Relativity question?

Question

As I understand it, time moves slower the closer you get to a large gravitational source. So, as I approach, say, Jupiter, does Jupiter appear to be spinning faster or slower? If I were to move to a point far outside the galaxy (that is, far away from all gravitational sources), but I took with me a telescope that allowed me to still clearly see Jupiter, would it appear to be rotating faster or slower than it would appear from a moon of Jupiter?

Answer 1

I beg to disagree with the Mullah, since my conclusion is just the opposite.  A clock in a gravitational field runs slower than a clock far removed from all gravitational influences by the factor sqrt(1+2φ/c^2) , where φ is the gravitational potential at the site of the clock (relative to φ=0 far from the source of the field).  Thus to an observer on Jupiter (or on a moon of Jupiter) it takes longer for that planet to make one revolution than to an observer on Earth where φ≈0 compared to Jupiter. I don't see what the frequency of the light has to do with that. I do agree as far as the proper frequency  of a light ray decreasing as it propagates away from Jupiter.  If you placed a spectrometer on Jupiter and measured the wavelength of light emitted by an atom, it would be the same as measured on Earth for the same transition.

I'm getting a bit rusty in this stuff, though.  I suggest looking in Pauli's famous paper. My copy isn't close at hand right now. I'm sure that there are people here that know this better than I do.

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I agree with the others after all.  You arrive at the right conclusion by straight-forward application of  the result of general relativity. Suppose you approach the planet with a clock.  As you do so, the rate of rotation of the planet stays the same, but your clock goes slower as you get closer to the planet. Thus your clock will have moved less during a revolution when you are close than when far away, making it look like the planet rotates faster.  Thus it appears to rotate slower when you are far away.  I gave that argument the first time but was dumb in drawing the reverse conclusion.

Answer 2

Time slows for YOU when you are in high energy states, so near a black hole or near the speed of light.  You won't be able to detect the effect of being in orbit around Jupiter.  It will be there, it's just small.  When time slows for you, your clock is running very slowly.  When you time a revolution of Jupiter, it will take a shorter time on your clock than on a distant or stationary observer's clock.  You'll see it going faster.  Increase your distance, and the reverse is true.  You need an awfully good atomic clock to measure the difference with any normal gravity field, though!  

Answer 3

Jupiter will appear to move slower when you are far.

You must think of things in terms of reference frames.   As long as you are in the same reference frame(as  an object i.e a clock or something) time will pass by at the same rate. If you are near Jupiter than you will be in the same reference frame as the spinning planet therefore it will rotate at its correct rotation speed.

Once your are in different reference frames times may move at different rates.   For someone far away (that is outside of the reference frame i.e acceleration due to gravity is much smaller) from Jupiter a clock near Jupiter will appear to tick slowly.   Therefore things will appear to move slower i.e the planet will rotate slower.

This is analogous to moving near light speed in a space shuttle.  The guy moving at light speed sees his clock ticking away at normal speeds (analogous to being near the planet).  The guy standing on earth looking up at the shuttle sees the shuttles clock ticking very slowly (analogous to being far way from jupiter).

Answer 4

Jupiter appears to spin slower to the observer who is far away from Jupiter.

This effect is easy to explain in simple terms. Lets say someone set a radio broadcasting station on the surface of Earth that broadcasts EM sine wave at ultra-low frequency f=1/day (one period per day).

This EM radiation consists of photons of frequency 1/day. Their energy is proportional to their frequency. As these photons move away against the force of Earth gravity they lose energy, and therefore their frequency decreases and period becomes more than 84,600 seconds.

To the remote observer period of this radio signal is obviously equal to apparent period of Earth rotation, that is to remote observer it takes more than 84,600 seconds for Earth to complete one revolution.