Gravitational Time Dilation Calculator — Formule
## Gravitational Time Dilation
General relativity predicts that clocks run slower in stronger gravitational fields.
### Formula
**t_far = t_near / sqrt(1 - 2GM / (rc^2))**
where the Schwarzschild factor 2GM/(rc^2) is the ratio of the Schwarzschild radius to r.
On Earth's surface, clocks run about 0.7 nanoseconds per second slower than clocks far from any gravity.
General relativity predicts that clocks run slower in stronger gravitational fields.
### Formula
**t_far = t_near / sqrt(1 - 2GM / (rc^2))**
where the Schwarzschild factor 2GM/(rc^2) is the ratio of the Schwarzschild radius to r.
On Earth's surface, clocks run about 0.7 nanoseconds per second slower than clocks far from any gravity.
Exemple Résolu
On Earth's surface (M = 5.972e24 kg, r = 6.371e6 m).
- 2GM/(rc^2) = 2 * 6.674e-11 * 5.972e24 / (6.371e6 * 8.988e16)
- = 7.972e14 / 5.726e23 = 1.392e-9
- sqrt(1 - 1.392e-9) = 1 - 6.96e-10
- t_far = 1 / (1 - 6.96e-10) = 1 + 6.96e-10 s
- Difference: 0.696 ns per second