The Orbit of the Moon around the Sun is Convex

http://www.math.nus.edu.sg/aslaksen/teaching/convex.html?HN_2

by ColinWright • 15 years ago

172 17 15 years ago

math.nus.edu.sg

sixwing• 15 years ago

this isn't a shaggy dog joke about the moon having an orbit closely conforming to a polygon with 13.37 (1337) sides?

praptak• 15 years ago

Yeah, this fact makes it awfully hard to draw realistically. Just try to draw a circle (Earth's orbit around the sun) and then a convex curve that crosses it from time to time. Pretty hard not to make it concave.

shasta• 15 years ago

You mean its hard to draw a circle and a square that intersect 8 times?

Sharlin2• 15 years ago

Given the Earth-Moon distance of about 380000 km and Earth-Sun distance of about 150000000 km, the lunar orbit deviates from Earth's orbit about 0.25% at most; if the Earth-Moon distance [1] were one meter, the maximum deviation would be ~2.5 millimeters. So, yeah, "awfully hard" just about describes the situation.

[1] The average distance - Earth's orbit is not a circle, after all.

wahnfrieden2• 15 years ago

Does the fact that the earths orbit is not a circle lead to an instability? So the deviation will change over time - whether by converging on a circle or spinning away. [totally naive question]

cmurphycode• 15 years ago

Wow.

I understood the argument that the speed of the Earth's orbit dominated the Moon's, but I was having a really tough time visualizing it. The wiki article (http://en.wikipedia.org/wiki/Orbit_of_the_Moon#Path_of_Earth...) has a diagram that explains it (http://en.wikipedia.org/wiki/File:Moon_trajectory1.svg)

gort• 15 years ago

Another argument is this:

The (wrong) graph has been drawn with 12 cycles, based on approximately 12 lunar months per year. But the result is obviously not to scale. If you try to draw it to scale, the truth jumps out at you; it can't have this form.

sambeau• 15 years ago

Spirograph is a lie!

euroclydon• 15 years ago

The spirals don't seem intuitive to me. Do most people really think the moon has a negative velocity during parts of its orbit about the sun?

jdpage• 15 years ago

Why wouldn't it? When it's going around the earth, it's going to be going in the opposite direction from the earth's orbit part of the time. The question is which motion is bigger.

JonnieCache• 15 years ago

That is the pattern the planets trace in the sky and for thousands of years people thought that was literally their path.

http://en.wikipedia.org/wiki/Apparent_retrograde_motion

In the ptolemeic system, the planets were thought to move with epicycles, or "wheels within wheels". This is why astrolabes had gears attached to gears.

http://en.wikipedia.org/wiki/Deferent_and_epicycle

Then copernicus came along and blew that all away with his heliocentric model, which was then given mathematical foundation by Johannes Kepler and his laws of planetary motion.

bluedanieru• 15 years ago

I would really like to meet these mathematicians who described it that way. I suspect he asked two and one of them was busy at that moment and not really paying much attention to his question.

josyula• 15 years ago

I thought it would look like a sine wave on a circle...Well but that totally unexpected. Do check the guys other writings they are really very interesting.

The Orbit of the Moon around the Sun is Convex

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