"You've never heard of the Millennium Falcon?...She's the ship that made the Kessel Run in less than 12 parsecs...She's fast enough for you old man." -Han Solo, Star Wars Episode IV: A New Hope

What do you do when you want to measure the distance of a nearby star and there are no computers, no spacecraft and no power plants to generate electricity? Well, what Friedrich Wilhelm Bessel did in 1838 was use trigonometry and the parallax effect to calculate the distance of a star based on the distance from the Earth to the Sun.

The Earth averages a distance (radius) of 92,955,807.27 miles or 149,597,870.7 km from the Sun. That distance - the length from the Earth's center to the Sun's center - is known as an "astronomical unit" or AU. One AU is one trip from the center of the Earth to the center of the Sun.

Astronomers took (and still take) advantage of this distance to help them measure how far away stars are from the Earth. To measure the distance, astronomers note the location of a star on one date - say Feb. 8. Half a year later, when the Earth is at the opposite point in its orbit (on the other side of the Sun), Aug. 9 in this case, the astronomer notes the star's location again.

Because the Earth has moved, the position of the far away star relative to the blanket of stars behind it also appears to move. This movement is called "parallax."

To understand how parallax works, stand at one end of the room, facing a poster on an opposite wall. Hold a pencil out in front of you at arms length and at eye level. Note what point on the poster is being covered by the pencil. Now close your left eye, keeping your right eye open. Next, close your right eye and keep your left eye open. Does the pen appear to move relative to the poster behind it? It should. That apparent movement is called parallax.

Imagine that your left eye is the Earth on one side of the Sun and your right eye is the Earth at the opposite point in its orbit, on the other side of the Sun. The pen is the star being studied and the poster is the trillions of stars beyond. Since astronomers know the distance between the Earth and the Sun, they can draw a triangle, with the Earth-Sun distance at its base, to measure how far away an object is. This technique is known as "triangulation" and is also used in navigation.

After they figured out how to use triangulation to measure the distances of stars, astronomers needed a unit to describe the distances of far-away objects. It take way too many feet, miles or kilometers to describe that kind of a distance. By 1913, astronomers had developed the unit, but needed a name. Astronomer Herbert Hall Turner came up with the term "parsec" which stands for the 'parallax of one arc second'.

The parsec was created so that astronomers had a handy astronomical unit. Its distance depends on the distance from the Earth to the Sun and also the divisions of a circle.

A circle is divided into 360 degrees. (If the circle were a pie, it would be divided into 360 perfectly equal slices.) Each of those degrees is divided into arc minutes, each equal to one sixtieth of a degree. (Very small slices cut from an original slice.) Arc seconds are one sixtieth of an arc minute. (Teeny, tiny, little slices shaved off of the very small slices.)

Let's pretend there is a star in the sky whose parallax (apparent movement) was the same width as one arc second. Now, let's draw a right triangle with the Earth-Sun distance as its base and this star as its top point. Lets put a mirror image of the triangle on top. The angle of the triangle originating from the star would be the parallax -- one arc second.

Through the rules of trigonometry, we can then figure out the length from the Sun to that imaginary star. That length is a parsec -- roughly 19 trillion miles or 31 trillion kilometers. It's 206,265 AU (or over 200,000 times the distance from the Earth to the Sun) -- almost 3.3 light-years long.

To appreciate how far a parsec is and how tiny an arc second is, think about an archery target. A regulation outdoor archery target is 80 cm across. The two lines of the tiny 'X' at the center of the target are each 4 mm (0.4 cm) long. If the parallax of one line was 4 mm, then the corresponding 'parsec' length would be just over a half mile -- 2,706 ft or 825 m.

Today, astronomers and astrophysicists still use the parsec as a celestial unit of measurement. They also use the light-year, a unit defined as the distance light travels in a vacuum in one Julian year...but that's an explanation for another day.

Let's get back to Han Solo and the Millennium Falcon. The Falcon would have made the Kessel run in some unit of time (10 minutes) and not a unit of distance. Water doesn't freeze at 32 furlongs, it freezes at 32 degrees Fahrenheit.

So, even though the Millennium Falcon can't do anything in 12 parsecs, at least Han Solo's smile can still be 12 parsecs wide.

Excellent explanation Echo

ReplyDeleteAn excellent article. Thanks

ReplyDeleteGreat explanation. Thank you very much. Just as a point of nerd interest, the Millennium Falcon had "special modifications" to the navigation computer. This allowed the ship to plot a course that most other ships wouldn't have been able to make, such as flying closer to stellar bodies or through a nebula. This would be risky, and as such most navigation computers would plot a course clear of those things. By taking the "short cut" the Millennium Falcon could arrive at its destination having traveled a shorter distance. Thus, it could make the kessel run faster than other ships, which would normally take a longer and safer route, by traveling less distance (in this case, less than 12 parsecs).

ReplyDeleteAnd, of course, traveling at high speeds results in length contraction, so a distance that measures 12 parsecs to a stationary person would be shorter to you if you were traveling faster. If my calculations are correct, when the Millenium Falcon is traveling at only 86% of the speed of light, 12 parsecs is contracted to only 9 parsecs.

ReplyDeleteTechnically, I guess, length is contracted no matter how fast you go, so anyone can make a 12 parsec trip in less than 12 parsecs. If the Kessel Run is actually 16 parsecs and you do it in less than 12, that means you can travel faster than 86% of the speed of light, which would indeed be impressive.

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