Question

The sun is more massive than the moon, but the sun is farther from the earth. Which one exerts a greater gravitational force on a person standing on the earth? Give your answer by determining the ratio Fsun/Fmoon.
Information:

Earth
mass 5.98 x 10^24 kg
radius (eqt) 6.38 x 10^6 m
Mean distance from the sun 1.50 x 10^11 m

Moon
mass- 7.35 x 10^22 kg
radius (mean) 1.74 x 10^6 m
mean distance from the earth 3.85 x 10^8 m

Sun
Mass- 1.99 X 10^30 kg
Radius 6.96 x 10^8 m

Answer 1

Answer:

178.4 times

Explanation:

We have Newton formula for attraction force between 2 objects with mass and a distance between them:

$F_G = G\frac{M_1M_2}{R^2}$

where $G =6.67408 × 10^{-11} m^3/kgs^2$ is the gravitational constant on Earth. $M_1, M_2$ is the masses of the 2 objects. and R is the distance between them.

From here we can calculate the ratio of gravitational force between the moon and the sun

$\frac{F_s}{F_m} = \frac{G\frac{MM_s}{R_s^2}}{G\frac{MM_m}{R_m^2}}$

We can divide the top and bottom by G and M

$\frac{F_s}{F_m}= \frac{M_s}{R_s^2}:\frac{M_m}{R_m^2}$

$= \frac{M_s}{R_s^2}\frac{R_m^2}{M_m}$

$= \frac{M_s}{M_m}(\frac{R_m}{R_s})^2$

$= \frac{1.99*10^{30}}{7.35*10^{22}}(\frac{3.85*10^8}{1.5*10^{11}})^2$

$= 27074830*6.59*10^{-6} = 178.4$

So the gravitational force of the sun is about 178 times greater than that of the moon to an object on Earth