Calculadora de Dilatação Temporal Gravitacional
Calcule como a gravidade afeta a passagem do tempo usando a relatividade geral. Determine a diferença temporal perto de corpos massivos.
Time at Infinity
1.000000000696042 s
Time at Infinity vs Proper Time (at surface)
Formula
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.
Exemplo Resolvido
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
Perguntas Frequentes
How does this affect GPS?
GPS satellite clocks are in weaker gravity and run about 45 microseconds per day faster. Without correction, GPS positions would drift by about 10 km per day.
What happens at a black hole?
As r approaches the Schwarzschild radius (2GM/c^2), the time dilation becomes infinite. Time appears to stop at the event horizon as seen from outside.
Has gravitational time dilation been measured?
Yes. The Pound-Rebka experiment (1959) measured the gravitational redshift over just 22.5 metres. Modern atomic clocks can detect differences over a height of 1 metre.
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