An asteroid, whose mass is `2.0 xx 10^(-4)` times the mass of Earth, revolves in a circular orbit around the Sun at a distance that is 3.0 times Earth's distance from the Sun. (a) Calculate the period of revolution of the asteroid in years. (b) What is the ratio of the kinetic energy of the asteroid to the kinetic energy of Earth?

Explanation

To solve the problem step by step, we will tackle part (a) and part (b) separately.

### Part (a): Calculate the period of revolution of the asteroid in years.

1. **Understanding Kepler's Third Law**: According to Kepler's Third Law of planetary motion, the square of the period of revolution (T) of a planet is directly proportional to the cube of the semi-major axis (R) of its orbit. Mathematically, this can be expressed as:
\[ T^2 \propto R^3 \]
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