Orbits

[stevo247]

I'm trying to get an accurate representation of the moon's orbit around the earth. It seems as though it is commonly characterized as going "round and round" the earth. I was under the impression that the moon kind of swerves in and out of the orbital path of the earth. I guess my question is, what is the path of the moons orbit around the sun? Is it a series of "loopty loops" or is it a wavy line?

[Janus]

Wavy line. Not only that, but it is a wavy line that always curves toward the Sun.

[kaneda]

Earth varies it's distance around the Moon by 27,000 miles, averaging 238,000 miles away. Essentially the Moon orbits the Sun but is pulled into a further orbit by the Earth.

[Klaynos]

A nice link I found....

 

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

[stevo247]

This analogy from that link was very helpful:

Imagine you're driving on a circular race track. You overtake a car on the right, and immediately slow down and go into the left lane. When the other car passes you, you speed up and overtake on the right again. You will then be making circles around the other car, but when seen from above, both of you are driving forward all the time and your path will be convex.

 

O.K. So now I'm wondering about the orbit of the earth around the sun. The sun, from what I remember, is moving towards something ?north? So if the sun is moving, then the orbital path of the earth is not a closed circle. Using a very complex modeling system (my fist and my finger), it looks like the orbital path of the earth is more like a spiral. Is that what it is?

[Riogho]

Kepler says ellipse!

[Klaynos]

Kepler says ellipse!

 

But that's relative to a static sun... if you do the earths orbit around the centre of the galaxy, what shape is it?

[stevo247]

O.K. So now I'm wondering about the orbit of the earth around the sun. The sun, from what I remember, is moving towards something ?north? So if the sun is moving, then the orbital path of the earth is not a closed circle. Using a very complex modeling system (my fist and my finger), it looks like the orbital path of the earth is more like a spiral. Is that what it is?

 

 

Kepler says ellipse!

 

 

But that's relative to a static sun...

 

 

So, if the sun is dynamic (it is moving right?), then is the idea that the earth has a closed elliptical orbit around the sun, not an accurate representation of reality?

[D H]

Kepler says ellipse!

Kepler wrote his empirical laws 400 years ago, before Newton. That objects have elliptical orbits is true only for the case of two isolated point masses. The solar system comprises multiple masses. Kepler's Laws are approximately correct. They are not exact.

So, if the sun is dynamic (it is moving right?), then is the idea that the earth has a closed elliptical orbit around the sun, not an accurate representation of reality?

Stevo, you are acting as if there is some representation of the Earth's orbit that is better than all others. From the perspective of a Sun-centric or solar system barycentric reference frame, the Earth moves in a nearly elliptic orbit around the Sun.

 

It is not an ellipse because of the Moon and Jupiter (and all of the other planets to a much lesser extent).

[stevo247]

Stevo, you are acting as if there is some representation of the Earth's orbit that is better than all others. From the perspective of a Sun-centric or solar system barycentric reference frame, the Earth moves in a nearly elliptic orbit around the Sun.

 

What is the representation of the Earth's orbit from the perspective of the Earth? Not that it's better, it just seems like a reasonable place to start.

[Sisyphus]

What is the representation of the Earth's orbit from the perspective of the Earth? Not that it's better, it just seems like a reasonable place to start.

 

From the perspective of the Earth, the Earth is motionless.

[D H]

From the Earth's perspective the Earth is of course stationary.

 

All reference frames are equally valid. All that it takes is to properly express the equations of motion of some system of objects with respect to some reference frame, and voila! out pops the behavior of those objects from the perspective of that frame. How easy (or hard) it is to express those equations of motion depends a lot on the choice of reference frame. I wish you lots of luck should you choose to model the Earth's atmosphere in a solar center barycentric reference frame. The obvious choice for this problem is an Earth-fixed frame (i.e., a frame moving with and rotating with the Earth). This frame on the other hand doesn't make a whole lot of sense if your goal is to modeling the motion of the moons of Jupiter or the motion of some planet orbiting some remote star.

[stevo247]

So, what frame of reference "sees" the Earths orbit as a spiral rather than a closed ellipse?

[Sisyphus]

So, what frame of reference "sees" the Earths orbit as a spiral rather than a closed ellipse?

 

Well, the real answer is "an infinite number of different reference frames," since you can set your reference frame as whatever you want. What I think you're going for, however, is probably the center of mass of the galaxy. That's usually the frame implicitly being used when talking about the "sun's motion." If the sun were moving north relative to that frame (which I actually don't know, but I'll take your word for it), the Earth would be moving in a helix (not a spiral, but commonly called one) relative to that same frame.

[swansont]

So, if the sun is dynamic (it is moving right?), then is the idea that the earth has a closed elliptical orbit around the sun, not an accurate representation of reality?

 

The center-of-mass of the earth-moon system would be more closely tracking the ellipse. As D H points out, you'd still have other perturbations.

[stevo247]

Is the shape of the Suns orbit around the center of the galaxy elliptical, with the planets having the shape of a helix?

 

Also, what is the orientation of the ecliptic plane of our solar system in relation to the galactic plane?

[Sisyphus]

Is the shape of the Suns orbit around the center of the galaxy elliptical, with the planets having the shape of a helix?

 

More or less. But those are definitely approximations, given the enormous complexities involved. The sun isn't moving "due north," either, so I suppose that means the planets move in kind of "slanted" or "leaning" helices.

 

Also, what is the orientation of the ecliptic plane of our solar system in relation to the galactic plane?

 

Well, objects in our solar system are not in just one plane - the planets alone vary by ten degrees or so, and comets and other objects are generally inclined a lot more. The galactic plane similarly isn't perfectly defined (it is, after all, about 1000 light years thick). However, roughly speaking, they're inclined about 60 degrees to one another.

[stevo247]

Sisyphus,

 

Thanks for clearing that up for me. I think I'm finally getting the general picture, approximately. If the galaxy is like a large disc, and our solar system is like a fried egg, it's not like the fried egg is oriented flat on the disc, but rather it's tipped towards perpendicular at 60 degrees as it orbits the center of the galaxy, with the planets having a helical orbit relative to the center of the galaxy. I wonder, does the motion of the sun during it's orbit move up or down at all or does it move closer or further away at all? Is there any “waviness” in it's orbit? Also, is the velocity constant or does it slow down or speed up at all?

[Sisyphus]

I wonder, does the motion of the sun during it's orbit move up or down at all or does it move closer or further away at all? Is there any “waviness” in it's orbit? Also, is the velocity constant or does it slow down or speed up at all?

 

As far as up and down and in and out, I don't know whether there are any overall trends. It would only be a perfect ellipse if the galaxy were a point mass, which it obviously isn't. It's 100,000 light years across, made up of billions of objects unevenly spread out, and we're inside it. So any particular star is going to be pulled around quite a bit by nearby objects, etc. The overall path would probably be close to an ellipse at the largest scale, but not necessarily, as it could get "slingshot" around through encountering other objects, or even the influence of other galaxies.

 

As for speeding up and slowing down: yes. The arms of the spiral are regions of denser matter, and act like traffic jams. Objects passing through the arms are slowed by gravity.

[Deja Vu]

Sisyphus,

I wonder, does the motion of the sun during it's orbit move up or down at all or does it move closer or further away at all? Is there any “waviness” in it's orbit?

 

The sun's orbit around the galactic core is mostly elliptical. And it does oscillate during it's orbit, it goes up and down relative to the galactic plane as it goes around the core.

[igosaur]

If the Earth is rotating faster than the Moon orbits giving rise to tidal forces which are speeding up the moons orbit and thus increasing it's distance from the Earth, will there come a point where the rotation of the Earth and the orbit of the Moon will match and then stay that way indefinitely or will it never quite catch up?

[Sisyphus]

If the Earth is rotating faster than the Moon orbits giving rise to tidal forces which are speeding up the moons orbit and thus increasing it's distance from the Earth, will there come a point where the rotation of the Earth and the orbit of the Moon will match and then stay that way indefinitely or will it never quite catch up?

 

Theoretically, it would eventually reach that point. But that would take 50 billion years, at which point the Earth and the Moon will long since have been destroyed by the death of the Sun.

[stevo247]

I can't remember how I came upon this question, but I thought it was interesting enough to write it down. Is there a simple way to explain this:

 

How is it that orbit speeds of planets orbiting the sun decrease steadily with distance from the sun, yet orbit speeds of stars circling the center of the Milky Way galaxy remain nearly constant?

Edited August 12, 2008 by stevo247
Typo

[swansont]

I can't remember how I came upon this question, but I thought it was interesting enough to write it down. Is there a simple way to explain this:

 

How is it that orbit speeds of planets orbiting the sun decrease steadily with distance from the sun, yet orbit speeds of stars circling the center of the Milky Way galaxy remain nearly constant?

 

[math]\frac{mv^2}{r}=\frac{GMm}{r^2}[/math]

 

[math] v = \sqrt{\frac{GM}{r}}[/math]

 

In the solar system, M is essentially a constant, so v decreases. However, if M were to increase at the same rate as r, v will be a constant.