Question

The weight of an object on a planet depends not only on its mass but also on its distance from the planets center this table lists weight of 80 kg on each planet in the solar system Uranus has more than 14 times as much mass as earth yet the gravitational force is less explain how this could be

Answer 1

The weight of an object, which is the force due to gravity, depends on the mass of the object and the gravitational acceleration at a location. Despite Uranus having more mass than Earth, its larger radius results in lower surface gravity, which explains why an object would weigh less on Uranus.

Step-by-step explanation:

The weight of an object is the force exerted on it due to gravity, and it depends on both the mass of the object and the gravitational pull at a given location. While Uranus has over 14 times the mass of Earth, its surface gravity is lower because of its significantly larger radius compared to Earth. This larger radius means that the surface is farther away from the center of the planet where the gravitational pull is strongest, leading to a weaker gravitational force exerted on objects at the surface.

Moreover, this gravitational force is calculated using the formula F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass. Even though Uranus has a greater mass than Earth, the greater distance from the center to the surface (higher r value) in the equation results in lesser gravity, and thus lesser weight of an object on the surface of Uranus compared to Earth.

Answer 2

You just pointed out that the gravitational force also depends
on the distance from the planet's center. The radius of Uranus
is about 4 times the Earth's radius. That fact alone means that
the gravitational force on the surface is 1/4² = 1/16 its value on
Earth's surface. So increasing the planet's mass by a factor of
14 doesn't compensate for the 1/16 reduction, and the gravitational
force on Uranus is less than on Earth.