The Cellar - 12/11/2002: Jupiter and Io

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- - 12/11/2002: Jupiter and Io (http://cellar.org/showthread.php?t=2523)

Dave: yup. I was pretending to wake up this morning and thought: whoa. I subtracted by the diameter. Wow I'm stupid!

I came over here as quick as I could to correct my mistake before anyone noticed, but it was too late :)

Quote:

Originally posted by Torrere
Io's orbit: 422,000 km from Jupiter
Jupiter's diameter: 142,984 km (at equator)

So Io would be 279,000 kilometers from Jupiter's surface. Quite a ways.

We can also reason the (the Velocity of Io) squared would equal (the Gravitational Constant) * (the Mass of Jupiter) divided by (the radius from center to center).

Mass(io)*V2 = 6.67*10^-11*Mass(io)*Mass(jupiter) / Radius(jupiter-to-io)

Then v2/r which gives us Jupiter's gravity as being able to pull Io toward it at 0.7 meters per second per second. By comparison, the Earth can pull on our moon at 0.0027 meters per second per second.

The math scares me more than the sheer size of jupiter. eek.

I guess my next question then becomes:
How do you define the "surface" of a gas giant?
I'm just curious, as I've seen/heard that statement made before and it doesn't make much intuitive sense (which is pretty much how I make it through life).

vaya con chichis!

I'd guess you'd define it by the edge of the atmosphere. :confused:

Quote:

Originally posted by Cam
I'd guess you'd define it by the edge of the atmosphere. :confused:

And just HOW do you define "edge of the atmosphere"? It's not like it's a solid boundry

It's because the sun, as far as Jupiter is concerned, is almost a point source of light. Here on earth, the sun makes a large disk.

Shadows of things like people and airplanes are fuzzy when the objects are far away because the sun is so much bigger than them. When the light source is bigger than the object, the umbra (see below) eventually disappears, and the shadow is all penumbra... and eventually, the shadow (in the case of something much smaller than the Sun) disappears entirely. In a room with a single unreflected halogen bulb (for our purposes a point source of light), every shadow will be perfectly sharp at any distance (all umbra, no penumbra).

Now, I don't have any fancy equations, but based on 1) Io's size, 2) the Sun's size, 3) the Io-Jupiter distance, 4) the Jupter-Io-Sun distance, and 5) the camera-Jupiter distance, we can see that the umbra of Io is still quite sharp, and there is very little penumbra to make it look fuzzy and far away.

http://www.schorsch.com/kbase/glossa...s/penumbra.gif

Quote:

Originally posted by Beletseri
I think it's just a matter of scale. It only looks close because Jupiter is so big.

I think what makes Io look close to Jupitor is the sharpness of the shadow. We are used to seeing the shadow of something farther away being more diffuse.

Now I'm guessing that there is less light scattering because of a lack of particulate matter between Io and Jupitor but hopefully someone here will have the real answer as to why the shadow is so sharp edged.

Fancy equations are fun.

I think it's interesting that the Earth has so little acceleration on the Moon. It is a long distance away though. I suppose this is what they mean when they say that there is gravity in space, it just doesn't seem to affect you very much.

Thanks dsviper. Nice explanation.

You know, you can actually see the shadows up the Galilean moons on the surface of Jupiter from down here on Earth. You need a telescope, of course, but not a particularly huge one. (You also have to discipline yourself to understand that when you see Jupiter or the Andromeda Galaxy or the Pleiades in your telescopes, it's not going to look like all the pictures we get back from Hubble and the various space probes.) Sky & Telescope used to (and probably still does) publish charts that show when the shadows were visible.