Mercury has an average disease to the sun of 0.39 au. in two or more complete sentences, explain how to calculate the orbital period of mercury and then calculate it.

88 Earth days

Explanation:

According to the Kepler Third  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”.

In other words, this law states a relation between the orbital period of a body (moon, planet, satellite) orbiting a greater body in space with the size of its orbit:

(1)

If we assume the orbit is circular and apply Newton's law of motion and the Universal Law of Gravity we have:

(2)

Where is the mass of the massive object and is the universal gravitation constant. If we assume constant and larger enough to consider  really small, we can write a general form of this law:

(3)

Where is in units of Earth years,   is in AU (1 Astronomical Unit is the average distane between the Earth and the Sun) and   is the mass of the central object  in units of the mass of the Sun.

This means when we are making calculations with planets in our solar system  .

Hnece, in the case of Mercury:

(4)

Isolating :

(5)

(6)

This means the period of Mercury is 88 days.