Given Newton's gravity formula, F=G*(M*m)/(r^2), what are the SI units of the universal gravity constant, G?

1 Answer
Mar 19, 2016

G has the SI units m^3/(kg*s^2)

Explanation:

F is the force of gravity: (kg*m)/s^2

M and m are masses, in kg

r is the distance between the masses, in m (meters)

This gives

(kg*m)/s^2 = G xx (kg^2)/(m^2)

m^2*(kg*m)/s^2 = G xx kg^2
m^2*(kg*m)/s^2*1/k^2 = G
m^2*(cancel(kg)*m)/s^2*1/k^cancel(2) = G
(m^3)/s^2*1/k = G
G = m^3/(kg*s^2)