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

1. Oct 14, 2011

### cahill8

When a stars radial velocity is measured in search for a planet, the planet imparts a radial velocity shift proportional to $m\sin i\text{ where }i$ is the orbital inclination of the planet with respect to our line of sight and $m$ 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 $m\sin i$ values by 1.33. I'm wondering where this value comes from?

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

Thanks

2. Oct 15, 2011

### cepheid

Staff Emeritus
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.