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 = [tex]\frac{GMm}{R^{2} }[/tex] ............. 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 = [tex]\frac{GMm}{R^{2} }[/tex]
⇒ g = [tex]\frac{GM}{R^{2} }[/tex]
Given that the distance between the Sun and Earth is 1.5 x [tex]10^{11}[/tex] m, then the gravitational field of the Sun on Earth,
gSE = [tex]\frac{GM}{(1.5*10^{11}) ^{2} }[/tex]
= [tex]\frac{GM}{2.25*10^{22} }[/tex] .................. 3
Given that the distance between the Sun and Neptune is 4.5 x [tex]10^{12}[/tex] m, then the gravitational field of the Sun on Neptune,
gSN = [tex]\frac{GM}{(4.5*10^{12}) ^{2} }[/tex]
= [tex]\frac{GM}{2.025*10^{25} }[/tex] ............. 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.
