Question

Calculate the acceleration due to gravity at Earth due to the Moon. (b) Calculate the acceleration due to gravity at Earth due to the Sun.

Answer 1

Answer:

a)  g’= 3.44 10⁻⁵ m / s²

b)  g ‘’ = 5.934 10⁻³ m / s²

Explanation:

For this exercise let's use the law of universal gravitation

         F = $G \frac{m M}{r^2}$

where m is the mass of the body under study, M the mass of the body that creates the force and r the distance between the bodies

         F = $m \ ( G \frac{M}{r^2} )$

the attractive force is called weight W = m g,

Thus

         g = $G \frac{M}{r^2}$

is called the acceleration of gravity

a) the acceleration created by the moon

       g' = G \frac{M}{r^2}

the mass of the moon is M = 7.36 10²² kg

the distance from the moon to the Earth's surface is

       r = D -R_e

       r = 3.84 10⁸ -6.37 10⁶

       r = 3.7763 10⁸ m

we calculate

     g’= $6.67 \ 10^{-11} \ \frac{7.36 \ 10^{22}}{ (3.7763 \ 10^8)^2}$

     g ’= 3.44 10⁻⁵ m / s²

b) the acceleration created by the sun

mass of the sun M = 1,9991 10³⁰ ka

the distance from the sun wears down the Earth's surface

        r = D -R_e

        r = 1.496 10¹¹ -6.37 10⁶

        r = 1.4959 10¹¹ m

let's calculate

       g ’’ = $6.67 \ 10^{-11} \frac{1.991 \ 10^{30}}{ (1.4959 \ 10^{11})^2 }$

       g ‘’ = 5.934 10⁻³ m / s²