Universal Law of Gravitation

• Newton's law of universal gravitation: every mass attracts every other mass.
• F = G m₁m₂ / r² — force proportional to product of masses, inversely proportional to square of distance.
• G = universal gravitational constant ≈ 6.67 × 10⁻¹¹ N·m²/kg².
• Gravitational force is always attractive; acts along line joining centres.

1. Formula — F = G m₁m₂/r²; r = centre-to-centre distance.
2. G — universal constant; same everywhere in universe (NCERT value).
3. Inverse square law — double r → F becomes 1/4.
4. Applies to — all objects: Earth–Moon, Earth–apple, Sun–planets.
5. Weakest fundamental force at everyday scales but dominates at astronomical scales.
6. Diagram (text) — two masses m₁, m₂ separated by r; forces on each equal and opposite (3rd law).
7. NCERT Ch. 10 — Cavendish experiment measured G (historical note).
8. Real world — tides (Moon's gravity on oceans); satellites orbit due to gravity.

If distance between two masses is halved, how does gravitational force change?

Step 1 — Original: F = G m₁m₂/r²
Step 2 — New distance r' = r/2
Step 3 — F' = G m₁m₂/(r/2)² = G m₁m₂/(r²/4) = 4F
Step 4 — Force becomes **four times** larger.
Step 5 — If one mass doubles and distance doubles: F' = G(2m₁)m₂/(2r)² = 2F/4 = F/2.

• Using surface distance instead of centre-to-centre r for planets.
• Misconception: gravity only acts near Earth (universal — acts everywhere).
• Confusing G (constant) with g (acceleration due to gravity).
• Thinking F = Gm₁m₂/r applies (missing square on r).
• Forgetting gravitational force acts on both bodies equally.

• Write the universal law of gravitation with symbols defined.
• What happens to F if r is tripled?
• Why is G called a universal constant?
• Is gravitational force ever repulsive?

Open the Practice tab for graded questions on Universal Law of Gravitation.