# Judging Jupiter's distance in the 1600's

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In the 1670's, the Danish astronomer Ole Roemer figured out the speed of light by knowing the distance from earth to Jupiter. How could he or anyone else back then figure out the distance of any of the planets?

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I think Roemer used the difference in the timing of orbits/eclipses of Jupiter's moons when viewed from different points of the earth's orbit - the change in timing being the time needed for the light to travel across the orbit of earth. he could have then calculated the speed of light in terms of earth orbits - but apparently he didn't - however he did show it had a finite speed. Huygens did do the sums and got a fairly amazingly accurate answer

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In the 1670's, the Danish astronomer Ole Roemer figured out the speed of light by knowing the distance from earth to Jupiter. How could he or anyone else back then figure out the distance of any of the planets?

Johannes Kepler had published his three empirical laws of planetary motion at least fifty years earlier.

Edited by ewmon
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Johannes Kepler had published his three empirical laws of planetary motion at least fifty years earlier.

Would that allow you to work out the distance from earth or the major axis of jupiters orbit? the law in question is the 3rd and that works on a common ratio or proportion. that is why I said that the speed of light could and was determined in terms of the size of earths orbit. I think you need newton to be able to get absolute distances rather than ratios.

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you know how long jupiter takes to orbit, you know how long the earth takes to orbit, you can measure angles with reasonable accuracy. take a measurement, wait a few months and retake. should give you a reasonable estimate.

of course, there are other methods but that is the simplest i can think of.

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you know how long jupiter takes to orbit, you know how long the earth takes to orbit, you can measure angles with reasonable accuracy. take a measurement, wait a few months and retake. should give you a reasonable estimate.

of course, there are other methods but that is the simplest i can think of.

Thanks for all of your answers. I asked this same question at work and someone came up with measuring the known distance of something on earth, then using that distance while accounting for the amount of magnification used to see Jupiter. I HATE the fact that there were people WAY WAY back then that are smarter than me now!

Edited by Jiggerj
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Thanks for all of your answers. I asked this same question at work and someone came up with measuring the known distance of something on earth, then using that distance while accounting for the amount of magnification used to see Jupiter. I HATE the fact that there were people WAY WAY back then that are smarter than me now!

What a minute. That won't work unless you know the size of Jupiter. Who determined the size of Jupiter and when?

Besides, as imatfaal said, from Wikipedia on Jupiter:

Both Giovanni Borelli and Cassini made careful tables of the motions of the Jovian moons, allowing predictions of the times when the moons would pass before or behind the planet. By the 1670s, it was observed that when Jupiter was on the opposite side of the Sun from the Earth, these events would occur about 17 minutes later than expected. Ole Rømer deduced that sight is not instantaneous (a conclusion that Cassini had earlier rejected[16]), and this timing discrepancy was used to estimate the speed of light.[76]

And go easy on yourself. Your comparing yourself to the crème de la crème in the world of science.

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What a minute. That won't work unless you know the size of Jupiter. Who determined the size of Jupiter and when?

Heck if I know. Every night I look at our own moon and I haven't a clue how to measure its size or distance. Best I can do is put my hand up and block the moon from my sight, so I'd say it's about an arm's length away.

What a minute. That won't work unless you know the size of Jupiter. Who determined the size of Jupiter and when?

Besides, as imatfaal said, from Wikipedia on Jupiter:

By the 1670s, it was observed that when Jupiter was on the opposite side of the Sun from the Earth, these events would occur about 17 minutes later than expected. Ole Rømer deduced that sight is not instantaneous (a conclusion that Cassini had earlier rejected[16]), and this timing discrepancy was used to estimate the speed of light

But this STILL wouldn't give them the size and distance of Jupiter. Would it?

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Heck if I know. Every night I look at our own moon and I haven't a clue how to measure its size or distance. Best I can do is put my hand up and block the moon from my sight, so I'd say it's about an arm's length away.

But this STILL wouldn't give them the size and distance of Jupiter. Would it?

No it's my arms length away - so unless we have the same length arms there is an experimental error.

Roemer did not use the size and distance of jupiter. He was able to use calculations and extrapolations to work out the time difference for events when measured at two different points:

1. When the earth was on the same side of the sun as jupiter (sun -> earth -> jupiter)

2. When the earth was the far side of the sun (earth -> sun -> jupiter)

He didn't exactly observe them in a straight line - but from other calculations he was able to work out what the time difference would be for the two straight line instances. He found that the event was 22 (or was it 17?) minutes late when the earth was the far side of jupiter. Now this either meant that Kepler's laws were wrong and the orbits of jupiters moons varied spectacularly - or as he correctly deduced that the light from the event was taking an extra 22 minutes to get to us. He could have then given a value for the speed of light based on the size of earth's orbit - but he didn't.

Huygens did a few years later and was fairly accurate - he said the speed of light travelled at 16 2/3 diameters of earths orbit per second

from Triate de la Lumiere - Huygens - here

Now in quantities of observations of these Eclipses, made during ten consecutive years, these differences have been found to be very considerable, such as ten minutes and more; and from them it has been concluded that in order to traverse the whole diameter of the annual orbit KL, which is double the distance from here to the sun, Light requires about 22 minutes of time.
But Sound, as I have said above, only travels 180 toises in the same time of one second: hence the velocity of Light is more than six hundred thousand times greater than that of Sound. This, however, is quite another thing from being instantaneous, since there is all the difference between a finite thing and an infinite.

Sound travels at ~340metres per second times 600,000 is 2*10^8 m/s which is not bad

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He found that the event was 22 (or was it 17?) minutes late when the earth was the far side of jupiter. ...

Huygens did a few years later and was fairly accurate - he said the speed of light travelled at 16 2/3 diameters of earths orbit per second

It was the 17 minutes figure, and the difference in time was between the Earth on the "near side" of the Sun (ie, the same side as Jupiter) versus the "far side" of the Sun (ie, the opposite side from Jupiter). From Wikipedia, the semi-major axis of Earth's orbit is 149,600,000 km, and the speed of light is 300,000 km/sec, so the time for light to transit the radius of Earth's orbit is 149,600,00/300,00 seconds, or 499 seconds, or 8 min 19 secs. And the time for light to travel the diameter of the Earth's orbit is twice the time of the radius, or 16 m 38 s, or about 17 minutes.

I didn't research Huygens claim stated above, but I think you meant 16 2/3 minutes for light to transit the diameter of Earth's orbit. The transit time of 16 2/3 minutes would be 16 m 40 s.

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Fine, I clicked on the + for you and imat because you are making me think. You remember the movie with the kids in the classroom and Ben Stein saying, "Anyone, anyone?" Do you remember the looks on their faces? Well, THAT'S how I look right now. lol

So, slipping into a time machine and going back to the 1600's, I don't know how far away Jupiter is, and I'm trying to figure out the speed of light. I DO know that one of the moons of Jupiter appears ahead of schedule when the earth is closest, and behind schedule when furthest away. Let's say there's a 15 minute difference.

Now we have this from Wiki:

"Rømer estimated that light would take about 22 minutes to travel a distance equal to the diameter of Earth's orbit around the Sun:"

If Romer doesn't know the speed of light at this point, then how in thee hell could he possibly estimate that????

Ehh, forget it. I'm getting whacked by toises and pieds and stuff that I just won't absorb. It's been fun though. Thanks guys.

Edited by Jiggerj
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It was the 17 minutes figure, and the difference in time was between the Earth on the "near side" of the Sun (ie, the same side as Jupiter) versus the "far side" of the Sun (ie, the opposite side from Jupiter). From Wikipedia, the semi-major axis of Earth's orbit is 149,600,000 km, and the speed of light is 300,000 km/sec, so the time for light to transit the radius of Earth's orbit is 149,600,00/300,00 seconds, or 499 seconds, or 8 min 19 secs. And the time for light to travel the diameter of the Earth's orbit is twice the time of the radius, or 16 m 38 s, or about 17 minutes.

I didn't research Huygens claim stated above, but I think you meant 16 2/3 minutes for light to transit the diameter of Earth's orbit. The transit time of 16 2/3 minutes would be 16 m 40 s.

Ewmon - not sure why you are correcting this - the figure that Roemer came up with and Huygens used was 22 minutes (even though it should have been around 17) See here Romer's detection of the speed of light and the text from Huygen's that I quoted. It is wrong - but it's amazing accurate for a first attempt at measuring a speed in a case where most people thought transmission was instantaneous.

And on Huygen's figure of 16 2/3 this is per minute - but it is earth diameters not earth orbit diameters (processing error in wetware between chair and keyboard) - apologies

And Jigger - if you get less whacked I am sure that between Ewmon and myself we could explain it (and I promise never to quite anything with a pied or a toise in again)

Edited by imatfaal
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And Jigger - if you get less whacked I am sure that between Ewmon and myself we could explain it (and I promise never to quite anything with a pied or a toise in again)

Ha! Thanks! But I went to other sites for a bit of research and that's where I got nailed with the mathematical language. I'm old and tired, so if it's not in inches, miles per hour, or ounces, I'm LOST.

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