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Which way is North?

Published on Nov 2, 2006 at 11:43 am. 1 Comment.
Filed under planets.

As planets and asteroids orbit the Sun, they rotate. However, the axis of their rotation is seldom the same as the axis of their orbit. The angle between the two is called the inclination. Earth is inclined about 23.4Â°. Mars is only a bit more, at 25.2Â°. But, Uranus is 97.9Â° inclined. Meaning that its rotational axis is nearly perpendicular to its orbital axis. In other words, it is laying on its side as it orbits the Sun. Venus is a whopping 177.4Â° inclined.

Whoa, there. An angle of 180Â° makes a straight line. If Venus had an inclination of 180Â°, then its rotational axis would be parallel to the orbital axis, so why wouldn’t that be a 0Â° inclination? For that matter, look at Uranus’ inclination. How can the angle between two axes be more than 90deg? Why not just measure the angle from the other direction? What gives?

Well, quite simply, the inclination isn’t just the angle between the two axes. Rather, it is the able between the north pole of the planet and the north pole of the planet’s orbit. So, that means that Venus’ north pole is pointed opposite the north pole of its orbit. Huh? How do you know which is the north pole?

For that matter, how do you know which is the north pole on any planet? Take Mars for instance. We know that it is a sort of bipolar planet. The southern hemisphere is higher in elevation, and much more heavily cratered than the northern hemisphere. Why, why do we call one hemisphere north and one south, and why are they opposite on Venus?

This has to do with how we define coordinates. By convention, we use what are called right handed coordinates. In this convention, the choices of coordinate axes are not totally arbitary, You can pick any axis as an x-axis, picking one way to be positive and the other to be negative. The only constraint on the y-axis, then, is that it be perpendicular to the x-axis. But, once you define those two, the z-axis is fixed. There is only one way to put it. It obviously has to be perpendicular to the other two, but the direction of positve is also fixed. The convention that we use is called the right hand rule because you can use your right hand as a tool to help remember which way is which. You hold your hand in the direction of the positive x-axis. Then you twist your hand, keeping it parallel to the x-axis, until you can curl your finters to point in the direction of the positive y-axis. Your thumb points in the direction of the z-axis. This is right handed coordinates.

Since the Cartesian coordinates that we use are right handed, it is no surprise that angular coordinates will be, too. In angular coordinates, you hold your right hand so that the fingers curl in the direction that an object is rotating. Your thumb will then point in the positive z direction or, in layman’s terms, the north pole. Do this for the rotation of a planet, and you get which end of the planet is the north pole. Do it for the planet’s orbit, curling your fingers in the direction that it orbits the Sun, and you find the north pole of the orbit.

So, now that you have the north poles, you can then measure in inclination between the two. But, if you do this, you notice something odd. Most of the planets rotate more or ness in the same direction that they orbit. Venus rotates the opposite direction (hence the nearly 180 degree inclination). The reason for this is still a bit of a mystery. Several theories have been put forth, but none has had any definitive evidence in its favor. We just don’t really know why Venus is strange.

But, that is how you know which end of a planet (or star) is the north pole.

-Astroprof

(Image credit: IAU, NASA, Astroprof)