Assume a circular orbit. If a planet's distance from it star is multiplied by 25 times, then by how many times is its orbital period T multiplied ?
Kepler’s Third Law. The square of the period is proportional to the cube of the distance from the star:
T²∼R³
If the distance is increased by 25,
then T² is increased by 25³, which means T is increased by the sqrt(25³)=125.