Newton’s Law of Universal Gravitation: Formula, Explanation & Examples
Discover one of the greatest scientific laws in history. Learn how every mass in the universe attracts every other mass, the inverse square law, and real-world applications from falling apples to planetary orbits.
What is Newton’s Law of Universal Gravitation?
In 1687, Isaac Newton proposed that **every particle of matter in the universe attracts every other particle** with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
This law explains why objects fall to the ground, why planets orbit the Sun, and why the Moon causes tides.
The Universal Gravitation Formula
Where:
F = Gravitational force (N)
G = Universal gravitational constant (6.67430 × 10⁻¹¹ N·m²/kg²)
m₁, m₂ = masses of the two objects (kg)
r = distance between the centers of the two masses (m)
Important Characteristics
- Inverse Square Law: Force decreases rapidly as distance increases (1/r²)
- Always Attractive: Gravity is never repulsive
- Acts at a Distance: No physical contact needed
- Very Weak Force: Compared to electromagnetic force, gravity is extremely weak
Real-World Implications
- Explains why planets orbit the Sun in elliptical paths
- Keeps the Moon in orbit around Earth
- Causes weight (W = mg) on Earth’s surface
- Responsible for ocean tides due to Moon and Sun
Real-Life Examples
Falling Apple (Newton’s Inspiration)
The same force that pulls an apple to the ground keeps the Moon orbiting Earth.
Planetary Orbits
Gravity keeps Earth in orbit around the Sun and provides the centripetal force needed.
Ocean Tides
The Moon’s gravitational pull causes bulges in Earth’s oceans, resulting in high and low tides.
Artificial Satellites
Satellites stay in orbit because gravitational force provides the necessary centripetal force.
Solved Practice Problems
Problem 1: Calculate the gravitational force between Earth (mass 5.97 × 10²⁴ kg) and the Moon (mass 7.35 × 10²² kg) if the average distance is 384,400 km.
F = G (m₁m₂)/r² ≈ 1.98 × 10²⁰ N
Problem 2: Why do astronauts feel weightless in space even though gravity still exists?
Answer: They are in free fall (orbit). Gravity provides centripetal force, but there is no normal force.
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