12/11/2002: Jupiter and Io
 

http://cellar.org/2002/jupiterio.jpg

A few days ago the Astronomy Pic of the Day gave us this one. I didn't know they re-used pics; I don't, as far as I know!

Because I'd seen and saved this one about a year ago, and then I wound up not using it. I always feel differently about things in the queue, but when I saw it again, I felt like I screwed up not posting it. This is really cool.

It's Jupiter and one of its moons, Io. And how detailed; it's like the earth as beauty concept. The little shadow of the little perfect marble against the big marble.

There is something remarkable about the earth as art and about this sort of thing, because not only is it beauty, it's a remarkable kind of beauty that you can think about on many different levels.

There is a shot of Io alone in the IotD archives in which I note that it's the same size as Earth's moon. That gives some perspective on the above.

Io is cool.
 

Ever since I was a little kid, Io has been my favorite moon. It's just cool, especially reading about the volcanic activity, etc. I almost feel robbed that we don't have really clear on-the-surface photos of it. Hopefully within our lifetime.

That look incredibly close to the planet. Not much margin for error in its orbit.

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

Plus we're basically looking at it through a big telephoto lens called "Hubble"! It tends to contract the distance between things.

Telescope?
 

Is it indeed from the Hubble, or one of the satellites to fly by in recent years? (Galileo, perhaps?)

From the site:
<blockquote>This true-color contrast-enhanced image was taken two years ago by the robot spacecraft Cassini, as it passed Jupiter on its way to Saturn in 2004. </blockquote>

Hmm... I think that's a rather poorly-worded sentence. Is this photograph from the future?

ok here's a question for someone.....

if Io is approximately the same size as our earth's moon (luna, isn't it??) and jupiter's gravity is x number of times earth's gravity...... how much farther away is Io from Jupiter's surface compared to earth and moon?

I don't have the answer, I was just pondering this and figured someone here would know... (someone always seems to be an expert on something here.... LOL :)

My intuition says that you need to know the period of its orbit, not its weight/size... after all, a screwdriver and the space shuttle are vastly different sizes, but both orbit earth with the same period at the same altitude.

You would measure the force on Io from Jupiter's center.

dasviper is correct about the relevence of size. Gravity is acceleration -- on Earth, everything is accelerated toward the center of the Earth at 9.8 meters per second, regardless of it's mass. (The greater the mass, the greater the force, but that force will have to act on proportionally greater mass).

As it happens, luckily, I was doing this somewhat recently and still have the figures.

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.

Hopefully I didn't confuse anybody. Can anyone check this?

Image of Io

If Io's orbit is 422,000km from Jupiter's center, and Jupiter's <b>diameter</b> is 142,984km, then Io's center would be 350,508km from Jupter's surface.

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.

Re: Io is cool.
 

I did my best to plant the idea of standing on Io in the heads of two little girls last night, just doing my part.

From the photojournal:

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 :)

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:

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

Shadows
 

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

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.