Calculadora de Dilatación Temporal GravitatoriaFórmula

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.

Ejemplo Resuelto

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