If I know the star’s mass and the radii of both the star’s and the planet’s circular orbits around the centre of mass of the system, how can I calculate the mass of the planet?
Good question. The barycenter or centre of mass of the system is where
mr = MR
where m is the mass of the smaller body and M is the mass of the larger body and r is the distance from the smaller body to the barycenter and M is the distance from the large body to the barycenter.
Example:
Let us find the mass or Earth. The mass of the sun is on the order of 10^30 kg (M). The distance from the Sun to it’s barycenter is on the order of 10^5 meters (R). The distance from the Earth to the barycenter is on the order of 1 AU or 10^11 meters (r).
Thus we get: m = MR/r = 10^(30 + 5)/10^(8) = 10^(35 – 11) = 10^24 kg
Indeed the mass of the Earth is on the order of 10^24 kg
Have you considered a career as narrator at BBC Science? Your voice fits well with the video
Ha. Not considered that. Had Barry White been alive I might have asked him to do a voice over and make girls just loose it when they saw my video
If I know the star’s mass and the radii of both the star’s and the planet’s circular orbits around the centre of mass of the system, how can I calculate the mass of the planet?
Hi Lil.
Good question. The barycenter or centre of mass of the system is where
mr = MR
where m is the mass of the smaller body and M is the mass of the larger body and r is the distance from the smaller body to the barycenter and M is the distance from the large body to the barycenter.
Example:
Let us find the mass or Earth. The mass of the sun is on the order of 10^30 kg (M). The distance from the Sun to it’s barycenter is on the order of 10^5 meters (R). The distance from the Earth to the barycenter is on the order of 1 AU or 10^11 meters (r).
Thus we get: m = MR/r = 10^(30 + 5)/10^(8) = 10^(35 – 11) = 10^24 kg
Indeed the mass of the Earth is on the order of 10^24 kg