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Then when the accelerator makes the return journey, Earths clock runs slow until the two are in perfect sync when the accelerator reaches Earth but then the Earth clock jumps forward another 302 years when the accelerator accelerates back into Earth's frame?

It makes no difference in this case if you are travelling away from or towards the Earth.

If the rocket had left at the beginning of the year 2000, it would arrive at the planet in 2528.57 (528.57 years later) according to Earth, but because moving clocks (relative to Earth in this case) slow down, the spacecraft clock would read the planet arrival date of 2377.47 (377.47 years later). If the rocket decided to return home after 2 years, then Earth would see it arrive back in 3059.14 (2 + 528.57 years later), but because moving clocks (relative to Earth in this case) slow down, the spacecraft clock would read 2756.94 (2 + 377.47 years later). This means the spacecraft would have aged 302.2 years less than if it had not gone on this round trip.        

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This is interesting, as you have tackled the problem from a different perspective. Here is my reasoning looking at the problem from the point of view of length contraction. L= L0√ 1 – v2/c2 L0 = Earth

> Who's the troll? I've been nothing but polite.   The difficulty is that you're full of baloney.

If anyone is interested, I did write up an introduction to relativity that has got good feedback for its clarity.   Anyone interested, I'll post a link -- but forums get annoyed with personal plugs, so you'll have to ask.

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It makes no difference in this case if you are travelling away from or towards the Earth.

If the rocket had left at the beginning of the year 2000, it would arrive at the planet in 2528.57 (528.57 years later) according to Earth, but because moving clocks (relative to Earth in this case) slow down, the spacecraft clock would read the planet arrival date of 2377.47 (377.47 years later). If the rocket decided to return home after 2 years, then Earth would see it arrive back in 3059.14 (2 + 528.57 years later), but because moving clocks (relative to Earth in this case) slow down, the spacecraft clock would read 2756.94 (2 + 377.47 years later). This means the spacecraft would have aged 302.2 years less than if it had not gone on this round trip.        

I know that the direction of travel doesn't matter. The difference in the time it takes from the destination/Earth's frame and the accelerator's frame is 151 years, so during the journey, the accelerator would see a clock on Earth moving slowly but when they reach the destination and accelerated again back into Earth's frame they have experience 151 years less time than the time on the Earth clock so during that acceleration phase they must see the Earth clock going from 151 years behind their own clock to 151 ahead of their own clock.

 

Then when they make the return journey the Earth clock will fall another 151 behind their own clock, this time bringing them to the same amount of elapsed time but then jumping forward 302 years again when the accelerator moves back into Earth's frame again.

 

Right?

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