# Thought question (Interstellar movie example)

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## Main Question or Discussion Point

In the movie Interstellar we see a planet close to the event horizon so when the astronauts land and get stuck on the planet for over an hour, many years passes for the guy on the spaceship and when they return he is an old man.
From what I understand, this is indeed what would happen and they consulted with scientists. Correct me if I am wrong.
My question is this. If the guy on the spaceship were to shine a very bright light towards a dark area of the surface of the planet for 30 seconds, being that time is moving much more slowly on the planet, would the light reflect back to him for much longer than he has it on?
Thanks,
Ben

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Orodruin
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If the guy on the spaceship were to shine a very bright light towards a dark area of the surface of the planet for 30 seconds, being that time is moving much more slowly on the planet, would the light reflect back to him for much longer than he has it on?
No.

Ibix
If the guy on the spaceship were to shine a very bright light towards a dark area of the surface of the planet for 30 seconds, being that time is moving much more slowly on the planet, would the light reflect back to
No. However observers on the planet would see a very dim glow for a very long time. Edit: wrong - see below.

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PeroK
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In the movie Interstellar we see a planet close to the event horizon so when the astronauts land and get stuck on the planet for over an hour, many years passes for the guy on the spaceship and when they return he is an old man.
From what I understand, this is indeed what would happen and they consulted with scientists. Correct me if I am wrong.
My question is this. If the guy on the spaceship were to shine a very bright light towards a dark area of the surface of the planet for 30 seconds, being that time is moving much more slowly on the planet, would the light reflect back to him for much longer than he has it on?
Thanks,
Ben
Basically, the round trip for the light from the ship to the planet and back must be a constant (leaving aside any relative motion between the ship and the planet). If the first of the light reflects back to the ship after $T$ seconds, then the last of the light (having taken a near identical path through spacetime) will return after $T + 30$ seconds.

I haven't seen the film, but I wonder what the orbital period of the planet would be measured on the ship's clock?

Ibix
I haven't seen the film, but I wonder what the orbital period of the
Very very much longer than that measured locally by the astronauts on the planet.

PeroK
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Very very much longer than that measured locally by the astronauts on the planet.
What sort of orbit was the planet in? Did they get greater time dilation from a highly elliptical orbit? I though the smallest stable circluar orbit was at $R = 6M$, where the time dilation factor is only $\sqrt 2$?

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No. However observers on the planet would see a very dim glow for a very long time.
I thought it would be the opposite and they would barely be able to detect the flash of light? If they were somehow able to watch the spaceship from the planet wouldnt they see the man aging very rapidly?
Hence the light would quickly flash?

pervect
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What sort of orbit was the planet in? Did they get greater time dilation from a highly elliptical orbit? I though the smallest stable circluar orbit was at $R = 6M$, where the time dilation factor is only $\sqrt 2$?
No. Kip Thorne used a rapidly roating Kerr black hole - rotating almost as much as is possible (extremal). He gives the detailed calculatoins in a book, which I skimmed once but don't recall the details of.

PAllen
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I don't see that anyone has noted this. The 30 second long pulse (per the rocket) would appear to be a tiny fraction of a second long per a surface observer. The reflected pulse would be similarly short per the surface, and thus 30 seconds as observed on the rocket, on return.

Ibix
Hence the light would quickly flash?
You are correct - I must have been asleep on Tuesday.

Ibix
What sort of orbit was the planet in? Did they get greater time dilation from a highly elliptical orbit? I though the smallest stable circluar orbit was at $R = 6M$, where the time dilation factor is only $\sqrt 2$?
To add to pervect's comment, you are correct for a Schwarzschild black hole, but orbits are different near a rotating black hole. Prograde and retrograde orbits are different, for example. Especially one with almost as much angular momentum as it's possible for it to have.

Orodruin
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I don't see that anyone has noted this. The 30 second long pulse (per the rocket) would appear to be a tiny fraction of a second long per a surface observer. The reflected pulse would be similarly short per the surface, and thus 30 seconds as observed on the rocket, on return.
... and likewise also blue-shifted ...

No. However observers on the planet would see a very dim glow for a very long time.
They would see a very bright glow for a fraction of a second. (Also, they probably will not actually see it as it is blue-shifted beyond the visible spectrum.)

Ibix
They would see a very bright glow for a fraction of a second. (Also, they probably will not actually see it as it is blue-shifted beyond the visible spectrum.)
Indeed. I think I was asleep on Tuesday. I got the orbital period question right, and failed to notice the contradiction.

PeroK
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Indeed. I think I was asleep on Tuesday. I got the orbital period question right, and failed to notice the contradiction.
It says here (excerpt from Kip Thorne's book) that the planet has an approximately Earth-sized orbit taking one hour, as measured remotely. The time dilation factor is seven years to one hour. An orbit would take about $0.06s$ proper time.

https://www.space.com/28077-science-of-interstellar-book-excerpt.html

... and likewise also blue-shifted ...
If my reasoning is correct, the 1 hour to 7 years blue shifts the cosmic microwave background to about 14.4 eV. I didn't attempt the intensity.