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How It Works
Newton's Law of Universal Gravitation states that every two objects 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). The gravitational constant G = 6.6726 × 10⁻¹¹ N·m²/kg².
This calculator also covers Kepler's Third Law (orbital period), gravitational acceleration, and escape velocity — all derived from the same underlying gravitational law.
Example Problem
What is the gravitational force between Earth (5.97 × 10²&sup4; kg) and a 70 kg person standing on the surface (r = 6.371 × 10&sup6; m)?
- F = G · m₁ · m₂ / r²
- F = 6.67×10⁻¹¹ × 5.97×10²&sup4; × 70 / (6.371×10&sup6;)²
- F ≈ 686 N (about 154 lbf)
Frequently Asked Questions
What is the gravitational constant G?
G is a fundamental constant (6.6726 × 10⁻¹¹ N·m²/kg²) that sets the strength of gravity. Unlike g (9.81 m/s² on Earth), G is the same everywhere in the universe.
What is Earth's escape velocity?
Earth's escape velocity is about 11.2 km/s (roughly 25,000 mph). Any object launched at this speed or faster will not fall back to Earth, ignoring air resistance.
How does gravity change with altitude?
Gravitational acceleration decreases with the square of the distance from a planet's center. At the altitude of the ISS (~400 km), g is about 8.7 m/s² — roughly 89% of the surface value.
Related Calculators
- Weight Equation Calculator — calculate weight from mass and gravitational acceleration.
- Circular Motion Calculator — analyze orbital and centripetal motion.
- Potential Energy Calculator — find gravitational potential energy (mgh).
- Force Equation Calculator — calculate force from mass and acceleration using F = ma.
- Projectile Motion Calculator — analyze trajectories under gravitational acceleration.
- Acceleration Converter — convert between m/s², ft/s², g-force, and other units.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.