What is Newton's Law of Gravitation?
Newton's Law of Gravitation explains why every mass in the universe pulls on every other mass — from an apple falling to Earth's surface to planets circling the Sun. It underlies orbital mechanics, tides, and satellite motion.
Newton's Law of Gravitation states that any two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = Gm₁m₂/r².
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Step-by-step worked examples
Two people of 50 kg each stand 2 m apart. Find the gravitational force between them.
F = G·m₁·m₂/r² F = 6.674×10⁻¹¹ × (50×50) / 2² F = 6.674×10⁻¹¹ × 2500 / 4 F ≈ 4.17×10⁻⁸ N
Find the gravitational force on a 70 kg person at Earth's surface (Earth mass 5.97×10²⁴ kg, radius 6.37×10⁶ m).
F = G·m₁·m₂/r² F = 6.674×10⁻¹¹ × (5.97×10²⁴×70) / (6.37×10⁶)² F = 6.674×10⁻¹¹ × 4.179×10²⁶ / 4.058×10¹³ F ≈ 687 N (matches weight ≈ mg = 70×9.8)
Earth (6×10²⁴ kg) and the Moon (7×10²² kg) are 3.8×10⁸ m apart. Find the gravitational force between them.
F = G·m₁·m₂/r² F = 6.674×10⁻¹¹ × (6×10²⁴×7×10²²) / (3.8×10⁸)² F = 6.674×10⁻¹¹ × 4.2×10⁴⁷ / 1.444×10¹⁷ F ≈ 1.94×10²⁰ N
Flashcards
Quick quiz
Q1.What is the formula for Newton's Law of Gravitation?
Q2.If the distance between two masses doubles, the gravitational force becomes…
Q3.What is the approximate value of the gravitational constant G?
Q4.Why does the Moon orbit the Earth rather than fly off in a straight line?
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Common mistakes
Confusing G (universal constant) with g (local gravitational acceleration). — Correct: G is fixed everywhere; g = GM/r² depends on the planet and distance.
Thinking gravity only exists between planets and stars. — Correct: All masses attract each other; the effect is just too small to notice for everyday objects.
Assuming force is inversely proportional to distance (1/r), not distance squared. — Correct: It's an inverse-square law: F ∝ 1/r², so distance has a much bigger effect.
Using diameter or surface distance instead of center-to-center distance for r. — Correct: r must be measured between the centers of mass of the two objects.
FAQ
What is the formula for Newton's Law of Gravitation?
F = Gm₁m₂/r², where G ≈ 6.674×10⁻¹¹ N·m²/kg², m₁ and m₂ are the masses, and r is the distance between their centers.
How do you calculate gravitational force between two objects?
Multiply the two masses, multiply by G, then divide by the square of the distance between their centers: F = Gm₁m₂/r².
What is Newton's Law of Gravitation in simple terms?
Every object with mass pulls on every other object with mass — bigger masses and shorter distances mean a stronger pull.
What is the difference between gravitational force and weight?
Weight is the specific gravitational force a planet exerts on an object's mass (W = mg); Newton's law is the general formula for any two masses.