Thought-Experiment with illustration - help me understand

[lovenugget]

The setup: You're in a spaceship rocketing around the earth, never breaking orbit. You have a video recorder constantly pointing inward toward the earth, capturing the events. You then begin accelerating to 99% the speed of light. After a few hours at this speed you decelerate to 1% c.

[URL]http://img827.imageshack.us/i/063011125454.jpg/[/URL]

What i want to know is this: What do I see when I play back the recording? Shouldn't i see the Earth rapidly aging due to the effects of time dilation?

I tried to get a solid answer from my physics teacher, but I'm not certain i adequately explained the perameters of the thought-experiment and never received a satisfying answer.

 

[rede96]

The setup: You're in a spaceship rocketing around the earth, never breaking orbit. You have a video recorder constantly pointing inward toward the earth, capturing the events. You then begin accelerating to 99% the speed of light. After a few hours at this speed you decelerate to 1% c.

[URL]http://img827.imageshack.us/i/063011125454.jpg/[/URL]

What i want to know is this: What do I see when I play back the recording? Due to time dilation shouldn't i see the Earth rapidly aging due to the effects of time dilation?

I tried to get a solid answer from my physics teacher, but I'm not certain i adequately explained the perameters of the thought-experiment and never received a satisfying answer.

I think the first problem is that I don't believe that you could orbit the Earth at 99% c. The escape velocity is much less than that so you would propel yourself into space.

However, what you would probably see if you were traveling away from the Earth at 99% is that time would appear to be running faster on earth. So when you playback your video it would seem like you were watching a speeded up version.

What I am not sure about (And I am sure that someone here will set me straight!) is what you would see whilst you accelerated, then traveled at a constant speed and then decelerated.

 

[lovenugget]

I understand that it would be physically impossible to stay in orbit around the Earth at 99% the speed of light... with this being a thought experiment I would like to ignore that fact. remember, the spaceship never leaves the orbit. it just keeps racing around the Earth during the acceleration/deceleration... I'm mainly interested in what i would see as the ship begins to decelerate from 99% c.

 

[JDoolin]

The question relates to what an observer would see on the rim of a great spinning wheel. I know that Misner/Thorne/Wheeler discussed this in section 2.8 of Gravitation, but I've long since sent the great tome back to the library.

I had some thoughts on the idea, myself, including some space-time diagrams, they are posted here: https://www.physicsforums.com/showthread.php?t=432025&page=2 in the thread "Relativistic Bike"

(And Yes, absolutely, you would see the Earth rapidly aging.)

 

[bcrowell]

What i want to know is this: What do I see when I play back the recording? Shouldn't i see the Earth rapidly aging due to the effects of time dilation?

Yes, this is correct.

A real-world experiment of this type (at less extreme speeds): http://en.wikipedia.org/wiki/Hafele-Keating_experiment

An animated simulation: http://www.anu.edu.au/Physics/Searle/ (near the end of the first video)

 

[JDoolin]

Oh, and I managed to get to your image; it's attached in the thumbnail.

One small point to make is, going from 99% of the speed of light to 1% of the speed of light is a trivial matter, when you consider that as you circle, you're going from .99c one way to .99c the other way.

Another point to make is that in the "twin paradox" it is the acceleration of the traveling twin that makes him end up being young while the other is old.

Another point to make is the proper-time on board your space-ship is growing very slowly compared to the Earth frame:

http://en.wikipedia.org/wiki/Proper_time#In_special_relativity

 

[pervect]

You couldn't do an unpowered orbit around the Earth at 99%c, but for the purposes of this experiment, you could do a powered orbit, where your rocketship provides the thrust needed to stay in orbit.

The signals you received from the Earth would be blueshifted, shifted higher in frequency. The resulting pictures would also appear as if they were being played back in a recorder at high speed, once you corrected for the doppler shifting of the frequency.

If the nose of your spaceship was always pointed in the direction of the orbit (somewhat unlikely, but easy to visualize), the Earth would not appear to be at right angles, but somewhat ahead of you. The rest of the stars would be concentrated in a small disk in front of you, similar to this picture:

http://www.exo.net/~pauld/stars/PD_images_relativ.html

This paper also has some black and white images, and the supporting math:
http://cartan.e-moka.net/content/download/248/1479/file/Astronave relativistica.pdf

The only thing that you really need to know to answer your original question is whether the light from the Earth is blue-shifted or red-shifted, the results in the paper are interesting but might be a bit advanced for high school - fun to look at the pictures, though.

 

[lovenugget]

Thank you all for your responses and for confirming what I imagined would happen. I looked at the mathematica notebooks you posted on the other thread Doolin. I really like mathematica and I'm interested in finding more (more like a collection) of mathematica notebooks relating to physics. Does anyone know where i can find more?

 

[JDoolin]

Yeah, there's a demonstration site: http://demonstrations.wolfram.com/

 

[lovenugget]

wow I'm not sure how i managed to overlook the demonstration page you provided. I've been looking for a similar page for months. i think it's great that they're made available to everyone, as opposed to being hoarded which the contributors and wolfram could easily have done. much appreciated.