The orbit around Sirius is elliptical.

It was notable for the fact that it was not moving in an asteroidal ellipse.

And that will be really cool.

About a billion miles away, here's what happens to Earth's orbit it becomes elliptical instead of circular.

While it's true that our orbit's not perfectly circular, those pictures in our science books, on TV, and in the movies give an exaggerated impression of how elongated our orbit is.

Ellipse Draw an ellipse

So this is my y axis, this is my x axis, and our path is going to be the unit circle.

Ellipse

An ellipse

Ellipse Shape

Ellipse Shape

And all that does for us is, it lets us so this is going to be kind of a short and fat ellipse.

Draws ellipses and circles

Superquadrics

A cyan ellipse

Cyan Ellipse

Elliptical Selection

elliptical dab ratio

Let me do an ellipse in another color.

If this is one focus point right here, and this is the other focus point, this ellipse could be defined as the set of all points, or the locus of all points, where if I take the distance of any one of these points that exist on the ellipse and take the distance to each of the locuses sorry, each of the focuses if I take that nope, I don't want to do that if I take that distance and add it to this distance, so

And in fact, what's even the relationship.

So Earth's orbit maybe looks something like that.

Elliptic Gradient

Change ellipse

Close ellipse

A lot of people have heard of an astronomer called Johannes Kepler and how he proved that planetary orbits are elliptical and that the sun is not at the center of the orbit.

And if I tilted it the other way, the ellipse would squeeze the other way.

You can do very similar thing for elliptical galaxies which is essentially same thing we've done for clusters.

Select Ellipsoid Model

Now, another super interesting, and perhaps the most interesting property of an ellipse, is that if you take any point on the an ellipse, and measure the distance from that point to two special points which we, for the sake of this discussion, and not just for the sake of this discussion, for pretty much forever, we will call the focuses, or the foci, of this ellipse.

So this is still elliptical shapes.

Superquadric ellipsoid

Superquadric Ellipsoid

superquadric ellipsoid

So that's the origin right there.

One month ago, the earth suddenly changed its elliptical orbit, and in doing so began to follow a path which gradually, moment by moment, day by day, took it closer to the sun.

Filled ellipse Draw a filled ellipse

Filled Ellipse

So, just to make sure you understand what I'm saying.

So the robot is obviously capable of executing any curve trajectory.

We can decompose rotation curves to the contributions from different components.

Orbital

It's really manifested there.

And there is a furthest point from the sun, and this is called aphelion, (a feel ion, ap helion).

Makes an elliptical or circular selection