Gravitational Force
Calculator
Results
- Gravitational force (N)
- 198,158,526,155,465,600,000
- Force exponent (log₁₀ N)
- 20.297012
Astronomy results
| Gravitational force (N) | 198,158,526,155,465,600,000 |
| Force exponent (log₁₀ N) | 20.297012 |
formula-map diagram
- Gravitational force (N)
- 198,158,526,155,465,600,000
- Force exponent (log₁₀ N)
- 20.297012
Astronomical relationship
Formula
F = G × m₁ × m₂ / r²= 1.9815852615547E+20
Note
This result is a simplified model: it applies the displayed textbook formula to the values you entered, assuming ideal spherical bodies, circular orbits, blackbody radiation and perfect optics, and ignoring atmospheric seeing, relativistic corrections beyond those stated, cosmological models and measurement uncertainty. Use published ephemerides and catalogue data for real observations.
More in Astronomy and space
See all →Frequently asked questions
What does Newton's law of universal gravitation calculate here?+
It calculates the attractive force between two masses using F = G(m₁m₂)/r², where G is the gravitational constant, m₁ and m₂ are the two masses, and r is the distance between their centers. The result is a force, in newtons, pulling each mass toward the other.
Why does doubling the distance between two masses reduce the force to a quarter?+
Gravity follows an inverse-square law, meaning force is proportional to 1/r². Doubling r therefore divides the force by 2² = 4, not by 2, which is why gravity weakens sharply with distance.
Why is gravitational force between everyday objects so small?+
The gravitational constant G is extremely tiny (about 6.674×10⁻¹¹ N·m²/kg²), so unless at least one mass is planet-sized, the resulting force is imperceptible. This is why we notice Earth's pull on us but never feel the pull of nearby furniture.
What distance value should I use if the objects are large, like planets?+
Use the distance between the centers of mass of the two objects, not the distance between their surfaces. For spherical bodies like planets, this is measured center-to-center, which is why planetary radius matters even when they're 'touching.'
Is this the same force responsible for keeping planets in orbit?+
Yes, this is the exact same gravitational force law that keeps planets orbiting the Sun and moons orbiting planets. Orbital velocity and orbital period calculations are both derived from this same force balanced against the required centripetal force.