# Is there a great difference in the pace of time on a Earth-like planet orbiting a BH at safe distance and on a ship orbiting this planet?

Another question about the Interstellar movie.

When the crew (or what's left of it) arrived near Miller's planet orbiting Gargantua, a team was sent to the planet to rescue Miller who was sent there to investigate if the planet could be habitable. One particle physicist (?) was left behind in a spacecraft orbiting the planet.

Now the particle scientist (who stayed in the spacecraft orbiting the planet) in the movie explained that if the team stayed a few hours on the planet he himself would have experienced much, much more time gone by (which turned out to be a bit more than 23 years).

But how is this possible? The planet falls freely around the BH (freely falling bodies experience no change in the pace of time because falling bodies experience no gravity so in their frame of reference spacetime isn't curved) and we see that the team experiences a gravity on the planet comparable to that of the Earth.

Which means that the time for the team progresses more or less at the same pace as on Earth (if they would find themselves in a big box, through which one cannot see anything they wouldn't be able to tell if they were staying on Earth or on Miller's planet, supposing the gravity on Miller's planet is the same as on Earth, which seems not too far from the truth). Let's assume (which I think is reasonable) that the progress of time on the part of Miller's planet facing Gargantua is the same as the progress of time on the part of the planet facing the other direction, so we only have to deal with the planet's gravity.

Each member of the team would feel (almost) no difference with walking on Earth, so you would think time progresses for them a bit slower (like on Earth) than for the guy left behind in the spacecraft orbiting the planet. He is freely falling towards Miller's planet and Gargantua and feels no gravity at all which means his pace of time is maximal. He (and the team) may be in an orbit where time goes slower because of the gravity of Gargantua, but this going slower of time is only experienced by objects at rest relative to the BH (think of a rocket staying put at a safe distance from a BH by using a superstrong thrust mechanism).

Wouldn't all this imply that when the team returns to the ship orbiting the planet, the ages of the team members and the particle physicist differ by a VERY SMALL amount, instead of the 23 years difference which the movie wants us to believe? Which is to say that the team members are just a VERY LITTLE bit younger than our particle physicist, instead of 23 years?

Note that I analyzed the problem in the (approximate) inertial frame of the freely falling planet and the freely falling spaceship orbiting Miller's planet.

• It has been some time since I saw the movie, but isn't the spaceship orbiting the black hole (at a further distance than Miller's planet) rather than the planet itself? Nov 7, 2019 at 6:40
• Are you sure they weren't concerned about the time passed on earth? Otherwise I think, as you do, that the one on the orbiter is just a bit older than the others. Nov 7, 2019 at 9:33
• @mmeent-I think you're right! But that wouldn't change the core of my question. Nov 7, 2019 at 13:57
• @Alchimista-They were indeed concerned about the time on earth. But that also is the case for the scientist in the orbiter but he was 23 years older when the rest of the team returned to the orbiter, so why shouldn't he also be 23 older compared to the people on Earth? There is hardly any difference between the man in the orbiter and the team on the planet. So why should they differ so much in age, compared to each other? I even doubt that the team (or the scientist left in the orbiter) becomes 23 years younger than people on Earth during the stay on the planet (orbiter). Nov 7, 2019 at 14:19

## 1 Answer

When you are in freefall in orbit around an object you are still in its gravitational field. If you were not you would just move away from it. Lower orbits have slower time frames because they are deeper in the gravity well, further slowed by higher speed in lower orbits. So a planet orbiting a black hole could have a slower rate of time the closer the orbit, if they were not torn apart by tidal forces. Here is a link to a graph of time dilations for objects orbiting Earth https://en.wikipedia.org/wiki/Gravitational_time_dilation#/media/File:Orbit_times.svg

• But how can, say an astronaut in a capsule out of which he can see nothing, tell the difference between freely orbiting a planet or being in empty space? In both cases he's weightless. Isn't time going slower for an astronaut because of the speed he has to have to maintain the orbit? True, time goes slower the closer you are to a planet. But this slower pace only applies to objects in REST with respect to the planet (like is, for example, the case for a spacecraft near a BH using it's thrust engines to prevent it from falling to the BH; at a safe distance of course). And wouldn't your answer Nov 7, 2019 at 14:37
• imply that the age difference between the man left in the orbiter and the rest of the team would be much smaller than 23 years because he as well as the team are orbiting the BH? The only difference being that the rest of the team walks on an "Earth-like" planet, so the rest of the team can't differ that much in age compared to the age of the scientist in the orbiter? Nov 7, 2019 at 14:42
• @descheleschilder Yes, if he would have orbited the planet close to the bh their time would have been very similar, I believe there was some silliness in the movie about him waiting farther away from the planet and bh. Also gravitational time dilation does not disappear if you are moving in a capsule in orbit, it is figured in with additional time dilation from speed, the blue, center curve in the graph from my link. Nov 7, 2019 at 15:16
• So if we imagine two astronauts in a blinded spaceship: one who makes a large number of orbits around the Earth somewhere on the blue line where there is a net gain in time and one who stays somewhere in outer space (traveling with the same velocity as the guy in the orbiting spacecraft, say with respect to the Sun) while the other performs his orbits. Both don't feel gravity in their ships. So how can it be that whilst they find themselves in the same situation (in a blinded spacecraft without feeling gravity), they differ a tiny amount in age when they meet (by bumping into eachother)? Nov 8, 2019 at 0:07
• Is it because a gravity field can't be homogeneous? So the guy in the orbiting spaceship DOES find himself in a different situation? Nov 8, 2019 at 0:09