Question

Assume that you stay on the Earth's surface. What is the ratio of the sun's gravitational force on you to the earth's gravitational force on you? Express your answer using two significant figures.

Answer 1

First, let's determine the gravitational force of the Earth exerted on you. Suppose your weight is about 60 kg. 

F = Gm₁m₂/d²

where

m₁ = 5.972×10²⁴ kg (mass of earth)

m₂ = 60 kg

d = 6,371,000 m (radius of Earth)

G = 6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²

F = ( 6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²)(60 kg)(5.972×10²⁴ kg)/(6,371,000 m )²

F = 589.18 N

Next, we find the gravitational force exerted by the Sun by replacing,

m₁ = 1.989 × 10³⁰ kg

Distance between centers of sun and earth = 149.6×10⁹ m

Thus,

d = 149.6×10⁹ m - 6,371,000 m = 1.496×10¹¹ m

Thus,

F = ( 6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²)(60 kg)(1.989 × 10³⁰ kg)/(1.496×10¹¹ m)²

F = 0.356  N

Ratio = 0.356  N/589.18 N

Ratio = 6.04