The distance of two planets from the sun are 10¹³ m and 10¹² m respectively. The ratio of time periods of the planets is

The time period of a planet’s revolution around the Sun is governed by Kepler’s Third Law, which establishes a relationship between the orbital period and the distance of the planet from the Sun. According to this law, the square of the orbital period of a planet is proportional to the cube of its average distance from the Sun. This means that as the distance of a planet from the Sun increases, its orbital period becomes significantly longer.

In this scenario, the distances of two planets from the Sun are 10¹³ meters and 10¹² meters, respectively. The ratio of their orbital periods can be determined using Kepler’s Third Law. For the first planet, which is farther from the Sun, the time period increases because the gravitational pull decreases with distance, resulting in a slower orbital speed.

Using the law, it is found that the ratio of the time periods of the two planets is 10√10. This value shows that the first planet, being ten times farther from the Sun, takes considerably longer to complete one revolution than the second planet. This result demonstrates the profound effect of distance on the orbital dynamics of celestial bodies in a solar system.