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I've often wondered how the starship navigation in Halo works, but I've never really seen anyone touch on it at all except in books, in which we get orders along the lines of "one-two-seven by zero-four-five." I believe, however, that I have determined the answer. I've noted that none of said numbers exceed three-hundred and sixty, if memory serves me well. This leads me to believe that UNSC navigation is based on an azimuth-elliptical degree system similar to x-y coordinates. The degrees system is much easier, as it negates the need for a third coordinate value and requires fewer calculations, saving time. Here's how I'm guessing it works:

Imagine your ship in space. Azimuth is defined as "The vector from an observer (origin) to a point of interest is projected perpendicularly onto a reference plane; the angle between the projected vector and the reference vector on the reference plane is called the azimuth." (Source: Wikipedia). So draw an imaginary circle around your ship that is parallel to the bridge's floor. Assume that zero degrees would be if you're facing straight out the front of the bridge with your back to the engines. The direction you want runs clockwise, so if you want to turn "right" (remember that all directions in space are relative) you would want to turn, say, 81 degrees.

Now, the elliptical would be perpendicular to the azimuth plane, where a line through the circle would run through the center of the ship. Degrees would start by traveling upwards from zero degrees in front of you. So if you wanted to travel to your rear and "up," you might want 175 degrees. Therefore your directive to the navigation officer would be "zero-eight-one by one-seven-five at half power," and you would travel to the rear and right at half speed.

Granted, this is just speculation, but it makes sense to me.

Update: Noticed an issue with my example. If you wanted to go to the rear 175 degrees then you wouldn't be able to go 81 degrees to your right, as your ship would have to go forward and backwards at the same time. Needs a bit of revising. Perhaps rules on what degrees a Captain may use, like they can't use more than 180 degrees for the elliptical, and the plane of the elliptical runs through their azimuth direction?

This is why navigating in space is a royal pain in the ass.

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