The planet Jupiter is more than 300 times as massive as the Earth But it so happens that a body would scarcely weigh three times as much on the surface of Jupiter as it would on the surface of Earth. Can you think of an explanation for why this is so? (Hint: Let the terms in the equation for gravitational force guide your thinking.)
To understand why a body would weigh much less on the surface of Jupiter compared to its mass, we need to look at the equation for gravitational force.
The equation for gravitational force between two objects is given by:
F = G * (m1 * m2) / r^2
Where:
- F is the force of gravity between the two objects
- G is the gravitational constant
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects
In this case, the mass of the body (m2) is the same on both Earth and Jupiter. However, the mass of Jupiter (m1) is much larger than the mass of Earth. Let's say m1 represents the mass of Jupiter, and m2 represents the mass of the body.
Since m1 (mass of Jupiter) is more than 300 times greater than m2 (mass of the body), the larger mass of Jupiter would exert a stronger gravitational force on the body.
However, the equation also includes the distance between the centers of the two objects (r). Since the body is on the surface of both Earth and Jupiter, we can consider r to be approximately the radius of each planet.
The radius of Jupiter is about 11 times greater than the radius of Earth. This means that the distance (r) between the center of Jupiter and the surface of Jupiter is much larger than the distance between the center of Earth and the surface of Earth.
When we substitute these values into the equation for gravitational force, we find that the larger mass of Jupiter is counteracted by the greater distance from its center. Consequently, the force experienced by the body on the surface of Jupiter is much weaker despite its large mass compared to Earth. The body would weigh only about three times as much on the surface of Jupiter as it would on the surface of Earth.