Estimate the approximate (minimum) mass of an exoplanet in a 3.312 day orbit around a 1.3 solar-mass star, where it is known that the radial velocity caused by orbital motion is 471 metres per second?
The planet has about 4 Jupiter masses.
Start with Newton's form of Kepler's third law:
Now for the Sun
The period is
Substituting the values gives the semi major
The radial velocity of the planet is
Rearranging the Kepler equation:
Taking the square root gives:
Substituting values gives
The momentum equation relates the sun star mass and velocity to the planet mass and velocity.
A solar mass is
Jupiter's mass is
This makes the exoplanet about 4 Jupiter masses.