Chapter 14, Problem 34A

Consider two planets: Mercury, close to the sun, and Uranus, far from the sun. Which of these planets has a period shorter than Earth’s period around the sun? Which has a period longer than Earth’s?

To determine

To identify: The planets having shorter period and longer period than Earth.

Answer to Problem 34A

Period of mercury is shorter than that of Earth and period of Uranus is longer than that of Earth.

Explanation of Solution

Given:

Mercury is close to Sun and Uranus is far from Sun.

Formula used:

As per Kepler’s third law of planetary motion, orbiting period of planet and the distance between planet and Sun are related as,

  ${\text{T}}^{\text{2}}\propto {\text{R}}^{\text{3}}$

The period of revolution of a planet around sun increases as the mean distance of the planet from sun increase. Since Mercury is closer to Sun than Earth, the mean distance between Mercury and Sun is the least. Hence, the period of Mercury is shorter than that of Earth around Sun. Uranus is far from Sun compared to Earth. Hence, the mean distance between Uranus and Sun is larger than that between Earth and Sun. Therefore, the period of Uranus is longer than that of Earth.

Conclusion:

Hence, period of mercury is shorter than that of Earth and period of Uranus is longer than that of Earth.