• Choose a month

  • Rapt in Awe

    My Journey through the Astronomical Year

    Think of this as a "companion text" to this, the main web site. Not required reading, butI hope you'll find it interesting and helpful.

Simply mind-boggling: Universal Measuring Sticks and Observing Logs

Measuring an 11-foot (meters) strip. (Click image for larger version.)

Measuring an 11-foot (3.4 meters) strip. (Click image for larger version.)

While simple, this project is next to impossible to depict well in a photograph because each “measuring stick” is just a few inches wide and more than 10-feet long. But build one and I bet you’ll find it a mind-bending experience!

I call this project the  Universal Measuring Sticks and Observing Logs and together these “measuring sticks” serve a simple function – they put into perspective the distance of each object you observe. And even if you don’t observe, they’ll help you get a handle on the incredible distances to the planets, stars, and other galaxies.

To do this our basic measuring unit will be the speed of light – 186,200 miles a second (300,000  kilometers a second). That, according to Einstein, is the speed limit for the universe. Nothing can go faster. So we simply ask ourselves how far will light go in a minute? An hour? A year?  Just starting with the distance travelled in a second boggles the mind – the distance that light travels in a single second would take it all the way around the Earth more than 7 times.  That is, it’s 24,902 miles around the Earth at the equator and if you divide that into 186,200 you get (rounded) 7.5 ( 40,076 km divided into 300,000 kmps gives you 7.5 as well). So our most basic unit, the light second, is already far larger than anything most of us have experienced. But at least it gives us a starting point to begin to get even more mind-numbing distances into perspective.

Materials needed for this project:
(2) 11-foot (or 3.3meter) lengths of adding machine tape*
pen or pencil(s)  – different colors helpful, but not necessary
calculator (helpful) or scrap paper

*You  can use any 11-foot strip of paper you have or create – but I found adding machine tape the easiest way to do this and it’s commonly available. Some might want to use four lengths and not use each side – or you might want to use a dozen sheets of ordinary paper. The goal is to make four scales each 10 feet (120-inches) long with little extra paper on each end to keep it neat.

We will actually make four measuring sticks, each a bit over 10 feet ( 3 meters) long. We need four because it is impossible to fit everything on a single scale and still have it readable.

Well, not absolutely impossible.  For example, the first and smallest scale used is for the solar system. On that scale, one inch  equals two light minutes. (If you’re using the metric system, then start with a scale of 25mm equals two light minutes – very nearly the same. ) That scale puts the moon just 1/100th  of an inch (a quarter of a millimeter) from Earth at one end with Neptune (and Pluto) near the other end.  But if we were to include the nearest star we observe in our northern hemisphere skies other than the Sun, it would  require a piece of adding machine tape 36 miles (57.9 kilometers) long! Possible – hardly practical. Oh – and were we to include the nearest galaxy we observe, the Andromeda Galaxy, we would need about 10 million miles (16 million kilometers)  of tape. Sort of defeats the purpose of a scale model! So it is for very practical reasons that we have created four measuring scales.

To use each scale start by putting a vertical line across your tape about 6-inches from the left hand edge. This is your starting point, which is, in all cases, Earth. To the left of this, put down the name of your measuring stick and the scale being used for that stick. To the right of this, calculate the distance to each item you observe, mark it and identify it on the scale. If you like, include the date observed.The result should look something like this measuring stick for the solar system – keep in mind this is just the first part – the whole “stick” goes onf or 10 feet.

This is the starting end of a solar system measuring stick.

This is the starting end of a solar system measuring stick.

General notes that apply to each stick

  • Light travels at 186,282 miles (300,000 km) a second. We use the speed of light as our measuring unit.
  • On the second and third scales in particular you may find that several objects are at, or near, the same distance, so to mark and identify them you will need to use the full width of the paper.
  • Distances up to 1,000 light years are pretty well known now and reasonably accurate because of measurements taken by the Hipparcos* satellite. Distances beyond this get increasingly fuzzy with many different indirect methods to determine them. For this reason you should regard all these distances as reasoned approximations. For close objects (within 1,000 light years) use sources written after the Hipparcos* measurements which were published in 1997.
  • Our distances are also an indicator of time – each distance tells us how long ago the light we see left an object. You may find it fun to mark all but the first scale with historical, evolutionary, and geological events on Earth. Such time references add to your perspective.

You can look up distances and calculate them to scale any time, but the real goal here is to reinforce the observing experience, so if you are observing , I suggest you use this more as a log and  mark your scale either when planning an observing session, or when reflecting on that session after observing. That way the abstract experience of learning and calculating distances is in your mind along with the real-life experience of observing the object.

The Scales – (If you prefer to work in metric, just change “1-inch” to 25mm – it will be close enough for these purposes.)

#1 The Solar System

Scale: 1-inch = 2 light minutes (or for those who want more precision, 120 light seconds*

Minimum distance in light hours, minutes, and seconds,  from the Earth to the moon and planets are:

  • Moon: 00:00:01.2  (that is 1.2 light seconds)
  • Venus 00:02:07  ( 2 minutes, 7 seconds)
  • Mars  00:03:02
  • Mercury  00:04:18
  • Sun 00:08:19
  • Jupiter  00:32:43
  • Saturn 01:06:28  ( 1 hour, 6 minutes, 28 seconds)
  • Uranus  02:23:35
  • Pluto 03:58:07**
  • Neptune 03:59:25

To calculate the distance on your Universal Measuring Stick, simply divide the time in minutes by 2, or the total time converted to seconds, by 120.

Example: Jupiter is 32 minutes, 43 seconds away. In seconds that is (32X60) + 43 or 1,920 seconds plus 43 which is 1,963 seconds. 1963/120 = 16, so Jupiter will be 16 inches away.

*Use 2 light minutes for reasonable approximations, or get more precise with seconds.

** yes, Pluto when closest to us is closer than Neptune when closest to us!

If you’ve made the solar system measuring stick, you should have the basic idea how and find the others easy.

#2 Our Stellar Neighborhood – to 2,600 light years

Scale: 1-inch = 21.6 light years

This scale covers most of what you can see with your naked eye –  as well as many things you can not see with the naked eye because they are too faint, but still fairly close to us. Well, close as astronomical objects go, but incredibly far away when it comes to what we’re used to.

(The entire solar system scale would be so small, it would be impractical to represent it on this scale with anything except the thinnest of lines right at the start.)

We’ll use some of our bright guidepost stars just for starters. Here are their distances in light years:

  • Polaris  430
  • Arcturus  37
  • Spica 262
  • Antares 600
  • Vega  25.3
  • Altair 16.8
  • Deneb 1,400
  • Big Dipper  80*

*This is an approximation covering the main stars of the Dipper which are really part of an open cluster.  With most asterisms the stars would be at various distances.

#3 Our home galaxy, the Milky Way – to 100,000 light years

Scale: 1-inch = 833 light years

(The previous scale would take up little more than the first three inches of this scale.)

This measuring stick takes us to some of the more distant open clusters, typical globular clusters, and some nebulae that are easy to observe with the naked eye, binoculars,or small telescopes.


  • Pleiades M45 440
  • Dumbell Nebula M27  1250
  • Orion Nebula M42  1,300
  • Ring Nebula M57 2,300
  • Open Cluster M37 4,400
  • Globular Cluster M13 25,000

#4 Our observable universe – to 100 million light years

Scale: 1-inch = 833,000 light years

(The entire previous scale would take up about the first one eighth of an inch on this one.)

While the Andromeda galaxy can be detected with the naked eye and observed with ordinary binoculars, most of what we include on this measuring stick takes us to the limit of what we usually observe with a backyard observatory that includes at least a  6-inch telescope. We can reach farther into the universe than this, but with anything past the middle point on this scale you see very little – and most of what you see at these distances justifies the term amateur astronomers usually use for these objects – faint fuzzies!


  • Andromeda Galaxy M31  2.5 million
  • Pair of galaxies beahind the Great Bear’s ears –  M81, M82  12 million
  • Whirlpool Galaxy M51 23 million
  • Leo Triplet Galaxies M65, M66, NGC 3628 35 million

Finally, getting the measure of the universe – here’s a brief tribute to the measurers – ancient and modern . . .

“HIPPARCHUS OF NICEA must have been an interesting fellow. He was a second-century B.C. mathematician, philosopher and astronomer. Using the only astronomical instrument available to him — his eyes — Hipparchus took on the daunting task of measuring the positions of the stars and planets as they passed overhead each night. He came up with a catalog of 1,080 stars, each of which he described simply as “bright” or “small.”
“Hipparchus wasn’t the first astronomer to pursue the science of astrometry, as the astronomical discipline of positional measurement is now called. However, his star catalog was the first of many compiled over the centuries by astronomers using ever-better instruments and techniques. From those measurements — all made from the Earth’s surface — astronomers have derived everything from basic stellar properties to estimates for the age of the universe.
“On August 8, 1989, the science of astrometry took a long-awaited leap to the stars. Riding aboard an Ariane rocket was the High Precision Parallax Collecting Satellite, otherwise known as Hipparcos. For the next three and a half years, Hipparchus’s 20th-century namesake measured the parallaxes and brightnesses of more than a million stars — despite a potentially crippling accident that sorely challenged the project’s architects.”

The above is quoted from this Web site: http://tinyurl.com/yurcq2 Go there for more details.


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: