Radial Velocity Question
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Radial Velocity Question
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?
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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atomic7732 Meteor
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Re: Radial Velocity Question
The measured (minimum) mass of a planet will the true mass of the planet times the sine of the inclination.
M_{RV} = M_{true} sin i (or simply "m sin i" for short)
And conversely,
M_{true} = M_{RV} / sin i.
The amplitude of the RV variations, K, is used to determine the mass of the planet using the following formula.
K = (2πa_{star} sin i) / P*√(1  e^{2})
Where a_{star} is the semimajor 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":
[(m_{star} sin i)^{3}) / (m_{star} + m_{planet})^{2})] = P / 2πG * K^{3}(1  e^{2})^{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
m_{p} sin i ~= (P/2πG)^{1/3} Km_{star}^{2/3} (1  e^{2})^{1/2}
M_{RV} = M_{true} sin i (or simply "m sin i" for short)
And conversely,
M_{true} = M_{RV} / sin i.
The amplitude of the RV variations, K, is used to determine the mass of the planet using the following formula.
K = (2πa_{star} sin i) / P*√(1  e^{2})
Where a_{star} is the semimajor 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":
[(m_{star} sin i)^{3}) / (m_{star} + m_{planet})^{2})] = P / 2πG * K^{3}(1  e^{2})^{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
m_{p} sin i ~= (P/2πG)^{1/3} Km_{star}^{2/3} (1  e^{2})^{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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Sirius_Alpha Admin
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Re: Radial Velocity Question
Interesting! Thanks.
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atomic7732 Meteor
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