The Kessel Run and the Parsec

“It’s the ship that made the Kessel Run in less than 12 parsecs!” – Han Solo, Star Wars: Episode IV – A New Hope (1977)

As hobby astronomers dust off their equipment for the summer months to start observing without freezing fingers, Hollywood used Memorial Day Weekend to punch out yet another terra blockbuster for Star Wars fans: “Solo: A Star Wars Story.”  Since we are soon running out of Roman numerals to denote original Star Wars movies (X) and tinsel town is risk averse to try anything new, every original character will get their own flick. Han Solo, a gung-ho, anti-imperial smuggler who has perennial issues with authority, famously boasted about his spacecraft, the “Millennium Falcon”, that it made the Kessel Run in less than 12 parsecs. For background information, the Kessel Run was a smugglers route used to transport a hallucinogenic drug from the mines of Kessel to a nearby distribution facility at the Si’Klaata Cluster. The normal route was 20 parsecs long and a buccaneering pilot needed to navigate an asteroid field and a black hole to safely move the bounty through interstellar space and past guarding imperial spacecraft. While we are not trying to peer review such outrageous claims of “making the Kessel Run in less than 12 parsecs”, we are more interested in asking ourselves “What is a parsec?” and “Why do we need it?” I will do my best to explain it as simple as possible so that you will understand it in less than 20 minutes.

A parsec is a word creation combining the words “PARallax” and “arcSECond.” Let’s start and dissect this monster. First, what is a parallax”?

“A parallax is the effect whereby the position or direction of an object appears to differ when viewed from different positions.” – Google Dictionary.

Here is an example you can do at home:

Hold a pencil in one hand close to your face against a background (like a wall). Maybe even line up the pencil with the edge of a doorframe as a reference point. Observe with only one eye open and then with only the other eye open — your observation points. Notice the “apparent” difference in the position of the pencil? The “real” position of the pencil of course didn’t change but your point of view did (the left eye versus the right eye). This apparent difference in position is called a “parallax” and is measured in degrees (refer to Image A below). Next, hold the pencil at arm’s length, line it up with your reference point (door frame) and repeat the observations with only one eye open. The “apparent” difference in the position of the pencil is now smaller. The farther away the object, the smaller the parallax angle. The closer the object, the larger the parallax angle!

Image A:

Image By Matthias SchmittIn order to calculate the unknown distance to the object we need two input variables:

The distance between your observation points is called the baseline. The apparent difference between measuring an object’s position from point A and Point B is called parallax. To measure the parallax is a bit trickier to measure but we have help from our good friend the circle, which is 360 degrees.

  • Parallax between observation A and B at arm’s length: 5.5 degrees. (Quite rudimentary, but if you stretch out your arms to each side you have 180 degrees, then half to 90 degrees etc. until you have an approximate angle for the change in observation with the left eye and right eye; be careful you might knock over an ice latte in the process).
  • Baseline 2 inches (measured between iris of left eye and right eye)

Turning the ratios from Image A into math, the baseline to the circumference of the large circle is equal to the parallax, the diameter angle to 360 degrees, we get the following formula:

Image By Matthias Schmitt

Obviously, this simple geometry not only applies to close objects, but to far away objects found in nature: a tree, a mountain (surveyors use this method) and to celestial objects as well. Let’s gather a few variables from famous astronomers’ experiments and see the results:

  Object Baseline Parallax Result
Schmitt 2018 Distance to pencil 2 inches (distance between eyes) 5.5°(Angle of two apparent positions of pencil) 20.8 inches calculated (measured 22 inches; error ±5.7% )
Erastothenes 200 BC Earth’s radius 490 miles (distance between Alexandria and Syene) 7.2°( Angle shadow between Syene and Alexandria) 3,978 miles (measured 3,986 miles; error ±0.2%)
Cassini 1673 Distance to Mars 4,400 miles (distance between Paris and French Guiana) Couldn’t find the actual numbers. Reverse calculation shows 0.0028 degrees. 87 million miles at Perihelion (Measured 93 million miles; ±7%) Distance

It is simply astounding how close scientists, except me of course, have calculated with simple means unimaginable distances and have come very close to actual numbers.

Since we now know what a parallax is, we can move on to the definition of a stellar parallax and then parallax arcsecond, or parsec.

Image B

Image By Matthias Schmitt

The largest possible baseline for an observer stuck on planet Earth is 2 AUs (Astronomical Units). Why? Because our distance (radius) to the Sun is defined as 1 AU. The largest diameter between two points in the elliptical orbit around the Sun is 2 AUs. We can measure a celestial object at two different times on our orbit, let’s say January 1st and July 1st. I know someone paid attention. It’s not exactly 182.5 days because February only has 28 days. We measure a distant star against the background stars, assuming that the background stars don’t move and ignoring the wobble of the Earth (let’s continue to simplify a little) and have the 2x parallax angle we need. Convention defines a star’s parallactic angle, more commonly its parallax, as half the apparent shift relative to the background. As these shifts are very small, astronomers find it more useful to measure the parallax in arc seconds rather than degrees. As there are 360 degrees in a circle, 60 arc minutes in a degree (the Moon has an angular diameter of approximately 30 arc minutes – your finger is about 1 degree held up at arm’s length) and there are 60 arc seconds in one arc minute. Hence, we can replace the 1° in our formula with 3,600 arc seconds and get arc seconds.

Image By Matthias Schmitt

Please remember: The use of the unit of length parsec only applies to measurements with the baseline of 1 AU.

Proxima Centauri displays the largest known stellar parallax, since it is the closest star. The parallax is 0.77”. Let’s plug this into our simplified formula above and we get 267,884 Astronomical Units or 4.23 Light Years. Now, we cannot send a spacecraft there and actually confirm that we are correct but no astronomer has ever falsified it.

In the January, 2016 issue of Eyepiece, Bart Erbach wrote about ESA’s magnificent Gaia spacecraft. One of its science objectives is to measure the distance to stellar objects by taking pictures 6 months apart and then comparing their parallax. Its instruments are so sensitive that it can measure the parallax of distant objects accurate to 6.7 microarcseconds (Source: ESA). A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth.

How distant a star can Gaia measure, you might ask?

Image By Matthias Schmitt

The Milky Way is 100,000 Light years across. The Gaia spacecraft would be able to resolve all the stars in our home galaxy but we have to take into consideration the luminosity, the magnitude of an object. Gaia can detect objects with a magnitude of 20.5, which is about 650,000 times fainter than an unaided eye can see. This will be good enough to measure the parallaxes of 1 billion stars within 25 kiloparsecs (81,500 light years) to 10% accuracy in our Milky Way galaxy.

Now we know what a parsec is and that we need it to measure the distance to celestial objects we otherwise could not figure out. The farther away an object, the smaller the angular diameter will be and given the resolving power of telescopes, we are limited to how far we can measure distances using that method.

Congratulations on stepping on the first rung of the Cosmic Distance Ladder.

With regards to Han Solo and his claim?* He might be a great navigator and complete the Kessel Run in less than 12 parsecs but he still needs to know what is a parsec.

*With the recent release of “Solo: A Star Wars Story”, Lucasfilm and Disney fixed the past error in astronomy terms made in the 1977 release of Star Wars: A New Hope.  The Kessel Run has been redefined as a route taken to the planet Kessel and back and not a fixed distance to be completed in a certain amount of time.  Han Solo found a shorter route through space to complete the Kessel run in a distance of just over 12 parsecs, which is the correct use of the distance measurement of a “parsec”.  Even Hollywood can learn science when it wants.

 

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