How Much Time Has Passed on Miller's Planet?

Why one hour on Miller's Planet equals seven years on Earth

Miller's Planet orbits Gargantua, a fictional supermassive black hole with about 100 million times the mass of the Sun. The orbit sits just outside the innermost stable circular orbit, which is the closest an object can circle a black hole and still hold a stable path.

General relativity predicts that clocks deeper in a gravitational field run slower than clocks farther out. On Earth the difference is far too small to notice. Near Gargantua it is severe. Time on the surface of Miller's Planet passes roughly 61,000 times slower than it does for a distant observer. Seven Earth years works out to 61,362 hours, which is where the film's one-hour-to-seven-years ratio comes from.

The physics behind the ratio

Kip Thorne, a theoretical physicist at Caltech, served as executive producer and worked out the orbital mechanics. He set a rule for the production early on: nothing in the film would violate established physical law, and anything speculative had to follow from real science.

That ratio put a hard constraint on Gargantua. For a planet to orbit close enough without being torn apart or pulled in, the black hole has to spin at almost the maximum rate general relativity permits. Thorne calculated it needs to fall within roughly one part in 100 trillion of that limit. He describes the full derivation in his book The Science of Interstellar, and published the related work on rendering the black hole with the film's visual effects team in Classical and Quantum Gravity in 2015. Thorne shared the 2017 Nobel Prize in Physics for the first direct detection of gravitational waves.

What the trip to the surface cost the crew

Cooper, Brand, and Doyle spend a little over three hours on the planet. Doyle dies there, and the Ranger takes on enough water that the engines have to drain before it can lift off. By the time they dock with the Endurance again, Romilly has been waiting 23 years, 4 months, and 8 days.

Cooper then sits down and watches more than two decades of video messages from his children in one stretch. His daughter Murph is close to the age he was when he left Earth.

Why the waves are so large

The planet is tidally locked to Gargantua, so the same side always faces the black hole. Gravity pulls harder on the near side than the far side, stretching the planet along one axis and compressing it along another. The planet also rocks slightly instead of holding perfectly still, and that motion drives the deformation back and forth.

The shallow ocean covering the surface responds by piling up into two standing tidal bulges around 1.2 kilometres high. The crew reads them as mountains on the horizon until one of them starts moving.

Gravitational time dilation outside the movie

The same effect turns up in ordinary technology. GPS satellites orbit about 20,200 kilometres up, where Earth's gravity is weaker, so their onboard clocks gain roughly 45 microseconds per day relative to clocks on the ground. Their orbital speed works in the opposite direction and costs them about 7 microseconds per day, leaving a net gain near 38 microseconds. Without corrections for both effects, GPS positions would drift by about 10 kilometres every day.

How this counter works

Both clocks measure real elapsed time since Interstellar's wide US release on November 7, 2014 at 00:00 UTC. The Earth column reports that figure directly. The Miller's Planet column divides it by 61,362, the number of hours in seven Earth years at 365.25 days per year.

This uses the round ratio stated in the film rather than a full relativistic calculation from Gargantua's mass and spin. The two agree to within about one percent.

The page was built by Tiempo Software. It is a single static HTML file with no backend, so both clocks run entirely in your browser and read from your own system time.

Sources and further reading

• Interstellar (film) Wikipedia. Release dates, plot, and production background.
• The Science of Interstellar Wikipedia. Kip Thorne's 2014 book explaining the film's physics, including Gargantua and Miller's Planet.
• Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar James, von Tunzelmann, Franklin & Thorne, Classical and Quantum Gravity 32, 065001 (2015). Published version.
• Gravitational time dilation Wikipedia. The underlying prediction of general relativity.
• Innermost stable circular orbit Wikipedia. Why the planet's orbit has to sit where it does.
• Tidal locking Wikipedia. Background on the mechanism driving the waves.
• Real-World Relativity: The GPS Navigation System Richard W. Pogge, Ohio State University. Source of the 45, 7, and 38 microsecond figures.
• Kip S. Thorne Caltech faculty profile. See also his 2017 Nobel Prize in Physics and Wikipedia entry.
• Interstellar (2014) IMDb. Cast, crew, and release information.

Interstellar (2014) was directed by Christopher Nolan, with Kip Thorne as executive producer and science advisor. This site is an unofficial fan project and is not affiliated with the film, Paramount Pictures, Warner Bros., or Legendary Pictures.