Suppose our sun had 4 times its present mass but the earth orbited it at the same distance as it presently does. What would be the length of the year on the earth under those conditions?

Question

Quizplus · Accepted Answer

The length of the year on Earth is determined by its orbital period around the Sun, which depends on the mass of the Sun and the distance of the Earth from the Sun. According to Kepler's third law, the square of the orbital period (T^2) is directly proportional to the cube of the semi-major axis of its orbit (r^3) divided by the mass of the sun (M). If the mass of the Sun were four times its current mass, the gravitational force would increase, causing the Earth to orbit faster. The orbital period T is proportional to (r^3/M)^0.5. If M increases by a factor of 4, then T decreases by a factor of (1/4)^0.5, which is 1/2. Therefore, the year would be half as long.

Suppose Our Sun Had 4 Times Its Present Mass but the Earth