How would you observe outside events on a spacecraft?

[Energize]

If you were traveling near the speed of light on a spacecraft moving away from the Earth how you would you observe events happening on the earth, at normal speed or in slow motion?

I can't work this out because I know light is always gaining on you at C even if you are traveling close to the speed of light away from it. As far as I can picture it, events would start off apearring at normal speed and then appear to get slower and slower as you get further away from the earth.

 

[meopemuk]

If you were traveling near the speed of light on a spacecraft moving away from the Earth how you would you observe events happening on the earth, at normal speed or in slow motion?

In slow motion.

Eugene.

 

[pervect]

If you were traveling near the speed of light on a spacecraft moving away from the Earth how you would you observe events happening on the earth, at normal speed or in slow motion?

I can't work this out because I know light is always gaining on you at C even if you are traveling close to the speed of light away from it. As far as I can picture it, events would start off apearring at normal speed and then appear to get slower and slower as you get further away from the earth.

If you observed the Earth through some sort of telescope, you'd see things happen in slow motion. However, the slowdown factor would be a constant. This is just the factor k in the Bondi approach to SR. If light flashes occur at an interval of 1 unit (say seconds) on the Earth, when they are received they will be separated by k units (say seconds) on the spaceship as viewed by the actual arrival time at the telescope on the spaceship. For a spaceship leaving Earth, k>1. This can also be regarded as a 'relativistic doppler factor'. For some equations, see http://scienceworld.wolfram.com/physics/RelativisticRedshift.html

Note that if you approached Earth, k<1, and you'd see things through your telescope as being sped up.

 

[meopemuk]

Note that if you approached Earth, k<1, and you'd see things through your telescope as being sped up.

I disagree with you here. Relativistic time dilation and Doppler shift are quite different things. An Earth clock observed from the spaceship will appear slow independent on whether the spaceship approches the Earth or moves away from it. (The relativistic time dilation depends on the magnitude of the relative velocity, not on its direction.) However the color of the clock (the frequency of light emitted by the clock) will look different. If the spaceship approaches the Earth the color will shift to the blue side of the spectrum. If the spaceship moves away, the color will look more red.

Eugene.

 

[Energize]

What would be observed if you were orbiting the earth?

 

[meopemuk]

What would be observed if you were orbiting the earth?

You will see that the clock on Earth runs slower for two reasons. First, the clock is moving with respect to you. Second, the clock is in a lower gravitational potential than your clock. Both these effects are easily observable, and these corrections are taken into account for clocks mounted on GPS satellites.

Eugene.

 

[pervect]

What would be observed if you were orbiting the earth?

There will be a periodic component to what you actually observe due to variable propagation delays as the distance from the ground station to the satellite varies.

If you are interested in the long-term trends and eliminate this periodic component by considering observations only when the satellite is directly over the ground station sending the signals, one will find that the satellite clocks on the average tick faster, which implies that the Earth clocks on the average appear to tick slower.

See for instance http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion.

Further, the satellites are in orbits high above the Earth ... <snip misleading sentence>.

A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)!

Note that the GR effects dominate the SR effects in this problem.

 

[pervect]

You will see that the clock on Earth runs slower for two reasons. First, the clock is moving with respect to you. Second, the clock is in a lower gravitational potential than your clock. Both these effects are easily observable, and these corrections are taken into account for clocks mounted on GPS satellites.

Eugene.

I agree with the overall conclusion (assuming that you are talking about the average rate at which the clock on the Earth ticks and ignore periodic changes), though I'm a bit leery about some of the details of your argument.

 

[Tracer]

I disagree with you here. Relativistic time dilation and Doppler shift are quite different things. An Earth clock observed from the spaceship will appear slow independent on whether the spaceship approches the Earth or moves away from it. (The relativistic time dilation depends on the magnitude of the relative velocity, not on its direction.) However the color of the clock (the frequency of light emitted by the clock) will look different. If the spaceship approaches the Earth the color will shift to the blue side of the spectrum. If the spaceship moves away, the color will look more red.

Eugene.

If you consider the color of the light as "the ticking of the Earth clock" Then the clock appears to run faster when the spaceship approaches the Earth and slower when the spaceship moves away from the Earth. All Earth based clocks would appear to run slower or faster in the same amount as the spectrum color changes.
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[AbedeuS]

Wait, if I was on a spaceship moving at just below c, wouldn't everything appear to be going extremely fast due to the fact that I was in a dilating time frame and Earth is in a less heavy one, when I arrive on Earth everyone will have aged dramatically weras I'd get off scott free is the idea I had when it came to relativity...

But if things appear to move slowly wouldn't that imply that I, as a astronaut would be the one in a less dilated reference frame? :S

 

[Doc Al]

If you consider the color of the light as "the ticking of the Earth clock" Then the clock appears to run faster when the spaceship approaches the Earth and slower when the spaceship moves away from the Earth. All Earth based clocks would appear to run slower or faster in the same amount as the spectrum color changes.

In discussing SR effects there is some ambiguity in the term "appear" or "see". Usually, when we sloppily say "moving clocks appear to run slow" what we really mean is that, based on our measurements (using our clocks) and after accounting for the travel time of the light signals we observe, we deduce that moving clocks run slowly. That's not necessarily what we literally see. (This is even more apparent when speaking of length contraction; in some cases you won't "see" the length contraction at all.)

As meopemuk points out (post #4), the Doppler shift is distinct from (but incorporates) time dilation. In a sense, the Doppler effect is an optical illusion, whereas time dilation is not. If you took into account the fact that the clock was moving towards you as you observed it, you'd say: Of course it appears to run faster, but that's just because succeeding images take less time to reach me; in "reality", the moving clock is actually running slowly due to time dilation.

In pervect's post (#3) he is talking about what you'd see in a telescope, whereas meopemuk is talking about the "actual" difference in clock rate due to relative motion.

 

[Tracer]

(quote) As meopemuk points out (post #4), the Doppler shift is distinct from (but incorporates) time dilation. In a sense, the Doppler effect is an optical illusion, whereas time dilation is not. If you took into account the fact that the clock was moving towards you as you observed it, you'd say: Of course it appears to run faster, but that's just because succeeding images take less time to reach me; in "reality", the moving clock is actually running slowly due to time dilation.

In pervect's post (#3) he is talking about what you'd see in a telescope, whereas meopemuk is talking about the "actual" difference in clock rate due to relative motion.
(unquote)

I was concerned about the meaning of "observation of the Earth clock" in the spaceship's reference frame. I took that to mean what would be seen by a telescope. Such an observation will show the clock runner faster or slower depending on whether the spaceship is moving towards or away from the Earth. Non-relativistic Doppler effects would obscure the actual relativistic time dilation differences in clock rates.
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[pervect]

I was concerned about the meaning of "observation of the Earth clock" in the spaceship's reference frame. I took that to mean what would be seen by a telescope. Such an observation will show the clock runner faster or slower depending on whether the spaceship is moving towards or away from the Earth. Non-relativistic Doppler effects would obscure the actual relativistic time dilation differences in clock rates.
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What you see with the telescope will be the doppler shift.

The simple case to analyze is the straight-line case where motion is directly toward or away from the source.

The formula for this case is given by the relativistic doppler shfit formula

in this wikipedia article, among other places.

Note that the doppler shift depends only on your relative velocity, not distance, So the doppler shift factor does not increase as you get further away.

To analyze the orbiting case in detail is more complex. First of all, one cannot neglect gravitational effects due to GR - in fact, they can be dominant, as the example of the GPS satellite shows.

I assume that you are tracking the signal from some ground station on the surface of the Earth. (The math would be easier if you were tracking some signal from the center of the Earth, but that's not very realistic).

You will see a periodic component of the doppler shift in this case - when the distance to your ground station is decreasing, you'll see "blueshift", when it increases, you'll see "redshift".

Suppose you did your clock comparisons only when the orbiting clock was directly "overhead" the clock on the Earth's surface. This will give you the non-periodic part of the doppler shift.