Hello, I don't understand why the orbital period of Io would appear to be slower if we are further away. I've been reading the wikipedia article and still don't understand :( - http://en.wikipedia.org/wiki/R%C3%B8mer%…
It would be much appreciated if someone can give a nice explanation. Thanks in advance!
It would be much appreciated if someone can give a nice explanation. Thanks in advance!
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OK
First IO and all the moons of jupiter have clockwork precision, they are like the hands of a clock.
So if you had a giant clock face on the floor and you watched the second hand going round you could use it to set your watch.
Now the moon is about 1.5 light seconds away, so if Neil Armstrong looked at this clock through a good telescope it would seem to be 1.5 seconds slow, because the image takes 1.5 seconds to get to the moon.
Likewise with Io, the earth orbital radius is 93 million miles from the sun so in six months it moves across the solar system 186 000 000 miles (about 15 light minutes)
so in six moths earth moves from close to Jupiter to 186 million miles further and Io seems to be 15 minutes late, Six months later we are close to Jupiter again and Io is running on time again
so just divide 186 million miles by 15 minutes (900 seconds) and you get the speed of light in miles per second
Edit,,, my typo I put 25 minutes, I meant 15
Edit 2,,, actually the time is more like 16 minutes 40 seconds than 15 but earth's orbit is not a perfect circle and jupiter is moving too so 15 is near enough
First IO and all the moons of jupiter have clockwork precision, they are like the hands of a clock.
So if you had a giant clock face on the floor and you watched the second hand going round you could use it to set your watch.
Now the moon is about 1.5 light seconds away, so if Neil Armstrong looked at this clock through a good telescope it would seem to be 1.5 seconds slow, because the image takes 1.5 seconds to get to the moon.
Likewise with Io, the earth orbital radius is 93 million miles from the sun so in six months it moves across the solar system 186 000 000 miles (about 15 light minutes)
so in six moths earth moves from close to Jupiter to 186 million miles further and Io seems to be 15 minutes late, Six months later we are close to Jupiter again and Io is running on time again
so just divide 186 million miles by 15 minutes (900 seconds) and you get the speed of light in miles per second
Edit,,, my typo I put 25 minutes, I meant 15
Edit 2,,, actually the time is more like 16 minutes 40 seconds than 15 but earth's orbit is not a perfect circle and jupiter is moving too so 15 is near enough
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The orbital speed doesn't appear to be slower (or faster) if we are further away. But it does change as we MOVE further away.
So at one distance (call it L), the orbital speed is seen as 42.5 hours per orbit. And at another distance (call it K), the orbital speed is still seen as 42.5 hours per orbit. But this is only if we could stay still at those distances. The fact is, we can't -- the Earth moves. So as we move from L to K, the light from Io takes longer to get to us, which makes it appear that Io is moving a bit slower.
So at one distance (call it L), the orbital speed is seen as 42.5 hours per orbit. And at another distance (call it K), the orbital speed is still seen as 42.5 hours per orbit. But this is only if we could stay still at those distances. The fact is, we can't -- the Earth moves. So as we move from L to K, the light from Io takes longer to get to us, which makes it appear that Io is moving a bit slower.