Gravitation
Universal Gravitation Calculator
Calculate the gravitational force between any two masses, or find distance or mass. Formula: F = Gm₁m₂/r².
Result
F = Gm₁m₂/r²
Step-by-Step Solution
Newton's Law of Universal Gravitation
Every mass in the universe attracts every other mass with a gravitational force. This force is proportional to both masses and inversely proportional to the square of the distance between their centres. Newton derived this law in 1687, unifying terrestrial mechanics (why apples fall) with celestial mechanics (why planets orbit).
F = Gm₁m₂/r²
G = 6.674×10⁻¹¹ N·m²/kg² | m₁, m₂ = masses (kg) | r = distance between centres (m)
💡 Gravity is the weakest of the four fundamental forces, but it has infinite range and is always attractive. This makes it dominant at astronomical scales where electromagnetic charges cancel out.
Real-World Applications
Planetary Orbits
Gravity between the Sun and planets provides the centripetal force to maintain elliptical orbits — Kepler's Laws.
Tides
The Moon's gravity pulls on Earth's oceans, creating tidal bulges. The Sun's gravity creates a secondary effect.
Spacecraft Navigation
Gravitational slingshots (Oberth effect) use planetary gravity to accelerate spacecraft without extra fuel.
GPS Satellites
GPS satellites must account for general relativistic effects of gravity on time to maintain centimetre accuracy.
Frequently Asked Questions
How did Newton discover the law of gravity?
Newton's key insight was that the same force causing an apple to fall also governs the Moon's orbit. By calculating the Moon's centripetal acceleration and comparing it to surface gravity (1/r² relationship), he derived the universal law in 1687.
What is the gravitational constant G?
G = 6.674×10⁻¹¹ N·m²/kg². It was first measured by Henry Cavendish in 1798 using a torsion balance. G is the same everywhere in the universe — it is a fundamental constant of nature.
Does universal gravitation differ from Einstein's general relativity?
Newton's law is an excellent approximation for most practical purposes. Einstein's general relativity improves on it for very strong gravity (black holes, neutron stars) or high velocities. For GPS, spacecraft and everyday engineering, Newton's formula is sufficient.