## Observing an object as it moves one lightyear away

A thought experiment.
Imagine you launch a spaceship from a space station that is fixed at a certain location (to eliminate the factor of Earth's orbit) and track its course, by powerful telescope, as it moves away from you to a distance of one light year. Let's say the journey takes ten years. At the point where the spaceship is one light year from you, the light which reflects from it to your telescope takes one year to reach you. This suggests that it would take 11 years to track the 10 year journey.
This is the question: If you are observing the spaceship consistently, how does the extra year squeeze in? Does the spaceship appear to slow down? Does it flicker out of sight and then reappear as your perception catches up to the relative position of the object?

I find it helpful to introduce a periodic element which can help track the motion of the spaceship. Let's say it has flaps which open and close periodically, in harmony with a defined distance traveled. Over the course of our 11 year observation, would the duration of each flap cycle increase, relative to the spaceship's distance? What if the ship stopped at its one light year destination?--Would the flaps suddenly speed up again?

Don't know the answer. Perhaps it is explained in terms of relativity. Can anyone explain it to me?

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 Quote by sandb232 This is the question: If you are observing the spaceship consistently, how does the extra year squeeze in? Does the spaceship appear to slow down? Does it flicker out of sight and then reappear as your perception catches up to the relative position of the object?
Light from the ship is reaching your eyes during the entire journey, so you always see the ship - no jumps, discontinuities, flickerng in and out of sight, or anything of that sort. All that's happened is that by the time the light from the ship reaches your eyes, the ship has moved on. That's true from the very beginning of the trip, and the effect increases as the ship moves further away and the light has further to travel.

 I find it helpful to introduce a periodic element which can help track the motion of the spaceship. Let's say it has flaps which open and close periodically, in harmony with a defined distance traveled. Over the course of our 11 year observation, would the duration of each flap cycle increase, relative to the spaceship's distance?
Not relative to the ship's distance, but to its speed. This is the intuitive explanation for the prediction (solidly confirmed by experiment) that a clock that is moving relative to you, such as the periodic flaps on the ship will run slow relative to you. Try googling for "relativity time dilation and see what you find... It's actually a lot of fun to figure this stuff out.

 What if the ship stopped at its one light year destination?--Would the flaps suddenly speed up again?
Yes. No velocity relative to you, so although you're seeing everything ten years delayed as the light gets to you, there's no time dilation effect, just the constant ten year offset.

 Don't know the answer. Perhaps it is explained in terms of relativity.
Yes, this is all special relativity. If your interest is historical, find the online copies of einstein's book "Relativity: The special and general theory" and his seminal paper "On the electrodynamics of moving bodies"; if your interest is to understand the more modern mathematical treatment used today, a decent undergraduate textbook is your best bet.

Avoid the pop-sci gee-whiz math-free books - they do more harm than good if you want understanding.

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 Quote by Nugatory Avoid the pop-sci gee-whiz math-free books - they do more harm than good if you want understanding.
I don't quite agree with this. I've read several math free or nearly math free books that do a good job of explaining a variety of topics. Just don't expect too much from them. They are more of an introductory to the topic than a reliable go-to source for discussing the physics of it. Some have encouraged me to find out more on the topic just because some of it was so...weird!

I would say most books you can find at a bookstore will do a decent job of introducing you to relativity. Practically every one that I've either bought or picked up and browsed through has looked, to my eyes at least, to be accurate. Just remember to buy a book that specifically about relativity. General guides to a wide range of subjects are interesting to read, and I have one or two, but they explain practically nothing.

## Observing an object as it moves one lightyear away

 Quote by Nugatory Yes, this is all special relativity.
Special relativity is not needed. This is just the doppler effect (Wikipedia- Doppler effect). The naive observed velocity is v(1-v/c) if the actual velocity is v. The speed of light enters into the calculation only because one is observing with light. If instead the rocket were shooting probes that had a constant velocity and could tell one the distance they had travelled (which one is naively assuming is the distance to the rocket when the probe arrives) one would use the speed of the probes in place of c. All of the processes one is observing occuring on the rocket will be slowed down by that same factor 1-(v/c).

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