Suppose the Sun were twice as massive as it actually is. What would be the orbital period of a planet at a distance of 10AU from the Sun?

Answer 1

For the actual sun's mass, according to Kepler's third law,
P^2/a^3 = 1 = P^2/1000
P = 31.6 years

For a sun that is twice as massive, the centripetal gravity force is twice as large, so V must increase by a factor of sqrt2 to balance it.

The period will be lower by a factor 1/sqrt2 due to the higher speed

Period = 31.6/1.414 = 22.4 years