Miller's Planet Time Dilation: Could 1 Hour Really Equal 7 Years?
In Interstellar, the crew of the Endurance land on a water world orbiting the black hole Gargantua, knowing that every hour they spend there will cost seven years back on Earth. They are delayed by a giant wave, and when Cooper and Brand return to the ship, Romilly has waited more than 23 years. It is one of the most memorable ideas in the film. But is it physics, or just a good story? The surprising answer is that it can work, but only under very specific conditions.
How much time dilation is that?
Seven years is about 61,000 hours, so on Miller's planet clocks must run about 61,000 times slower than clocks on Earth. For comparison, time on Earth's surface runs slower than in deep space by less than one part in a billion, about 60 microseconds per day. Miller's planet needs an effect around a hundred trillion times stronger.
Only a black hole can slow time that much. Gravity slows clocks (this is gravitational time dilation), and so does fast motion. A planet orbiting very close to a black hole gets both at once.
Why a non-spinning black hole can't do it
Start with the simplest kind of black hole, a non-spinning (Schwarzschild) one. Planets cannot orbit just anywhere around it. The closest stable circular orbit is at three times the Schwarzschild radius. Any closer and the orbit is unstable: the slightest nudge sends the planet spiralling in or flying out.
At that innermost stable orbit, clocks run only 1.41 times slower than far away. That is the limit, and it is the same for every non-spinning black hole, however heavy. One hour on the planet would cost about 1.4 hours on Earth, nowhere near seven years.
Could you hover instead?
A clock that hovers at a fixed height, rather than orbiting, can get as much time dilation as you like by going close enough to the horizon. To reach a factor of 61,000 next to a black hole as heavy as Gargantua, you would need to hover about 80 metres above an event horizon that is roughly 300 million km in radius.
Holding that position would take a constant acceleration of nearly a billion g. No planet, ship or person could do it. Miller's planet has to be in orbit, which brings us back to the problem above.
How Gargantua's spin makes it possible
Real black holes spin, and a spinning (Kerr) black hole drags the space around it into a whirl. Kip Thorne, the physicist behind the film's science, explains in The Science of Interstellar that this whirling motion stabilises orbits much closer to the horizon. The faster the spin, the closer the innermost stable orbit gets, and the stronger the time dilation.
To get 1 hour = 7 years, Thorne found that Gargantua must spin within about one part in 100 trillion of the maximum spin a black hole can have, with Miller's planet on the innermost stable orbit. That is an extreme value, but it is allowed by general relativity.
Check the numbers yourself
We built a black hole time dilation calculator with a Miller's planet preset. It uses the standard formula for circular orbits around a Kerr black hole (Bardeen, Press & Teukolsky, 1972). With a spin of 0.999 999 999 999 987 (1.3 parts in 100 trillion below the maximum), it gives:
- Time dilation factor: about 61,900, so 1 hour on the planet ≈ 7.06 years on Earth.
- The 23 years Romilly waits correspond to about 3.3 hours on the planet, which matches the film.
- For a black hole of 100 million Suns, the planet orbits about 150 million km from the centre and goes round once every 1.7 hours, as seen from far away.
Try changing the spin. At 0.9 the factor drops to about 2.7; at 0.998, a common estimate for the fastest spins real black holes reach, it is only about 11. The film's number depends on that extreme spin.
Why Gargantua has to be so heavy
Thorne gives Gargantua a mass of about 100 million Suns. Mass doesn't change the time dilation (that depends only on spin and on how many horizon-radii away you are), but it does change the tides. At the same relative distance, tidal forces get weaker as the black hole gets heavier, falling as one over the mass squared. A lighter Gargantua would stretch Miller's planet apart.
Even so, the tides are strong. In his book, Thorne suggests the huge waves the crew meet could come from the planet rocking back and forth under Gargantua's tidal pull.
What the film skips
- How Gargantua looks. The film's images of Gargantua were rendered with a much slower spin, for clarity. See Gargantua explained.
- Blueshifted light. Time dilation works both ways: light falling in from the rest of the universe arrives with its frequency boosted, strongly in some directions. The faint cosmic microwave background would be shifted towards much more energetic light.
- Getting there. Reaching an orbit that close and leaving again takes enormous changes in speed, far more than the film's quick trips in the Ranger suggest.
FAQ
- Is the 1 hour = 7 years ratio scientifically possible? In principle, yes, for a planet on the innermost stable orbit of a black hole spinning within about one part in 100 trillion of the maximum rate. Real black holes are not thought to spin quite that fast.
- Would the astronauts feel time passing slowly? No. Their watches, heartbeats and thoughts all run normally. The difference only appears when they compare clocks with Romilly and with Earth.
- Why did Romilly age 23 years when the others barely aged? He stayed on the Endurance, parked far enough from Gargantua that its time dilation was small. His clock kept pace with Earth's, which is why the messages from home waiting on board cover the same 23 years.
- Could you use this to go back in time? No. Time dilation only lets you age less than others, which is a one-way trip to the future. See wormholes and time travel.
Try a simulation or calculator
- Black hole image simulation — upload an image and see gravitational lensing
- Black hole embedding diagram — visualize curvature as an embedded surface
- Wormhole embedding diagram — explore throat geometry parameters
- Black hole calculators: Schwarzschild radius and time dilation (including Miller’s planet)
- Gallery: ray-traced black holes and wormholes
- Browse all articles