What is the acceleration due to Earth's gravity at a distance of 10 Earth radii from Earth's center?

Answer 1

For any mass m

F = G(mM / r²)

m = mass of object

M = mass of Earth

r = distance between centers of mass of the two objects

G = universal gravitational constant ( 6.6743 x 10^-11 Nm²/kg² )

Now the force on m is also F = ma so we can write

ma = G(mM / r²)

a = GM / r²

Plug in for G, M (5.972 × 10²⁴ kg), and r = 10 * R_earth = (10 * 6371000 ) m to get the acceleration.

Notice how the acceleration is independent of the object's mass, as expected.