# What is the diference between law of gravitation and universal law of gravitation?

Aug 14, 2018

Law of gravity on Earth has been simplified from the universal law.

#### Explanation:

Newton's universal law of gravitation:

${F}_{1} = {F}_{2} = G \cdot \frac{{M}_{1} \cdot {M}_{2}}{{r}^{2}}$

This gives the forces acting on two masses ${M}_{1}$ and ${M}_{2}$ where the centers of mass are at distance $r$ from each other.

G is the gravitational constant 6.674×10^(−11) N(m/(kg))^2

Because we are usually dealing with gravity near the surface of the earth it is possible to simplify the above to combine the constant factors into one approximate constant.

Using the mass of Earth as a constant for ${M}_{1}$, and the radius of Earth as a constant for $r$ we get

F = 6.674×10^(−11)N(m/(kg))^2 * (( 5.97219*10^24) kg*(M_2))/ ((6.3710 * 10^6)m^2)

$\text{ } = 9.819844 \cdot \left({M}_{2}\right) N k {g}^{-} 1$

$F \approx 9.8 N k {g}^{-} 1 \cdot {M}_{2} \text{ }$ (force due to gravity near surface of Earth)