Gravitational Force Calculator

📚 How It Works

Newton's Law of Universal Gravitation

Every mass attracts every other mass with a force proportional to their masses and inversely proportional to the square of the distance between them:

F = G × (m₁ × m₂) / r²

Where G = 6.674 × 10⁻¹¹ N⋅m²/kg² (gravitational constant)

Weight vs. Mass

Mass is the amount of matter in an object (measured in kg). It's the same everywhere.

Weight is the gravitational force on an object (measured in N). It varies with location:

W = m × g

Where g is the local gravitational field strength (9.8 m/s² on Earth's surface)

Gravitational Field Strength

The gravitational field strength at a point is the force per unit mass:

g = G × M / r²

This determines the acceleration of any object at that location.

Escape Velocity

The minimum velocity needed to escape a body's gravitational pull:

v_escape = √(2GM/r)

• Earth: 11.2 km/s (40,300 km/h)
• Moon: 2.4 km/s (8,600 km/h)
• Sun: 617.5 km/s (2.2 million km/h)

Inverse Square Law

Gravitational force decreases with the square of distance. If you double the distance, the force becomes 1/4 as strong. Triple the distance → 1/9 the force.

Real-World Applications

• Satellites: Must have enough velocity to stay in orbit without falling or escaping
• Tides: Caused by the Moon's gravitational pull on Earth's oceans
• Planetary Motion: Planets orbit the Sun due to gravitational force
• Black Holes: Escape velocity exceeds the speed of light