Astronomers discover an exoplanet (a planet of a star other than the sun) that has an orbital period of 3.87 earth years in its circular orbit around its sun, which is a star with a measured mass of 3.59 x 1030 kg. find the radius of the exoplanet's orbit.

Given the orbital period and mass of the exoplanet, its radius of orbit is 4.488 × 10¹¹m.

Given the data in the question;

To determine the radius of the exoplanet's orbit, we use the equation from Kepler's Third Law:

Where, T is the period of the orbit of the exoplanet, G is the Gravitational Constant, M is the mass of the star and r is orbital radius.

We make "r", the subject of the formula

We substitute our given values into the equation

Therefore, given the orbital period and mass of the exoplanet, its radius of orbit is 4.488 × 10¹¹m.

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Explanation:

This problem can be solved using the Third Kepler’s Law of Planetary motion:

“The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”.  

This law states a relation between the orbital period of a body (the exoplanet in this case) orbiting a greater body in space (the star in this case) with the size of its orbit:

(1)  

Where:

is the period of the orbit of the exoplanet (considering )

is the Gravitational Constant and its value is  

is the mass of the star

is orbital radius of the orbit the exoplanet describes around its star.

Now, if we want to find the radius, we have to rewrite (1) as:

(2)  

(3)  

Finally:

This is the radius of the exoplanet's orbit