Newton's Law of Universal Gravitation Calculator
Newton's Law of Universal Gravitation states that every point mass attracts every other point mass with a force proportional to the product of their masses and inversely proportional to the square of their center-to-center separation r.
Mutual attractive force in Newtons
Mass of first body in kilograms
Mass of second body in kilograms
Separation radius between centers of mass in meters
Step-by-Step Calculation
Newton's Law of Universal Gravitation states that every point mass attracts every other point mass with a force proportional to the product of their masses and inversely proportional to the square of their center-to-center separation r.
Real-World Reference Values
CODATA universal constant of gravitation
At mean orbital separation r = 384,400 km
Doubling separation r reduces gravity by 75%
20-Row Comparison Table
Gravitational Force (F) · Primary Mass (m₁)
| # | Primary Mass (kg) | Gravitational Force (N) | Δ % |
|---|---|---|---|
| 01 | 1.0000e+9 kgCurrent | 0.66743 N | 0.00% |
| 02 | 7.2368e+27 kg | 4.8301e+18 N | +723684210526315872256.00% |
| 03 | 1.4474e+28 kg | 9.6602e+18 N | +1.4473684210526317e+21% |
| 04 | 2.1711e+28 kg | 1.4490e+19 N | +2.1710526315789476e+21% |
| 05 | 2.8947e+28 kg | 1.9320e+19 N | +2.8947368421052635e+21% |
| 06 | 3.6184e+28 kg | 2.4150e+19 N | +3.61842105263158e+21% |
| 07 | 4.3421e+28 kg | 2.8981e+19 N | +4.342105263157895e+21% |
| 08 | 5.0658e+28 kg | 3.3811e+19 N | +5.065789473684211e+21% |
| 09 | 5.7895e+28 kg | 3.8641e+19 N | +5.789473684210527e+21% |
| 10 | 6.5132e+28 kg | 4.3471e+19 N | +6.513157894736842e+21% |
| 11 | 7.2368e+28 kg | 4.8301e+19 N | +7.23684210526316e+21% |
| 12 | 7.9605e+28 kg | 5.3131e+19 N | +7.960526315789475e+21% |
| 13 | 8.6842e+28 kg | 5.7961e+19 N | +8.68421052631579e+21% |
| 14 | 9.4079e+28 kg | 6.2791e+19 N | +9.407894736842106e+21% |
| 15 | 1.0132e+29 kg | 6.7621e+19 N | +1.0131578947368422e+22% |
| 16 | 1.0855e+29 kg | 7.2451e+19 N | +1.085526315789474e+22% |
| 17 | 1.1579e+29 kg | 7.7281e+19 N | +1.1578947368421054e+22% |
| 18 | 1.2303e+29 kg | 8.2111e+19 N | +1.2302631578947369e+22% |
| 19 | 1.3026e+29 kg | 8.6942e+19 N | +1.3026315789473684e+22% |
| 20 | 1.3750e+29 kg | 9.1772e+19 N | +1.375e+22% |
Frequently Asked Questions
What value of G is used by this calculator?+
The solver uses the CODATA recommended value G = 6.67430 × 10⁻¹¹ m³·kg⁻¹·s⁻².
Why is r measured from the center of mass rather than the surface?+
By Newton's Shell Theorem, a spherically symmetric body attracts external objects as if all its mass were concentrated at its geometric center.
How do I solve for orbital distance r given a known gravitational force?+
Click SOLVE FOR on r to evaluate r = √((G × m₁ × m₂) / F).