Question

Uranus has more than 14 times as much mass as earth, yet the gravitational force is less. how can that be?

Answer 1

Answer:

By the force of universal attraction

Explanation:

The gravitational attraction of a large body (planet) on an object on its surface can be calculated with the same equation of universal gravitation

       F = G m1 m2 / r²

Where G is the Universal gravitation costing 6.67 10⁻¹¹ N m²/Kg², m1 the mass of the planet, r the distance that we can take equal to the average radius of the planet and m2 the mass of the object that we can leave out, what remains of the equation is called acceleration of the planet's gravity, let's write the equation explicitly

        g = G m1 / r²

We look for the data of the two planets, for the earth, they are 5.98 10²⁴ kg and 6.37 10⁶ m for their mass and radius, respectively; for Uranus we have 8.68 10²⁵ Kg and 2.54 10⁷ m; Let's calculate the values ​​of the acceleration of gravity for each

Earth

       g = 6.67 10 -11 5.98 10 24 / (6.37 10 6) 2

       g = 9.87 m / s

Uranus

       g2 = 6.67 10 -11 8.68 10 25 / (2.54 10 7) 2

       g2 = 8.97 m / s

We can see that the gravity of Uranus is less than the gravity of the earth.

This could be intuited since the force of gravity depends on the inverse of the square of the distance and only proportionally with the mass.

Answer 2

It has more mass, yes. But it has less of a gravitational pull because it is farther away from the sun than the Earth is