Earth is 1.5 ✕ 1011 m from the Sun. Neptune is 4.5 ✕ 1012 m from the Sun. How does the gravitational field of the Sun on Neptune (gSN) compare to the gravitational field of the Sun on Earth (gSE)?

The gravitational field of the Sun on Earth is greater than the gravitational field of the Sun on Neptune.

Explanation:

From Newton's law of universal gravitation,

F = ............. 1

where F is the force, G is the gravitational constant, M is the mass of the bigger object, m is the mass of the smaller object and R is the distance between their centers.

Also, Newton's second law of motion state;

F = mg ................ 2

where F is the force, m is the mass and g is the gravitational force.

Equating 1 and 2,

mg =

⇒ g =

Given that the distance between the Sun and Earth is 1.5 x m, then the gravitational field of the Sun on Earth,

gSE =

       = .................. 3

Given that the distance between the Sun and Neptune is 4.5 x m, then the gravitational field of the Sun on Neptune,

gSN =

        = ............. 4

Comparing equations 3 and 4, it can be observed that gSE > gSN.

The gravitational field of the Sun on Earth is greater than the gravitational field of the Sun on Neptune.

this would be about 43%