Gravitational Time Dilation Calculator
Calculate gravitational time dilation near a massive body: t_far = t_near / sqrt(1 - 2GM/(rc^2)).
kg
m
s
Time at Infinity
1.000000000696042 s
Extra Time per Second (ns)0.6960 ns
Time at Infinity vs Proper Time (at surface)
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.
Exemple Résolu
On Earth's surface (M = 5.972e24 kg, r = 6.371e6 m).
- 012GM/(rc^2) = 2 * 6.674e-11 * 5.972e24 / (6.371e6 * 8.988e16)
- 02= 7.972e14 / 5.726e23 = 1.392e-9
- 03sqrt(1 - 1.392e-9) = 1 - 6.96e-10
- 04t_far = 1 / (1 - 6.96e-10) = 1 + 6.96e-10 s
- 05Difference: 0.696 ns per second