If an asteroid is 4 au from the sun, what is the period of revolution around the sun for the asteroid?

8 years

Explanation:

According to Kepler’s 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”:

(1)

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

However, if is measured in years (Earth years), and is measured in astronomical units (equivalent to the distance between the Sun and the Earth: ), equation (1) becomes:

(2)

This means that now both sides of the equation are equal.

Knowing and isolating from (2):

(3)

(4)

Finally:

This is the period of the asteroid

gas and liquid

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