If the Earth were orbiting a ten solar mass star,at a distance of 1 astronomical unit,how would its orbital period be affected?
A)It would be unchanged
B)It would be about 1/3 of a year
C)It would be about 3 years
D)It would be about 1/10 of a year

Question

Quizplus · Accepted Answer

The orbital period of a planet is determined by Kepler's third law, which states that the square of the orbital period is directly proportional to the cube of the semi-major axis of its orbit, divided by the mass of the star around which it orbits. If the Earth were orbiting a star with ten times the mass of the Sun at the same distance (1 astronomical unit), the gravitational force would be stronger, causing the Earth to orbit faster. The orbital period $T$ is proportional to $\sqrt{\frac{1}{M}}$, where $M$ is the mass of the star. Therefore, with a tenfold increase in the star's mass, the orbital period would decrease, making it about 1/3 of a year.

If the Earth Were Orbiting a Ten Solar Mass Star,at