Gravitational Force Calculator
Calculates the gravitational force between two masses and the orbital velocity of a satellite at a given distance. Ideal for physics students, astronomy enthusiasts, and anyone modelling orbital mechanics.
About this calculator
Newton's Law of Universal Gravitation states F = G × m₁ × m₂ / r², where G = 6.674 × 10⁻¹¹ N·m²/kg², m₁ and m₂ are the two masses in kg, and r is the distance between their centres in metres. The orbital velocity of a small body around mass m₁ at distance r is v_orb = √(G × m₁ / r). The formula used here combines both outputs: the first term gives gravitational force (N) and the second term gives orbital velocity (m/s, scaled by 1000 for km/s display). Escape velocity is √2 times the orbital velocity. These relationships underpin everything from satellite launches to planetary science.
How to use
Consider the Earth (m₁ = 5.972 × 10²⁴ kg) and the Moon (m₂ = 7.342 × 10²² kg) separated by r = 3.844 × 10⁸ m. Gravitational force = 6.674 × 10⁻¹¹ × (5.972 × 10²⁴ × 7.342 × 10²²) / (3.844 × 10⁸)² ≈ 1.982 × 10²⁰ N. Orbital velocity = √(6.674 × 10⁻¹¹ × 5.972 × 10²⁴ / 3.844 × 10⁸) ≈ 1,018 m/s ≈ 1.018 km/s, matching the Moon's known orbital speed very closely.
Frequently asked questions
How does distance affect gravitational force between two objects?
Gravitational force follows an inverse-square law: doubling the distance reduces the force to one-quarter of its original value. This means gravity weakens very rapidly with separation — at ten times the distance, the force is only 1/100th as strong. This principle explains why astronauts feel weightless in orbit (they are in free-fall, not truly beyond gravity's reach) and why planets closer to the Sun experience stronger solar gravity than outer planets.
What is the difference between orbital velocity and escape velocity?
Orbital velocity is the speed needed for a circular orbit at a given altitude: v_orb = √(GM/r). Escape velocity is the minimum speed to break free from a body's gravity well entirely: v_esc = √(2GM/r). Escape velocity is always exactly √2 ≈ 1.414 times greater than circular orbital velocity at the same distance. For Earth at its surface, orbital velocity is about 7.9 km/s and escape velocity is about 11.2 km/s.
Why is the gravitational constant G so small and hard to measure?
G = 6.674 × 10⁻¹¹ N·m²/kg² is intrinsically tiny, meaning gravity is by far the weakest of the four fundamental forces. It is hard to measure precisely because gravitational signals between lab-scale masses are swamped by vibrations and electromagnetic noise. The first measurement by Cavendish in 1798 used a torsion balance, and modern determinations still rely on similar principles. Despite centuries of effort, G remains the least precisely known fundamental constant in physics.