## What do all the angles in a table for a planet's orbit mean? (Advanced)

What do all the angles in a table for a planet's orbit mean? Or how do astronomers describe the orientation of a planet's orbit in space?

This can be confusing as a whole, so I'll try to break it into parts. You should also follow along on this diagram from Wikipedia as you read through this:

http://en.wikipedia.org/wiki/Orbital_elements

Just like we choose the Greenwich meridian on the Earth as a reference for longitude, we have to choose references in the sky to measure all our angles from. For planets orbiting the Sun, the most common reference plane is the ecliptic (gray plane in the image)--the plane in which the Earth orbits. For moons orbiting a planet, it's normally the planet's equatorial plane.

Now you have to put in the plane in which the planet (yellow plane). In general the ecliptic and the planet's orbital plane are inclined, and the angle between the planes is the inclination.

The line where the two planes meet is called the line of nodes. The position of the line matters, because due to extra forces acting on the planets' orbits, the whole orbital plane can rotate, and the line of nodes will spin around in the reference plane (this is important for things like eclipses).

So if you want to tell someone how the orbit is oriented, you first have to tell them how the orbital plane (or equivalently, the line of nodes) is oriented. For that we have to agree on an arbitrary reference direction, and measure the angle between that direction and the ascending node. You'll notice that the planet passes through the two endpoints of the line of nodes. The ascending node is the point where the planet is coming from below the plane and crosses to being above it.

The conventional reference direction is the line of ares (that's the symbol on the wikipedia page). This is the direction toward Earth on the spring equinox (remember that the gray plane is the Earth's orbital plane, so the Earth will be at a specific place on the spring equinox). It might seem arbitrary, and it many ways it is--but the Greenwich meridian is just as arbitrary! You just need to pick one. The angle measured counterclockwise from the line of Ares is called the longitude of the ascending node. This is the green angle capital Omega in the diagram.

But even if someone has told you how to orient the orbital plane, they still have to tell you how to orient the orbit within the plane (which way does pericenter point?). This angle we measure in the direction the planet is orbiting, from the line of ascending node (blue lowercase omega in the diagram). This angle is called the argument of pericenter.

Finally, if you want to say where the planet is in its orbit at a particular time, you measure the angle from pericenter to the planet (the red nu in the diagram). This angle is called the true anomaly.

#### Dan Tamayo

Dan Tamayo was a PhD student working with Professors Joe Burns and Phil Nicholson.  Dan is interested in orbital dynamics generally, but his research has focused on debris generated at the outermost gravitational reaches of the giant planets by the Jovian planets' irregular satellite populations.

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