Gravitational Potential Calculator
Calculate gravitational potential using V = −GM/r and potential energy U = mV.
What Is Gravitational Potential Calculator?
This calculator implements Calculate gravitational potential using V = −GM/r and potential energy U = mV. — a core relationship in physics.
The formula follows from fundamental principles and applies across a wide range of physical scenarios.
Pay attention to units and sign conventions when using these calculations in practice.
Results are valid within the stated assumptions; real systems may deviate at extremes.
Formula Reference Table
| Solve For | Formula | Notes |
|---|---|---|
| Gravitational potential | V = −GM/r | J/kg; always negative |
| PE of mass m | U = mV = −GMm/r | J |
| Escape from surface | v_esc = √(2GM/R) = √(−2V_surface) | m/s |
| Potential difference | ΔV = GM(1/r₁ − 1/r₂) | J/kg |
| Orbital KE | KE = −U/2 = GMm/(2r) | Virial theorem |
| G | G = 6.674×10⁻¹¹ N·m²/kg² |
3 Worked Examples
M_E = 5.972×10²⁴ kg, R_E = 6.371×10⁶ m.
- V = −GM/r = −6.674×10⁻¹¹×5.972×10²⁴/6.371×10⁶
- V = −6.253×10⁷ J/kg
- Escape speed: v = √(−2V) = √(1.251×10⁸) = 11,186 m/s
100 kg satellite at r = 6.771×10⁶ m.
- V = −GM/r = −5.897×10⁷ J/kg
- U = mV = 100×(−5.897×10⁷) = −5.897×10⁹ J = −5.9 GJ
V = −2×10⁷ J/kg near Earth (M=5.972×10²⁴).
- r = −GM/V = 6.674×10⁻¹¹×5.972×10²⁴/2×10⁷
- r = 3.985×10¹⁴/2×10⁷ = 1.99×10⁷ m ≈ 3.13 Earth radii
Real-World Applications
Common Mistakes to Avoid
SI units.
Correct variant.
Ideal conditions.
Check conventions.
Check squaring.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This relationship connects mass, distance, orbit or spacetime behavior through gravitation and astrophysical scaling. Assumption: Many calculations assume spherical bodies, point masses, circular orbits, weak fields or Newtonian gravity; relativistic regimes require the stated correction.