Radial Velocity Question

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Radial Velocity Question

Post by atomic7732 on 4th May 2011, 9:55 pm

Lets say that a star's system is moving at 45 degrees relative to us... And a planet is detected, is the measured mass and velocity of the star half of the true mass? Or is there some square function?

And how do they find the mass of a planet given the velocity the star is moving and the mass of the star?

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Re: Radial Velocity Question

Post by Sirius_Alpha on 5th May 2011, 2:03 am

The measured (minimum) mass of a planet will the true mass of the planet times the sine of the inclination.

MRV = Mtrue sin i (or simply "m sin i" for short)

And conversely,

Mtrue = MRV / sin i.

The amplitude of the RV variations, K, is used to determine the mass of the planet using the following formula.

K = (2πastar sin i) / P*√(1 - e2)

Where astar is the semi-major axis of the star around the system barycentre, P is the orbital period, and e is the eccentricity. The K value can be used to find the masses of the two components with the "mass function":

[(mstar sin i)3) / (mstar + mplanet)2)] = P / 2πG * K3(1 - e2)3/2

Where G is the gravitational constant. In a planetary system, since the mass of the star will be much greater than that of the planet, you can simplify the mass function down to

mp sin i ~= (P/2πG)1/3 Kmstar2/3 (1 - e2)1/2


Last edited by Sirius_Alpha on 5th May 2011, 2:15 am; edited 2 times in total (Reason for editing : Corrected some math.)

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Re: Radial Velocity Question

Post by atomic7732 on 5th May 2011, 8:47 pm

Interesting! Thanks.

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