The Kessel Run in Less than Twelve Parsecs

The millennium falcon seen just off-angle from head-on.

You’ve never heard of the Millennium Falcon?… It’s the ship that made the Kessel Run in less than twelve parsecs. – Han Solo

If you’ve seen Star Wars: A New Hope, you’ll have heard the above quote. People often think Solo refers to his ship’s speed when he says this, but that is not the case. A parsec is a unit of length, not of time! In fact, it is defined as the distance from the sun to an astronomical object such that the parallax angle (the angle between lines from the Earth and the Sun to that object) is one second of arc. Parallax One parsec is the distance from the Sun to a nearby astronomical object that has a parallax angle of 1 second of arc.

A schematic drawing of the angle of 1 arcsec and the distances 1 parsec and 1 au. A line is drawn between a star and a body labeled with a distance of 1 parsec. An object is orbiting the star labeled with a distance of 1 au. From two opposite sides of the orbit lines are drawn to the distant object. The lines from the orbiting body and the sun to the distant object are marked as having an angle of 1 arcsec.

One parsec is the distance from the Sun to a nearby astronomical object that has a parallax angle of 1 second of arc.

Using this information, we will calculate the length of a parsec in meters.

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Deriving the Lorentz Factor

The Lorentz Factor is defined as \gamma = 1 / \sqrt{1 - v^2 / c^2} with v the relative velocity between two reference frames (or two objects, if you will) and c the speed of light. This is the factor with which length contracts and time dilates between two reference frames. For example, if you’d sit in a rocket that was traveling at 80% the speed of light relative to your family on Earth, the Lorentz Factor would be \gamma = 1 / \sqrt{1 - 0.8^2} = 1 \frac{2}{3}.

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