Answer:
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 = ![\frac{GMm}{R^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7BGMm%7D%7BR%5E%7B2%7D%20%7D)
⇒ g = ![\frac{GM}{R^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7BGM%7D%7BR%5E%7B2%7D%20%7D)
Given that the distance between the Sun and Earth is 1.5 x
m, then the gravitational field of the Sun on Earth,
gSE = ![\frac{GM}{(1.5*10^{11}) ^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7BGM%7D%7B%281.5%2A10%5E%7B11%7D%29%20%5E%7B2%7D%20%7D)
=
.................. 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 = ![\frac{GM}{(4.5*10^{12}) ^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7BGM%7D%7B%284.5%2A10%5E%7B12%7D%29%20%5E%7B2%7D%20%7D)
=
............. 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.