# 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?

##### 1 Answer

The planet has about 4 Jupiter masses.

#### Explanation:

Start with Newton's form of Kepler's third law:

Where

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.