Gravitational Time Dilation: A 2D Simulation

The physical parameters in this simulation are scaled to enhance the time dilation effect.

What is Gravitational Time Dilation?

According to Albert Einstein's Theory of General Relativity, **gravity warps spacetime**. A massive object, like a black hole, creates a strong gravitational field that causes time to pass more slowly for objects nearby than it does for objects far away. This is the phenomenon of **gravitational time dilation**.

A classic example of this is the movie *Interstellar*. In the film, Cooper and Brand visit **Miller's Planet**, which orbits extremely close to a massive black hole named **Gargantua**. Dr. Romilly stays on the **Endurance** spaceship, far from the black hole's intense gravity. When Cooper and Brand return after spending just a few hours on the planet, they discover that 23 years have passed for Romilly.

This simulation allows you to recreate and understand this exact phenomenon. The **Endurance** (blue dot) is in a weak gravitational field and its clock runs normally. **Miller's Planet** (red dot) is in a strong gravitational field, so its clock runs slower. You can observe this by comparing their clock displays and the rotation of their clock hands.

The Key Formula

The relationship between time in a strong gravitational field and a weak one is given by the formula for time dilation in a static gravitational field:

$$ \Delta t_{near} = \Delta t_{far} \sqrt{1 - \frac{R_s}{r}} $$

Drag the slider to move **Miller's Planet** closer to the black hole. You will see its clock run slower, just like in the movie!

Endurance Clock: 0.00 sec
Miller's Planet Clock: 0.00 sec