Question

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)?

Answer 1

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

Step-by-step explanation:

From Newton's law of universal gravitation,

F =
`(GMm)/(R^(2) )` ............. 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 =
`(GMm)/(R^(2) )`

⇒ g =
`(GM)/(R^(2) )`

Given that the distance between the Sun and Earth is 1.5 x
`10^(11)` m, then the gravitational field of the Sun on Earth,

gSE =
`(GM)/((1.5*10^(11)) ^(2) )`

=
`(GM)/(2.25*10^(22) )` .................. 3

Given that the distance between the Sun and Neptune is 4.5 x
`10^(12)` m, then the gravitational field of the Sun on Neptune,

gSN =
`(GM)/((4.5*10^(12)) ^(2) )`

=
`(GM)/(2.025*10^(25) )` ............. 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.