That sentence is a lie!

@ Flying sardines: (May 14th, 2009 at 1:59 pm )

Ironically enough, some people would consider your post there to be pointless!

Thanks for all the input. I understood about the L2 point and the station keeping required. I guess it’s the animation that is the most confusing that is found at
http://www.esa.int/SPECIALS/herschelplanck/SEMVW10YDUF_1.html#subhead4

It shows the satellite orbiting the L2 point at some huge distance. Looks to be greater than the orbit of the moon around the Earth. Maybe if the animation continued longer, the “orbit would condense to a very small station keeping orbit.

Astronomynut Said:
May 14th, 2009 at 1:42 pm

Phil,

The ESA webpage says that the spacecraft will travel to and ORBIT the L2 Lagrange point. Not orbit at that point, it says will orbit the L2 Lagrange point. They even have a nifty little animation showing the path to get there and the orbit once at L2.

How can a spacecraft orbit a virtual point in space?

Google “Interplanetary Superhighway” if I haven’t explained the concepts well enough. Past halo orbits, my intuition is hanging by the skin of its teeth.

Lagrange points are the places in space where the gravity of two objects adds or subtracts just right to keep a third (the satellite) in an orbit it wouldn’t ordinarily be able to maintain. For L1, L2, and L3, the ones in a line drawn through the other two, Sun and Earth in this case, it’s usually explained like the nearer object is pulling on the satellite to allow it to orbit at a speed that keeps it in that line. Specifically, with L2, which lies on the far side of the Earth, the Earth is pulling down because if the satellite was going around the sun that fast it would zoom out to a farther orbit and slow down relative to Earth.

To understand a Halo orbit, a Lyapunov orbit, and a Lissajou orbit, you need to add some dimensions beyond a line. If you think of the Earth having the satellite on a leash, it gets a bit clearer. At L1, the satellite is orbiting closer to the Sun than Earth and would naturally want to go around faster than Earth. At L2, the satellite is orbiting farther than Earth and would naturally want to go around slower than Earth. The Earth uses its gravity to tug it around at the same speed. If you plotted this out, the satellite would need more energy to move out away from the Sun-Earth line and this energy curve would look like a U shape PERPENDICULAR TO the Sun-Earth line, so it settles back to the bottom of the U right on the Sun-Earth line. This is the ’stable’ part of quasi-stable.

If you look at the satellite’s tendency ALONG the Sun-Earth line, though, It’s actually an upside down U (or lower case n, sans serif). That is, if you move the satellite just slightly closer or further to the Sun than the sweet spot it quickly moves even further away from the sweet spot. This is why it is quasi-stable, it is only stable in one direction. In fact, putting the two curves together in three dimensions, you wind up with a saddle shape with the spine along the orbital path. As long as the satellite is on the spine of the saddle everything is fine, but it’s like balancing a marble on a saddle. It’s really fiddly.

But, if you take that saddle and attach it to a string anchored at you sweet spot and swing it around perpendicular to the Sun-Earth line (i.e. add a bit of centripetal motion) you wind up with what describes the possible paths of the satellite in an orbit around the sweet spot. The length of the string is the size of the orbit. Blur that out and it looks like the inside of a donut. The larger the donut, the flatter the saddle is. So adding that bit of motion around the sweet spot makes it easier to maintain your position along the Sun-Earth line. And the orbit looking from a place along the Sun-Earth line looks like a halo projected against the stars. Thus, the name. In three dimensions, though, it looks like a ring that’s been hammered against a sphere the size of the Lagrange point’s orbit around the Sun.

A Lyapunov orbit is the same sort of idea but the orbit lies within the plane of the Earth’s orbit around the Sun, the varying speed of the orbit pulls it back up the saddle. A Lissajou orbit is essentially a hybrid of the two that moves both out of the plane of Earth’s orbit and in and out along (but not on) the Sun-Earth line.
I think that last bit’s right.

Have I mentioned yet that I think this book rocks?

Anyway, just had to tell you that I followed through on my promise.

I going to school to become an elementary ed teacher, and the grades I’d love to teach is anywhere from 4th to 6th grade. I can already tell you that I will be using some of your book in my classroom. Your book makes astronomy interesting, while the “standard” science textbook for elementary grades makes even an astronomy enthusiast want to take a long nap. So I fully plan on making my lessons a hell of a lot more interesting and exciting, and one of those ways of livening things up will be with your book.

Thanks again for the fantastic book,

Hava