Quick Answer

The gravitational force between Earth and the Moon is approximately 1.98 × 10²⁰ N. Two 1 kg masses 1 meter apart experience a force of 6.674 × 10⁻¹¹ N.

Solve For Force (F) Mass 1 (m₁) Mass 2 (m₂) Distance (r)

Mass 1 (kg)

Mass 2 (kg)

Distance (m)

Common Examples

Input	Result
m₁ = 5.972×10²⁴ kg (Earth), m₂ = 7.342×10²² kg (Moon), r = 3.844×10⁸ m	F ≈ 1.98×10²⁰ N
m₁ = 1 kg, m₂ = 1 kg, r = 1 m	F = 6.674×10⁻¹¹ N
m₁ = 5.972×10²⁴ kg (Earth), m₂ = 80 kg (person), r = 6.371×10⁶ m	F ≈ 784.5 N
F = 784.5 N, m₁ = 5.972×10²⁴ kg, r = 6.371×10⁶ m	m₂ ≈ 80 kg

How It Works

Newton’s law of universal gravitation

\[F = \frac{G m_1 m_2}{r^2}\]

Where:

• F = gravitational force in Newtons (N)
• G = gravitational constant = 6.674 × 10⁻¹¹ N m²/kg²
• m₁ = mass of the first object in kilograms (kg)
• m₂ = mass of the second object in kilograms (kg)
• r = distance between the centers of the two masses in meters (m)

The gravitational constant G

G = 6.674 × 10⁻¹¹ N m²/kg² is one of the fundamental constants of nature. It was first measured by Henry Cavendish in 1798 using a torsion balance. Its small value explains why gravity between everyday objects is imperceptible — two 1 kg masses 1 meter apart attract each other with a force of only 6.674 × 10⁻¹¹ N, roughly 15 billion times weaker than the weight of a grain of sand.

Rearranged forms

• Force: F = G m₁ m₂ / r²
• Mass 1: m₁ = F r² / (G m₂)
• Mass 2: m₂ = F r² / (G m₁)
• Distance: r = √(G m₁ m₂ / F)

The inverse square law

Gravitational force decreases with the square of the distance. Doubling the distance reduces the force by a factor of four. Tripling the distance reduces it by a factor of nine. This inverse square relationship means gravity weakens rapidly with distance but technically never reaches zero.

Worked example

A 70 kg person stands on Earth’s surface. Earth’s mass is 5.972 × 10²⁴ kg and its radius is 6.371 × 10⁶ m.

F = (6.674 × 10⁻¹¹ × 5.972 × 10²⁴ × 70) / (6.371 × 10⁶)²

F = (2.788 × 10¹⁶) / (4.059 × 10¹³)

F ≈ 687 N

This is the weight of a 70 kg person at Earth’s surface, consistent with W = mg = 70 × 9.81 = 686.7 N.

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Frequently Asked Questions

What is the gravitational constant G?

G = 6.674 × 10⁻¹¹ N m²/kg² is the universal gravitational constant. It appears in Newton's law of gravitation and determines the strength of gravitational attraction between any two masses. It was first measured by Henry Cavendish in 1798 and is one of the most precisely measured constants in physics, though it is also one of the hardest to measure accurately due to the weakness of gravitational forces.

Why is gravity so weak compared to other forces?

Gravity is the weakest of the four fundamental forces by many orders of magnitude. The electromagnetic force between two protons is roughly 10³⁶ times stronger than the gravitational force between them. Gravity dominates at cosmic scales only because it is always attractive and acts over unlimited range, while electromagnetic forces can cancel out between neutral objects. The small value of G (6.674 × 10⁻¹¹) reflects how weak gravity is at the particle scale.

Does gravity work in space?

Yes. Gravity acts everywhere in the universe with unlimited range. Astronauts in the International Space Station experience about 90% of Earth's surface gravity. They feel weightless because they are in free fall — the station and its occupants are continuously falling toward Earth while moving fast enough sideways to keep missing it. This is orbital motion, not the absence of gravity.

How does distance affect gravitational force?

Gravitational force follows an inverse square law: F ∝ 1/r². Doubling the distance reduces the force to one-quarter of its original value. At three times the distance, the force drops to one-ninth. This relationship means gravitational force weakens rapidly as objects move apart, but it never completely disappears regardless of distance.

What is the difference between g (9.81) and G (6.674×10⁻¹¹)?

G (uppercase) is the universal gravitational constant, G = 6.674 × 10⁻¹¹ N m²/kg², the same everywhere in the universe. g (lowercase) is the local gravitational acceleration at a planet's surface. On Earth, g ≈ 9.81 m/s². The relationship between them is g = G M / r², where M is the planet's mass and r is its radius. On the Moon, g ≈ 1.62 m/s²; on Mars, g ≈ 3.72 m/s².

Learn More

How to calculate gravitational force

Newton's law of gravitation explained with worked examples: Earth-Moon force, surface weight, inverse square law, and gravitational acceleration on other planets.