50points! find the period of revolution for the planet mercury, whose average distance from the sun is 5.79e10. mass of sun is 1.99e30kg, mass of mercury is 3.3e23kg

According to 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”.

In other words, this law states a relation between the orbital period of a body (planet Mercury in this case) orbiting a greater body in space (the Sun) with the size of its orbit.

This Law is originally expressed as follows:

  (1)

Where;

is the Gravitational Constant and its value is

is the mass of the Sun

   (2)

   (3)

   (4)

Solving and taking into account that :

   (5)

Finally:

>>>>This is the period  of revolution for the planet Mercury