Gravitational Force Calculator

How to use this calculator

1. Enter Mass 1 and Mass 2 in kilograms. For planetary bodies, you can use known values (for example, Earth ≈ 5.972e24 kg, Moon ≈ 7.35e22 kg).
2. Enter the distance between the centers of the two masses in meters. For surface-level problems, this is roughly the planet’s radius; for orbits, it is radius + altitude.
3. We apply F = G × m₁ × m₂ ÷ r² using G ≈ 6.674 × 10⁻¹¹ N·m²/kg².
4. Review the gravitational force output in newtons and compare it to familiar forces like weight (mg) on Earth’s surface.
5. Optionally, adjust masses or distance to see how the gravitational pull changes with different configurations or on different celestial bodies.

Inputs explained

Mass 1 (kg)

The first object’s mass in kilograms. This might be a planet, moon, star, spacecraft, or any other body. For example, Earth ≈ 5.972e24 kg, the Moon ≈ 7.35e22 kg.

Mass 2 (kg)

The second object’s mass in kilograms. This could be an astronaut, satellite, spacecraft, or another celestial body.

Distance between centers (m)

The center-to-center distance between the two masses in meters. For surface problems, use the planet’s radius (plus altitude). For orbiting objects, use the orbital radius (planet radius + altitude).

When to use it

• Estimating gravitational attraction between planets, moons, and spacecraft in astronomy or orbital mechanics problems.
• Checking physics homework exercises on Newton’s law of gravitation and comparing results to mg near Earth’s surface.
• Comparing how much lighter or heavier an object would feel on other planets or moons by changing planetary mass and radius.
• Building intuition about how mass and distance influence gravitational pull in different scenarios, from lab experiments to astrophysics.

Tips & cautions

• Always use center-to-center distance between bodies, not surface-to-surface distance, for accurate application of F = Gm₁m₂/r².
• For near-surface weight, the gravitational force should match mg (mass × local gravitational acceleration). Use radius and mass of Earth or another planet to cross-check this relationship.
• Keep all units in SI (kg for mass, meters for distance) to avoid errors; convert miles, kilometers, or pounds before entering.
• When comparing different worlds, remember that surface gravity g ≈ G × M ÷ R², where M is planet mass and R its radius; you can use this to check your gravity-force results.
• Assumes point masses or perfect spheres with uniform density; real bodies with irregular shapes or mass distributions can deviate from this simple model.
• Ignores relativistic effects, tidal forces, and perturbations from other nearby masses; those can be significant in some astrophysical contexts.
• Assumes a vacuum and static configuration; it does not compute orbital trajectories, time evolution, or gravitational potential energy explicitly.
• Accuracy suffers if you mix units or use approximate constants inconsistently; stick to SI units and the given G value for best results.

Worked examples

Deep dive

FAQs

Does this calculator handle non-spherical or extended bodies?

It assumes point masses or spherically symmetric bodies. Irregular shapes and non-uniform density distributions require more advanced methods (integration or numerical gravity models).

Can I use this for orbital design or trajectory planning?

You can use it to estimate gravitational forces at particular distances, but full orbital design needs time-dependent simulations, multiple bodies, and often perturbation analysis. Treat this as a first-order check only.

How is this related to weight (mg)?

Near a planet’s surface, the gravitational force F from the planet on an object is what we call the object’s weight. If you solve F = Gm₁m₂/r² for g = F/m₂, you recover g ≈ GM/r², which is the familiar surface gravity formula.

Do relativistic effects matter here?

Not in this tool. For most everyday and many astronomical problems, Newtonian gravity is sufficient. For extremely strong fields or very high precision (like near black holes or in GPS satellite calculations), general relativity becomes important.

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