?

Thanks

 

[cepheid]

I don't have a derivation for this number, but it seems like your phrase, "Assuming a uniform distribution of i" is where the discrepancy might come about. It could very well be that the i values are weighted in some way, to take into account that some inclination angles are observationally more likely than others.

I mean, for one thing, if i = 0 (or is it pi -- whichever one corresponds to the system being face-on), then there IS no radial component to the planet's velocity.