$1.$Use Kepler$$s third law to answer the following

questions:

a$.$Determine the period $($the time it takes to orbit the Sun$)$ of an imaginary planet that orbits the

Sun at a distance of $10$ AU$.$

b$.$Determine the distance between the Sun and a planet with a period of $5$ years.

c$.$Imagine two bodies, one twice as large as the other, orbiting the Sun at the same distance.

Which of the bodies, if either, would complete its orbit around the Sun in less time? Explain.