Newton's law of gravitation
Every mass pulls every other
- The Earth pulls you down — and you pull the Earth up, just as hard.
- Every pair of masses attracts, anywhere in the universe.
- Newton captured it in one equation.
The law of gravitation
- $F = \dfrac{G m_1 m_2}{r^{2}}$ — an attractive pull along the line joining the masses.
- $G = 6.67 \times 10^{-11}\ \dfrac{\text{N}\cdot\text{m}^2}{\text{kg}^2}$ is the universal constant.
Practice
Newton's law of gravitation gives the force between two masses as:
The pull is proportional to each mass and inversely proportional to the distance squared.
Practice
Gravity is always attractive.
Yes — masses only ever pull together; there is no gravitational repulsion.
An inverse-square law
- The force falls off as $\dfrac{1}{r^{2}}$.
- Double the separation → the force drops to a quarter.
Practice
Two masses attract with $40\ \text{N}$ at separation $r$. What is the force at separation $2r$?
Inverse-square: $\dfrac{40}{2^{2}} = \dfrac{40}{4} = 10\ \text{N}$.
Practice
If both masses are doubled (same distance), the gravitational force becomes:
$F \propto m_1 m_2$, so doubling each multiplies the force by $2 \times 2 = 4$.
Spheres act as points
- A uniform sphere pulls (from outside) exactly like a point mass at its centre.
- So you can treat the Earth as a point mass at its centre.
Practice
A uniform sphere attracts outside objects as if all its mass were at its centre.
Yes — from outside, a uniform sphere behaves exactly like a point mass at its centre.
You've got it
Key idea
- $F = \dfrac{G m_1 m_2}{r^{2}}$ — always attractive, along the joining line
- it is an inverse-square law: double $r$ → quarter the force
- a uniform sphere acts as a point mass at its centre