Physics / Unit 4: Circular Motion and Gravity
4.4 Universal Gravitation
Notes
Newton's law of universal gravitation: every two masses attract each other with a force $\displaystyle F = \frac{G m_1 m_2}{r^2}$.
- $G = 6.67 \times 10^{-11} \text{ N·m}^2/\text{kg}^2$; $r$ is the distance between the centers.
- It is an inverse-square law: double the distance and the force drops to one fourth.
- Doubling one mass doubles the force.
- The force is tiny for everyday objects and large only when at least one mass is huge, like a planet.
- Example: two 1,000 kg masses 1 m apart: $\displaystyle F = \frac{(6.67 \times 10^{-11})(1000)(1000)}{1^2} = 6.67 \times 10^{-5} \text{ N}$.
Practice
The distance between two asteroids triples. The gravitational force between them becomes:
$\displaystyle F \propto \frac{1}{r^2}$, and $\displaystyle \frac{1}{3^2} = \frac{1}{9}$.
Both masses in a pair are doubled and the distance stays the same. The force becomes:
$F \propto m_1 m_2$, so $2 \times 2 = 4$.
Which statement about gravity between Earth and you is correct?
This is a Newton's third law pair; Earth's large mass is why its acceleration is tiny.
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