Answer to Question #285661 in Mechanics | Relativity for Kaye

Question

Interestingly, when the value of G was first measured, people all over the world were very excited because the mass of the earth can now be measured through Newton's law of universal gravitation. Using the radius of the earth, r = 6.40 X10 m, calculate its mass Consider a 1 Kg ball on the floor.

Answer 1

Weight of an object on Earth =

Gravitational force exerted on an object by the Earth

$mg=\frac{GMm}{R^2}$

$g=\frac{GM}{R^2}$

$M_e=\frac{gr^2}{G}$

Put value

$$M_e=\frac{9.81\times(6400000)^2}{6.67\times10^{-11}}=6.024\times10^{24}Kg$$