Answer to Question #234858 in Classical Mechanics for Exatelle

Question

Suppose that the force on a 1kg mass on the surface of the earth is 10N and that the radius of the earth is about 600 km. Then the force on an 8kg mass placed at a point 2000 km from the center of the earth will be?

Answer 1

$F =G\frac{mM}{R^2}$

$\text{for a mass of 1 kg on the ground:}$

$F_1 = 10N$

$R_1=600km=6*10^5m$

$F_1=G\frac{M}{(6*10^5)^2}$

$\text{for a mass of 8 kg at a distance of 2000 km}$

$\text{from the center of the earth:}$

$R_2= 2000km = 2*10^6m$

$F_2=G\frac{8M}{(2*10^6)^2}$

$F_2=8F_1\frac{(6*10^5)^2}{(2*10^6)^2}=7.2N$

$\text{Answer:}7.2N$