Chapter 13, Problem 51A

The planet Jupiter is about 300 times as massive as Earth, but an object on its surface would weigh only 2.5 times as much as it would on Earth. Can you come up with an explanation? (Hint: Let the terms in the equation for gravitational force guide your thinking.)

To determine

To explain:The weight of an object on the surface of Jupiter is $2.5$ times the weight on Earth.

Explanation of Solution

Introduction:

Gravitational force is the attractive force between two objects that possess mass. This force continuously attempts to pull the bodies together and never tries to push them away from each other. Thus, it is attractive in nature. The force of gravity is one of the fundamental forces in nature that is responsible for the interactions among the objects in nature. This is the weakest force among the four fundamental forces in nature (Strong nuclear force, Electromagnetic force, weak nuclear force, and gravitational force).

The force of gravity $\left(F\right)$ experienced by an object of mass $\left(m\right)$ on the planet can be written as,

  $F=\frac{GMm}{d^2}=mg$

  $\left(1\right)$

Where,

G is gravitational constant, $G=6.67\times {10}^{-11}\text{ N}\cdot {\text{m}}^2/{\text{kg}}^2$

  $g$ is acceleration due to gravity, $g=9.8{\text{ m/s}}^2$

  $M$ is mass of the planet,

  $m$ is mass of an object,

  $d$ is distance between the planet and an object.

Every object on the surface of a planet will experience its weight only due to the force of gravity. As shown in the equation (1), the force of gravity experienced by an object on the surface of a planet is directly related to the mass but it is inversely related to the square of the radius.

The planet Jupiter is about $300$ times as massive as Earth and also it has radius $11.2$ times that of Earth.

Hence, the objects weight on the surface of a planet Jupiter is,

  $\frac{300}{{\left(11.2\right)}^2}=\frac{300}{125.44}=2.39\approx 2.5$

This means that it is 2.5 times the weight on Earth.