Gravitational Time Dilation RechnerFormel

## 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.

Lösungsbeispiel

On Earth's surface (M = 5.972e24 kg, r = 6.371e6 m).

  1. 2GM/(rc^2) = 2 * 6.674e-11 * 5.972e24 / (6.371e6 * 8.988e16)
  2. = 7.972e14 / 5.726e23 = 1.392e-9
  3. sqrt(1 - 1.392e-9) = 1 - 6.96e-10
  4. t_far = 1 / (1 - 6.96e-10) = 1 + 6.96e-10 s
  5. Difference: 0.696 ns per second