Simple question about relativity?

Question

Assume a spaceship is traveling directly towards you at a constant speed of half the speed of light and you are able to observe a clock on board the spaceship using a telescope. What would you actually see. Would you see the clock moving faster or slower than your own, and by how much?

Good answers so far. I asked the question because I believe you would actually observe the clock running FASTER, which is what is at odds with most physics classes teach. To see why, imagine the ship as it leaves a station 1 light year from earth. You, the earth observer will see the ship leave the station after 1 years time. During this year, the ship will have travelled half the distance to Earth. In one more year, the ship will arrive at Earth. So you will see the ship travel the 1 light year distance apparently in only 1 year. The ship's clock will have appeared to be running at twice its normal speed NEGLECTING RELATIVITY. If we include relativity we will actually observe the clock at rate = 2*.866 = 1.732 times its normal rate. Bottom line - there is a distorting effect due to the changing distance which is separate from relativity. Thoughts?

Answer 1

james is right, but it would have to be a VERY special telescope that could counteract the 'blue shift' and bring the radiation frequency into a visible range.

Answer 2

The clock would appear to be moving more slowly by the amount:sqrt(1-v^2/c^2)=sqrt(3/4)=.866; or at .866 the rate that a clock in the observers inertial frame would move.

Answer 3

GPS satellites already demonstrate this. Their on-board rubidium clocks are sufficiently accurate that they can, and do, report their on-board times that are affected by relativity and gravity:
http://en.wikipedia.org/wiki/Global_Positioning_System#Relativity