More a Sun question than a Java question
This is just for fun-
Every school kid learns that the sun is 93 million miles away (he probably doesn't learn that the aphelion and perihelion differ by 3 million miles). How was that determined?
You can easily compute the distance to the moon by knowing the size of the earth and then applying Kepler's relationships, but what about the sun?
The sun is only 1/2 of a degree in angular size, and since it's more than 100x the size of the earth, even if you tried to measure the parallax difference with observatories at the poles on the day of an equinox (when the earth's axis is perpendicular to the line to the sun, and hence when the parallax would be greatest), your measurement would likely be swamped by the refraction of light passing through the atmosphere.
Presumably, the sun's chromosphere will reflect radar nicely, so one could accurately measure the distance with radar- on the other hand, radar's only been around for about 60 years... so another question is when, historically, was the distance to the sun first determined with reasonable accuracy?
Kepler's relationships can give the relative orbits of planets in the solar system, and so if you make the (coincidentally accurate) assumption that Venus is about the same size as the earth, measuring the angular size of Venus will tell you its distance, and therefore the distance to the sun.
So when was the distance to the sun first accurately determined, and how?
[1499 byte] By [
thomasfly] at [2007-9-26 2:21:11]
1. http://scruffy.phast.umass.edu/a114/lectures/lec02/node7.html2. http://scruffy.phast.umass.edu/a114/lectures/lec03/node2.html3. http://www.csc.tcd.ie/~tass/astronomyonline/astronomyonline/market/collaboration/solpar/#chap1
well, the world did not need Kepler to figure out the Earth's distance form the sun. The Mayan's new the distance to the sun thousands of years ago and it is highly suspect that the ancient Egyptians knew also. Many ancient cultures (and not so ancient cultures) used triangulation and other simple mathmtical tools to determine the distance to the sun.
One example is using two markers that are a known distance apart. Then you measure the shadows (at the same time of day of course.) Use the height of the marker and the length of it's shadow to discover the angle the the light is coming in at. With that you can use simple geometric concepts like complimentry angles to get the angles for the big triangle between the sun and the two markers, and you already have the distance to between the markers so now you have an obtuse trianlge pointing at the sun. With that you can draw a right angle underneath the sun that uses a leg of the obtuse triangle, and with a couple more geomerty concepts and a little trig you have the distance to the sun.
Actually, a considerable number of school kids learn that the Earth is 150 million kilometers from the Sun.
btw- my answer was triangulation which is close to paralax (paralax uses a background comparision to gather triangulation info)
I think that your assumption that using the sun's paralax would not work is faulty. We have used paralax on many planets that are a much smaller size than the sun and, of course, the light reflected off of those planets is far weaker than what the sun emits.So the sun sounds like it would be the most accurate object in the universe (biggest, realatively close, and a high light intesity) to use paralax on. The only problem being that since the sun is so bright it's background is hidden and so I don't think early use the technique.
DrClap- "same difference" as we used to say :^)
amishslayer- that's not a very nice thing to do! Could be dangerous too- didn't you ever see that movie with Harrison Ford where he was just hanging out pretending to be Amish, and punched out that guy who picked a fight with him? But you missed my point, the angle subtended by observatories at the poles (i.e., the greatest distance possible between observers, at least before the space age) from the sun is only 1/200th a degree, whereas for example, at the horizon atmospheric refraction is slightly more than the diameter of the sun itself (the sun "rises" about 2 minutes before it rises- i.e., than if the atmosphere suddenly disappeared). So to measure the sun's distance to +/- 10% accuracy, you'd have to determine the parallax difference to +/- 1/2000th degree... or 1/120,000th radian (the size of a quarter as seen from 2 miles away).
GLJdotcom- a Duke dollar 4 u! I tried a Google search on this question a while back and basically came up empty. I thought of the thing about the moon's phases, but again there, you only have 1/400th radian to work with, and the moon isn't a perfect sphere, and you probably need radio communications to coordinate observations over long distances, etc., etc. Your last link evidently holds the answer though.
well, a modified triangluation technique (that used a well or a hole in the ground) made up for the short distance between the markers. I do remember learning this in advanced physics in high school... it has been some time so I have forgotten many of the details... sorry.
That technique also gave the cultures information on the radius of the earth so that they could correct their measurements for it's curvature.
and one last thing... using the paralax technique (versus a ground based triangulation) only requires that our perspective changes. If we cannot move a great enough distance on the ground then we can let earth move that great distance in space, compare the change in the background of the sun and discover the angle, and I beleive if you introduce more paralax observations (such as other stars) and use that information, then you can figure out the distance to the sun.
Yeah, it's the relative motion of the planets that accounts for the wiggly motion of Mars, for example, relative to the stars. Likewise, the distance to nearby stars was initially measured by taking sightings 6 months apart- of course, to translate parallax into miles, you have to know the distance to the Sun!
The nearest star is about 24 trillion miles away- resulting in a parallax the size of the quarter 2 miles away. But you can "photograph" such small angles if the star is near a much more distant star. Doesn't work for the Sun of course because you can't photograph stars from the earth that are near the Sun.
Seems to me that the subject should have been more along the lines of "entirely a sun question, and nothing whatever to do with Java."
Anyway, this cracked me up:
[[With that you can use simple geometric concepts like complimentry angles ]]
I can hear it now, two triangles walking down the street:
"Good morning, Obtuse. My, you're looking smashing today!"
"Why thank you, Equilateral, you're looking quite smart yourself!"
Rich :)
And as the Scarecrow would say, "The sum of the squares of any two sides of an isoceles triangle is equal to the square of the third side." To this day, I blame the Wizard of Oz for me not making an 800 on my math SAT. :^(
Anyhow, this is (very) tangentially a Java question: http://forum.java.sun.com/thread.jsp?forum=54&thread=153636
hey, I'm glad I could made someone chuckle... this clearly is a "I don't wanna work cause it's Monday" topic. Anyway, I should watch my spelling of "complementary" so I can avoid further confusion ;)
15 years ago I took some public domain software, added a half-ass user interface, and for the next 5 years I was richer than Bill Gates (who went across town, bought an OS from Seattle Software...)
