Gravitational Force Calculator: Newton's Law of Gravitation
Newton's Law of Universal Gravitation, published in Principia Mathematica in 1687, states that any two objects with mass attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres: F = G m1 m2 / r^2. The gravitational constant G = 6.67430 x 10^-11 N m^2 kg^-2 (NIST CODATA 2018) sets the absolute scale of this attraction. While superseded by Einstein's General Relativity for high-precision and strong-field applications, Newton's law remains accurate enough to design interplanetary spacecraft trajectories, model tidal forces, and compute orbital mechanics. Surface gravity, g = G M / R^2, determines how heavy objects feel on a planet's surface. This calculator covers both applications: enter two masses and a separation to compute gravitational force, or select a body to instantly see its surface gravity. All planetary parameters are sourced from the NASA Planetary Fact Sheet.
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Newton's Law of Universal Gravitation
F = G × m1 × m2 / r²
where G = 6.67430 x 10^-11 N m^2 kg^-2 (NIST CODATA 2018), m1 and m2 are the masses in kilograms, and r is the distance between centres of mass in metres. The force F is in Newtons. Both masses experience equal and opposite forces (Newton's third law).
Surface gravity
g = G × M / R²
where M is the body's total mass and R is its radius. Surface gravity determines the weight of an object on the surface: W = m g.
Planetary surface gravity comparison
| Body | Mass (kg) | Radius (m) | Surface g (m/s^2) |
|---|---|---|---|
| Earth | 5.972 × 10^24 | 6,371,000 | 9.82 |
| Moon | 7.342 × 10^22 | 1,737,000 | 1.62 |
| Mars | 6.39 × 10^23 | 3,389,500 | 3.72 |
| Jupiter | 1.898 × 10^27 | 69,911,000 | 24.79 |
Source: NASA Planetary Fact Sheet (2024).
Frequently asked questions
What is the gravitational constant G?
The gravitational constant G = 6.67430 x 10^-11 N m^2 kg^-2 is one of the fundamental constants of nature. It sets the absolute strength of gravitational attraction between any two masses. G was first measured by Henry Cavendish in 1798 using a torsion balance experiment and remains one of the least precisely known fundamental constants, with a relative standard uncertainty of about 22 parts per million in the 2018 CODATA values.
What is the inverse-square law?
Newton's law of gravitation states that gravitational force is inversely proportional to the square of the distance between the centres of mass: F = G m1 m2 / r^2. Doubling the distance reduces the force to one quarter. Tripling the distance reduces it to one ninth. This inverse-square relationship also applies to light intensity, electric force (Coulomb's law), and any other quantity radiating uniformly from a point source into three-dimensional space.
Why does gravity weaken so rapidly with distance?
Gravity weakens with the square of distance because gravitational influence spreads outward over the surface of an ever-expanding sphere. The surface area of a sphere grows as 4 pi r^2, so the force per unit area (and the force on a test object) falls as 1/r^2. The same geometric argument applies to any radiated field in three-dimensional space. This is why even the enormous gravity of the Sun has a small effect on spacecraft very far from it.
Why do astronauts feel weightless in orbit?
Astronauts on the International Space Station are not beyond Earth's gravity: at orbital altitude (~400 km) g is still about 8.7 m/s^2, roughly 89% of surface value. They feel weightless because the station and everyone inside it are in free fall together toward Earth. The station's horizontal velocity is high enough that Earth's surface curves away as fast as the station falls, creating a perpetual orbit. Weightlessness is the sensation of being in free fall, not the absence of gravity.
How does surface gravity differ across planets?
Surface gravity g = G M / R^2 depends on a planet's mass M and radius R. Mars has only about 38% of Earth's surface gravity (3.72 m/s^2) because although it is less massive, its lower density and smaller radius together produce a weaker surface pull. Jupiter has 2.53 times Earth's surface gravity (24.79 m/s^2) due to its enormous mass. The Moon's surface gravity is about 16% of Earth's (1.62 m/s^2), which is why astronauts could leap so dramatically during Apollo missions.