Orbital Velocity Calculator
Calculate circular orbital velocity, period, and escape velocity for any altitude around Earth, Mars, Moon, Jupiter, Sun, or a custom body. Includes orbit types reference.
Gravitational Force Calculator
Calculate gravitational force between two masses using Newton's law of universal gravitation F = Gm₁m₂/r². Includes escape velocity, orbital speed, and potential energy.
kg
kg
m
Gravitational Force⧉
1.9805e+20 N
F = Gm₁m₂ / r²
Acceleration of m₁⧉
3.3163e-5 m/s²
Due to m₂
Acceleration of m₂⧉
0.0027 m/s²
Due to m₁
Gravitational PE⧉
-7.6130e+28 J
U = −Gm₁m₂ / r
Escape Velocity (from m₂)⧉
159.6737 m/s
v = √(2GM/r)
Orbital Velocity⧉
1,024.5294 m/s
Circular orbit at this distance
Force Magnitude (Log Scale)
1.9805e+20 N
Celestial Body Reference
| Body | Mass | Radius | Surface g |
|---|---|---|---|
| Sun | 1.989 × 10³⁰ kg | 6.96 × 10⁸ m | 274 m/s² |
| Earth | 5.972 × 10²⁴ kg | 6.371 × 10⁶ m | 9.81 m/s² |
| Moon | 7.342 × 10²² kg | 1.737 × 10⁶ m | 1.62 m/s² |
| Mars | 6.417 × 10²³ kg | 3.390 × 10⁶ m | 3.72 m/s² |
| Jupiter | 1.898 × 10²⁷ kg | 6.991 × 10⁷ m | 24.79 m/s² |
| Saturn | 5.683 × 10²⁶ kg | 5.823 × 10⁷ m | 10.44 m/s² |
Planning notes, formulas, and examples
About the Gravitational Force Calculator
Newton's Law of Universal Gravitation states that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula F = Gm₁m₂/r² — where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²) — is one of the most important equations in physics.
This Gravitational Force Calculator lets you enter any two masses and the distance between them to compute the gravitational attraction. It also derives related quantities: the acceleration each mass experiences due to the other, the gravitational potential energy of the system, escape velocity, and circular-orbit velocity at that distance.
Use the celestial presets to explore common gravitational cases such as Earth–Moon, Earth–Sun, or two ordinary objects on a desk. The reference table includes mass and radius data for major solar-system bodies so you can model surface gravity, orbital distance, or escape speed without looking up every constant manually.
When This Page Helps
Computing gravitational forces by hand requires handling very large or very small numbers in scientific notation, which is error-prone. This calculator accepts scientific notation inputs, performs the inverse-square calculation automatically, and shows related values like potential energy and escape velocity without extra steps.
How to Use the Inputs
- Enter Mass 1 (m₁) in kilograms. Scientific notation like 5.972e24 is accepted.
- Enter Mass 2 (m₂) in kilograms.
- Enter the distance between the centers of the two masses.
- Select the distance unit: meters, kilometers, or astronomical units (AU).
- Read the gravitational force, accelerations, potential energy, escape and orbital velocities.
- Use the preset buttons to load famous celestial pairs.
- Consult the celestial reference table for mass and radius data of solar-system bodies.
Formula used
Newton's Law of Universal Gravitation:
F = G × m₁ × m₂ / r²
Gravitational Potential Energy:
U = −G × m₁ × m₂ / r
Escape Velocity:
v_esc = √(2GM / r)
Circular Orbital Velocity:
v_orb = √(G(m₁+m₂) / r)
Where:
G = 6.674 × 10⁻¹¹ N·m²/kg²
m₁, m₂ = masses (kg)
r = center-to-center distance (m)Example Calculation
Result: 1.982 × 10²⁰ N
The gravitational force between the Earth (5.972 × 10²⁴ kg) and the Moon (7.342 × 10²² kg) at a distance of 384,400 km is approximately 1.98 × 10²⁰ newtons.
Tips & Best Practices
- Use scientific notation (e.g. 5.972e24) for very large or small masses.
- The distance must be center-to-center, not surface-to-surface.
- For surface gravity, set the distance equal to the body's radius.
- Compare your results against the celestial reference table to verify reasonableness.
- Gravitational PE is always negative; it approaches zero as distance approaches infinity.
Newton's Universal Gravitation
Published in 1687 in the Principia Mathematica, Newton's law of universal gravitation unified terrestrial and celestial mechanics for the first time. The same force that causes an apple to fall also keeps the Moon in orbit. The gravitational constant G was not measured until over a century later by Cavendish, confirming the quantitative prediction.
Applications in Astronomy and Engineering
Gravitational calculations are essential for orbital mechanics (satellite trajectories, interplanetary missions), tidal predictions (the Moon and Sun's pull on Earth's oceans), geodesy (measuring Earth's gravitational field variations), and astrophysics (binary star systems, galaxy dynamics). The James Webb Space Telescope orbits at the L2 Lagrange point, a gravitational equilibrium position calculated using these principles.
From Newton to Einstein
Newton's gravity is an excellent approximation for most practical purposes. Einstein's General Relativity, published in 1915, describes gravity as curvature of spacetime and is needed for extreme conditions: strong fields (near black holes), high speeds, or precision requirements (GPS satellites require relativistic corrections).
Sources & Methodology
Last updated:
Frequently Asked Questions
G = 6.674 × 10⁻¹¹ N·m²/kg² (SI). It sets the scale of gravitational attraction in Newton's law.
G is an extremely small number. Two 1 kg masses 1 meter apart attract each other with a force of only 6.67 × 10⁻¹¹ N — far below human perception. Gravity only becomes significant when at least one mass is astronomical (planets, stars).
Newton's formula works well for most everyday and astronomical cases. Very strong gravitational fields or extremely high speeds require general relativity.
1 AU ≈ 1.496 × 10¹¹ meters, the average Earth–Sun distance. It is convenient for expressing distances within the solar system.
Force tells you the instantaneous pull between two masses. Gravitational potential energy tells you how much work is needed to separate them to infinity.
Yes. Set one mass to a 1 kg test object and the distance to the body's radius; the resulting force per kilogram gives surface gravity.
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