Newton's Law of Universal Gravitation

1. Understanding the Law

• Every object in the universe attracts every other object with a force that:
  • Is directly proportional to the product of their masses.
  • Is inversely proportional to the square of the distance between them.
• Formula: $F = G \frac{m_1 m_2}{r^2}$

where:

• $F$ = gravitational force $(N)$
• $G$ = gravitational constant $(:highlight[6.67 \times 10^{-11} \, \text{Nm}^2\text{kg}^{-2}])$
• $m_1, m_2$ = masses of the two objects $(kg)$
• $r$ = distance between their centres $(m)$

2. Graphical Representations

• $F \propto m_1 m_2 →$ Straight-line graph through the origin.
• $F \propto \frac{1}{r^2} →$ Hyperbola (as distance increases, force decreases rapidly).

4. Key Takeaways

• Gravity acts over any distance, no matter how large.
• Larger mass = stronger gravitational force.
• Greater distance = weaker gravitational force.
• Explains planetary motion and astronomical calculations.