Gravitational Time Dilation Calculator
Calculate how gravity affects the passage of time according to Einstein's General Relativity
Calculate Gravitational Time Dilation
Time interval to be affected by gravitational time dilation
Gravitational Object
Time Dilation Results
Formula: Δt' = Δt / √(1 - 2GM/rc²)
Time interval (no gravity): 0.000000 seconds
Gravitational potential: 0.000e+0 J/kg
Distance from center: 0.000e+0 km
Relativistic Analysis
Real-World Examples
GPS Satellites
38 microseconds/day faster due to reduced gravity
At ~20,000 km altitude
Sun's Surface
67 seconds/year slower than Earth
Due to Sun's strong gravity
Black Holes
Extreme time dilation near event horizon
Time nearly stops at Schwarzschild radius
Physical Constants
Understanding Gravitational Time Dilation
What is Gravitational Time Dilation?
Gravitational time dilation is a phenomenon predicted by Einstein's General Theory of Relativity, where time passes more slowly in stronger gravitational fields. The closer you are to a massive object, the slower time moves relative to an observer in a weaker gravitational field.
Physical Mechanism
- •Gravity curves spacetime, affecting the flow of time
- •Clocks run slower in gravitational wells
- •Effect becomes extreme near black holes
- •Essential for GPS satellite accuracy
Mathematical Formula
Δt' = Δt / √(1 - 2GM/rc²)
Δt' = Δt / √(1 - rs/r)
- Δt': Time interval affected by gravity
- Δt: Time interval in flat spacetime
- G: Gravitational constant
- M: Mass of gravitating object
- r: Distance from object's center
- c: Speed of light
- rs: Schwarzschild radius (2GM/c²)
Note: As r approaches the Schwarzschild radius, time dilation approaches infinity.
Applications and Examples
GPS Technology
GPS satellites experience less gravitational time dilation than receivers on Earth, causing their clocks to run faster by about 38 microseconds per day.
Without correction, GPS would be off by several kilometers per day.
Atomic Clocks
Ultra-precise atomic clocks can measure time dilation effects from elevation differences of just one meter on Earth's surface.
This has been verified in laboratory experiments.
Astrophysical Objects
Near neutron stars and black holes, time dilation becomes extreme. At a black hole's event horizon, time appears to stop for distant observers.
This affects observations of matter falling into black holes.