Gravitational Force Calculator
Calculate gravitational force, mass, or distance using F = G × m₁ × m₂ / r².
Related: | | |
What is Gravitational Force?
Gravitational force is the mutual attraction between any two objects with mass. Newton's law of universal gravitation states that every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them:
F = G × m₁ × m₂ / r²
where G = 6.67430×10⁻¹¹ N·m²/kg² is the gravitational constant, m₁ and m₂ are the masses, and r is the distance between their centers of mass. Despite being the weakest of the four fundamental forces, gravity dominates on astronomical scales because it is always attractive and has infinite range.
Gravitational Forces in the Solar System
| Bodies | Mass 1 | Mass 2 | Distance | Force (N) |
|---|---|---|---|---|
| Earth – Sun | 1.989×10³° kg (Sun) | 5.972×10²⁴ kg (Earth) | 1.496×10¹¹ m | 3.54×10²² |
| Earth – Moon | 5.972×10²⁴ kg (Earth) | 7.342×10²² kg (Moon) | 3.844×10⁸ m | 1.98×10²⁰ |
| Sun – Jupiter | 1.989×10³° kg (Sun) | 1.898×10²⁷ kg (Jupiter) | 7.786×10¹¹ m | 4.16×10²³ |
| Earth – Satellite (ISS) | 5.972×10²⁴ kg (Earth) | 4.2×10⁵ kg (ISS) | 6.771×10⁶ m | 3.68×10³ |
| Mars – Phobos | 6.417×10²³ kg (Mars) | 1.06×10¹⁶ kg (Phobos) | 9.376×10⁶ m | 5.17×10¹⁵ |
| Earth – 1 kg mass on surface | 5.972×10²⁴ kg (Earth) | 1 kg | 6.371×10⁶ m | 9.82 |
| Sun – Earth | 1.989×10³° kg (Sun) | 5.972×10²⁴ kg (Earth) | 1.496×10¹¹ m | 3.54×10²² |
| Pluto – Charon | 1.309×10²² kg (Pluto) | 1.586×10²¹ kg (Charon) | 1.964×10⁷ m | 3.60×10¹¶ |
Related Calculators
Authoritative References
Frequently Asked Questions
What is gravitational force?
Gravitational force is the attractive force between any two objects with mass. It is described by Newton's law of universal gravitation: F = G × m₁ × m₂ / r², where G is the gravitational constant (6.67430×10⁻¹¹ N·m²/kg²).
Who discovered the law of universal gravitation?
Sir Isaac Newton published the law of universal gravitation in 1687 in his work Philosophiæ Naturalis Principia Mathematica. The story goes that he was inspired by watching an apple fall from a tree, realizing the same force that pulls the apple also holds the Moon in orbit.
What is the value of G?
The gravitational constant G = 6.67430×10⁻¹¹ N·m²/kg². It is one of the fundamental physical constants and is extremely difficult to measure precisely because gravity is so weak compared to other fundamental forces.
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. Tripling the distance reduces it to one-ninth. This is why gravity weakens rapidly as objects move apart.
How does mass affect gravitational force?
Gravitational force is directly proportional to the product of the two masses: F ∝ m₁ × m₂. Doubling either mass doubles the force. Doubling both masses quadruples the force.
What is the gravitational force between the Earth and the Sun?
The gravitational force between Earth and Sun is approximately 3.54×10²² N. This enormous force provides the centripetal force that keeps Earth in its orbit around the Sun.
What is the gravitational force between the Earth and the Moon?
The gravitational force between Earth and Moon is approximately 1.98×10²⁰ N. This force causes the Moon to orbit Earth and is also responsible for ocean tides via tidal forces.
What is the gravitational force on Earth's surface?
On Earth's surface, a 1 kg mass experiences about 9.82 N of gravitational force. This is what we call weight: F = mg, where g ≈ 9.82 m/s² at sea level.
What is the difference between mass and weight?
Mass is a measure of the amount of matter in an object, measured in kilograms. Weight is the gravitational force exerted on that mass: W = mg. Your mass is the same everywhere, but your weight changes with gravity — on the Moon you weigh about 1/6 of your Earth weight.
What is the inverse-square law?
The inverse-square law means a physical quantity is inversely proportional to the square of the distance from the source. For gravity, F ∝ 1/r². This also applies to light intensity, electric fields, and sound intensity.
What is the Cavendish experiment?
The Cavendish experiment, performed in 1797–1798 by Henry Cavendish, was the first to measure the gravitational constant G. It used a torsion balance with lead spheres to detect the tiny gravitational attraction between laboratory masses.
How is G measured today?
Modern measurements of G use techniques like laser interferometry, atom interferometry, and precision torsion balances. Despite advances, G remains the least precisely measured fundamental constant, with uncertainty of about 22 parts per million.
What is the gravitational force between two people?
Two 70 kg people standing 1 m apart experience a gravitational force of about F = G × 70 × 70 / 1² ≈ 3.3×10⁻⁷ N. This is tiny compared to Earth's gravity and completely unnoticeable.
How does gravity compare to other fundamental forces?
Gravity is the weakest of the four fundamental forces. It is about 10³⁶ times weaker than the strong nuclear force, 10²⁵ times weaker than electromagnetism, and 10²⁹ times weaker than the weak nuclear force. However, gravity dominates at large scales because it is always attractive and has infinite range.
What is Einstein's theory of gravity?
Einstein's general relativity (1915) describes gravity not as a force but as a curvature of spacetime caused by mass and energy. Massive objects warp spacetime, and this curvature tells objects how to move. This theory explains Mercury's orbit, gravitational lensing, and black holes.
What are gravitational waves?
Gravitational waves are ripples in spacetime predicted by Einstein in 1916 and directly detected by LIGO in 2015. They are produced by accelerating masses, such as merging black holes or neutron stars, and travel at the speed of light.
What is a black hole's gravity?
A black hole has such intense gravity that nothing, not even light, can escape beyond its event horizon. The gravitational force near a stellar-mass black hole can be millions of times stronger than on Earth's surface.
What is the gravitational force inside a spherical shell?
Newton's shell theorem states that inside a uniform spherical shell, the net gravitational force is zero. This is because the mass above cancels out the gravitational pull from all directions.
What is free fall?
Free fall is motion under the influence of gravity alone, with no other forces (ignoring air resistance). In free fall, all objects accelerate at the same rate, g ≈ 9.82 m/s² on Earth, regardless of mass — as demonstrated by Galileo and famously by Apollo 15's hammer-and-feather drop on the Moon.
What is the difference between g and G?
Lowercase g is the acceleration due to gravity on Earth's surface (about 9.82 m/s²). Capital G is the universal gravitational constant (6.67430×10⁻¹¹ N·m²/kg²). G is universal; g varies slightly with location on Earth.
How does gravity vary on Earth?
Gravity on Earth varies from about 9.763 m/s² (Nevado Huascarán, Peru) to 9.833 m/s² (Arctic Ocean surface). Variations are due to altitude, latitude (Earth's rotation and shape), and local density differences in the crust.
What is the gravitational force at the center of Earth?
At the center of Earth, gravity is zero. As you descend into Earth, gravity decreases linearly with distance from the center (assuming uniform density), reaching zero at the center due to the shell theorem.
What is tidal force?
Tidal force arises from the difference in gravitational force across an object. The Moon pulls more strongly on Earth's near side than its far side, creating tidal bulges. Tidal forces also cause tidal locking (Moon always shows the same face) and can tear apart moons near a planet (Roche limit).
What is the Roche limit?
The Roche limit is the minimum distance at which a celestial body can orbit another without being torn apart by tidal forces. For Earth and a Moon-density satellite, the Roche limit is about 18,470 km. Inside this limit, tidal forces overcome self-gravity.
How does gravity affect time?
According to general relativity, stronger gravity slows time — a phenomenon called gravitational time dilation. Clocks run slightly slower at sea level than on mountaintops. GPS satellites must correct for this effect (about 45 microseconds per day) to maintain accuracy.
What is the Lagrange point gravity?
Lagrange points are positions where the gravitational forces of two large bodies (e.g., Earth and Sun) balance the centripetal force of a smaller object. At these five points (L1–L5), a satellite can remain stationary relative to the two bodies. L2 is home to the James Webb Space Telescope.
How is gravity used in space travel?
Gravity assists (slingshots) use a planet's motion to change a spacecraft's trajectory and speed. The Voyager missions used gravity assists from Jupiter, Saturn, Uranus, and Neptune to reach interstellar space. This technique saves enormous amounts of fuel.
What is the gravitational binding energy of Earth?
Earth's gravitational binding energy is approximately 2.5×10³² J — the energy required to disperse all of Earth's mass to infinity. This is roughly equivalent to the Sun's total energy output for one week.
Does antimatter fall up or down?
Experiments suggest antimatter falls downward, just like ordinary matter. The ALPHA-g experiment at CERN in 2023 confirmed that antihydrogen atoms fall with gravitational acceleration close to g, consistent with Einstein's equivalence principle.
What is the hierarchy problem?
The hierarchy problem asks why gravity is so much weaker than the other fundamental forces. One proposed solution is extra spatial dimensions that dilute gravity's strength. This is an active area of research in theoretical physics.