Size Scales in Astronomy

William P. Blair, Johns Hopkins University

Version 1.3, October 2004

Here are some demonstrations for use in the classroom that should help put the sizes and distances of astronomical objects into a more understandable perspective. These demonstrations are effective for ALL age groups, although adjusting the level of detail for the youngest ages groups is recommended. The idea here is to communicate the relative sizes and distances of various objects, without getting overly caught up in the accuracy of the comparisons. (An interesting Middle School level activity would be to make a more accurate solar system scale model that would fit in the school yard as a follow-on project.)

1. The Earth-Moon System

The moon is our closest neighbor in space, and yet even its distance and size relative to the earth are often misunderstood. Also, especially amongst the younger age groups (who have some notion that people have actually been to the moon and back, but don't know the details), there seems to be a general misconception that the Space Shuttle can fly to the moon (since it goes up into outer space!). Here is a simple demonstration that I have found effective for making some sense out of the earth-moon system for general audiences.

Many catalogs and outlets such as "The Nature Company" carry inflatable "beach ball" earth globes; I have one that is about 16 inches in diameter, which is big enough to be generally visible and recognizable in a classroom or small auditorium setting (even from the back of the room!). [Depending on your audience, this same globe can be used with a slide projector or other light source in an otherwise darkened room to demonstrate day and night (the earth's rotation) and the tip of the earth's axis relative to the direction to the sun, which causes the seasons. See my write-up on Some Basic Astronomy Demonstrations for Early Elementary Ages.]

Here is the basic information needed for the demonstration: the scaled distances and sizes.

```                           Table 1

Earth/Moon System Scaled to 16-inch Earth

Parameter           Real Distance/Size     Scaled Distance/Size
-----------------   -------------------    ---------------------

Earth (diameter)         12,756 km              16.0 inches
Moon (diameter)           3,476 km               4.4 inches
Moon (distance)         384,400 km              40.2 feet
Sun (diameter)        1,392,000 km             145.5 feet
Sun (distance)      150 million km       15,700 feet = nearly 3 miles!

Shuttle Orbit               350 km               0.4 inches above
(typical)                                        beach ball (!)
Int'l Space Station         402 km               0.5 inches above
beach ball

Note: 1 km (kilometer) = 0.6 miles, and 1 inch = 2.54 cm (0.0254 meter)
if you want to convert any units.)
```

Even from the above table, you can probably see where this is going! In any event, here's what I do:

After some preliminary discussion to set the stage, set the beach ball on a table (or have a volunteer hold the ball). For the moon, you can use a softball or styrofoam ball of 4-5 inch diameter, OR I have found it convenient to take a white balloon out of my pocket and blow it up to the approximate size. (That way you can ask the audience how big the moon is relative to the earth and have them say "Stop!" when they think it is the "right" size.)

Once the size of the moon has been established, ask about the distance of the moon from the earth on this scale. Again, I start with the moon right next to the earth and ask the audience to call out "Stop!" when they think it is the right distance away. I start slowly at first, then take larger and larger steps until I approach about 40 feet. (Depending on your setting, you may be out in the hallway by this point!) Again, getting it exactly 40 feet away is not the point--only that the separation is very large compared with most people's expectations. I usually make it a point to reinforce at this point that the moon transcribes a big circle around the earth at this distance, taking about a month (27 days) to make the circuit.

If convenient, you can have a volunteer hold the "moon" at the approximate distance while you come back to "earth." Now bring the Space Shuttle into the picture. Obviously a "scaled" shuttle on this scale would be invisible, so I usually use a small (approx. 3 inch) space shuttle model (which can be obtained from various NASA or Smithsonian gift shops, or even a local toy store) and make a joke about the scale being wrong (just to make sure there are no misunderstandings on this point!). Now have a countdown and blast the shuttle "into orbit"--only half an inch above the surface of the beach ball! I usually make one or more of the following points (while the audience picks their jaws up off the floor):

• That even this close to the earth's surface, one is already in "outer space."
• That everything we know that is alive in the Universe is below the tenuous atmosphere surrounding the earth, on the "surface" of the beach ball, if you will.
• That the space shuttle is really a space "truck" for getting to low-earth orbit, but it cannot fly out anywhere near the moon.
• That putting people on the surface of the moon (let alone on the surface of another planet) is a totally different capability from placing them in orbit about the earth.

At this point, depending on the audience and the overall goals of your presentation, you can take the further step of describing the relative size and distance of the sun on this same scale (see Table above). Again, exact numbers are less important than the overall effect. A distinctive landmark at approximately the right distance adds a nice touch. For instance from Hopkins Homewood campus I would probably say, "On this scale, the sun is a big ball of glowing gas about 150 feet in diameter sitting in the Inner Harbor!"

2. The Sun, the Earth and the Solar System

This demonstration just takes the above idea a step further. It can be used in conjunction with the above, or as a separate demonstration, again depending on size and age of audience and amount of time available.

In this demonstration, we use the diameter of the sun as our yardstick, and look at the solar system on this scale. The tables below gives some of the basic information for two different scalings of interest, although by no means do these both have to be used in a given presentation.

```                             Table 2a

Solar System Scaled to 3-inch Sun

Parameter           Real Distance/Size     Scaled Distance/Size
-----------------   -------------------    ---------------------

Sun (diameter)          1,392,000 km          3 inches (tennis ball or
small orange)
Mercury (distance)         0.39 AU            10.4 feet
Mercury (diameter)         4880 km            0.01 inches (grain of sand)
Venus (distance)           0.72 AU            19.1 feet
Venus (diameter)          12112 km            0.03 inches (grain of sand)
Earth (distance)    150 million km = 1 AU     26.6 feet
Earth (diameter)         12,756 km            0.03 inches (grain of sand)
Mars (distance)        228 million km         40.9 feet
Mars (diameter)           6,800 km            0.015 inches (grain of sand)
Jupiter (distance)         5.20 AU            138  feet
Jupiter (diameter)      142,984 km            0.30 inches (cherry pit)
Saturn (distance)          9.54 AU            253  feet
Saturn (diameter)       120,536 km            0.26 inches (cherry pit w/rings!)
Pluto (distance)          39.54 AU          1050.0 feet (>3 football fields)
Pluto (diameter)          2,300 km           0.005 inches (very small sand grain!)

Next nearest star   4.3 light years =        1420 miles(!) or 2370 km
(Proxima Centauri)    25 trillion miles =   (roughly from Baltimore to Dallas!)
42 trillion km

-------------------------------------------------------------------

Table 2b

Solar System Scaled to 12-inch Sun

Parameter           Real Distance/Size     Scaled Distance/Size
-----------------   -------------------    ---------------------

Sun (diameter)          1,392,000 km          12 inches (basketball) or
Mercury (distance)         0.39 AU            41.5 feet
Mercury (diameter)         4880 km            0.05 inches (grain of sand)
Venus (distance)           0.72 AU            76.6 feet
Venus (diameter)          12112 km            0.11 inches (small pebble)
Earth (distance)    150 million km = 1 AU    106.4 feet
Earth (diameter)         12,756 km            0.12 inches (small pebble)
Mars (distance)        228 million km        163.6 feet
Mars (diameter)           6,800 km            0.06 inches (grain of sand)
Jupiter (distance)         5.20 AU            552  feet
Jupiter (diameter)      142,984 km            1.2 inches (ping pong ball)
Saturn (distance)          9.54 AU           1012  feet (>3 football fields)
Saturn (diameter)       120,536 km            1.04 inches (ping pong ball w/rings!)
Pluto (distance)          39.54 AU          4200 feet (almost 0.8 miles)
Pluto (diameter)          2,300 km          0.02 inches (very small sand grain!)

Next nearest star   4.3 light years =        5680 miles(!) or 9088 km
(Proxima Centauri)    25 trillion miles =   (roughly from Baltimore to Hawaii!)
42 trillion km

-------------------------------------------------------------------

Note: 1 AU = "astronomical unit" is defined to be the mean distance from
the earth to the sun.  Since we are interested in "relative" distances,
I choose to keep the table as simple as possible and scale distances
relative to this yardstick.

Also, Pluto's orbit is relatively non-circular, so the number given is
an average.

1 "light year" = the distance light travels in one year, at a rate of
186,282 miles per second (roughly 300,000 km per second), or about 5.8
trillion miles.  (Unhappily, \$5.8 trillion is about the size of the
US national debt, which puts THAT in a different perspective, too!)

```

Again, start by setting the stage: that we will take the entire sun and scrunch it down to a 3-inch ball. A tennis ball (or lacrosse ball) is about right, but I have also used a small orange or tangerine to good effect (especially since the Florida Orange Growers Association would have us believe that oranges are "captured" sunshine!).

Now go through a few steps from the table above. It is good to include the earth as a reference point, and Jupiter because it is the largest planet. Including Saturn (the next planet out from Jupiter) is nice because it shows how quickly the distances get very large for the outer solar system, and Pluto, for better of for worse, is recognized as the most distant planet (although no longer considered to be the "edge" of the solar system--but that is another topic). That Pluto is more than three football fields away from the "orange" sun can be made even more effective if you are standing on or near a football field at the time! Also, reinforce the idea that these distances are the radii of the orbits--that each planet sweeps out a big "circle" in its trek around the sun.

The zinger here, of course, is if you make the last step in the table above (to the NEXT nearest star). Pictures of star clusters or nearby galaxies are misleading in a sense because the true distances between objects are not often placed in the proper context. Our Galaxy, the Milky Way, is a huge spiral of stars about 100,000 light years across. About 100 BILLION star populate the Galaxy. The sun and its nearest stellar neighbors are quite similar in size and temperature, and so the "orange" remains a good size reference. However, the distance is another matter altogether. Instead of using feet or football fields, we must increase the yardstick to miles or kilometers. The next nearest star to the sun is another orange-sized object more than 1400 miles away! I leave the possibility of describing the size of the Milky Way on this scale (100,000 ly, which scales to 33 million miles!) to your discretion, but I think in general this distance loses its meaning to most people.

3. Other Scalings

You can generate other scalings to your heart's content; really all you need is a good astronomy textbook with some numbers and a few props of the right approximate dimension. Here I mention just two others: one that "combines" the above two demonstrations into one (shorter) demonstration, and one that takes another big step out into the Universe.

a) Intermediate Scaling Example

In many situations you may want to set the scale for more than just the earth--moon system, but leaving the earth as a totally insignificant grain of sand may be going too far for your tastes. I have used the following scaling and effectively combined some highlights from both of the above demonstrations into one presentation with good results. In this one, we let the earth be scaled down to 3-inches (instead of the sun), which keeps most of the sizes and distances within the realm of understanding. I find it particularly effective to use an earth "ball" or paperweight with the continents marked. Squishy earth balls of about the right dimension are available in many gift or toy shops at very reasonable prices.

```                             Table 3

Solar System Scaled to 3-inch Earth

Parameter           Real Distance/Size     Scaled Distance/Size
-----------------   -------------------    ---------------------

Earth (diameter)         12,756 km              3 inches
Moon (diameter)           3,476 km            0.8 inches (ping pong ball)
Moon (distance)         384,400 km            7.5 feet
Sun (diameter)          1,392,000 km         27.3 feet
Sun (distance)    150 million km = 1 AU      0.55 miles (=0.9 km)
Jupiter (distance)         5.20 AU            2.9 miles (from sun)
Jupiter (diameter)      142,984 km            2.8 feet
Saturn (distance)          9.54 AU            5.2 miles (from sun)
Saturn (diameter)       120,536 km            2.4 feet
Pluto (distance)          39.54 AU           21.7 miles (from sun)
Pluto (diameter)          2,300 km            0.5 inch (small rubber ball
or crumple up some tin foil)

Next nearest star   4.3 light years          156,000 miles (or more than 6/10ths
of the way to the moon on the
"real" scale of things!)
```

In this presentation, you can still do the "earth-moon separation" demonstration from above to good effect, but the "shuttle above the earth" part (less than 0.1 inch on this scale) may be too small. Likewise, the nearest star being 156,000 miles on this scale gets rather large, but in combination with Pluto being only 22 miles from the sun it may still have the desired effect.

```b)  The Universe Beyond...
(...or from the sublime to the ridiculous!)
```

As we try and step out from the regions adjacent to the sun, to the scale of our Galaxy, the nearby galaxies, and finally the distant Universe, it becomes very difficult for most people to fathom the true immensity of the distances involved. Obviously "miles" or "kilometers" are no longer useful units, and even the venerable "light year" becomes only marginally acceptable. Even the nearest large galaxy, the "Andromeda" galaxy (also known as Messier 31, or M31) is at a staggering distance of some 2 million light years away (with the hopefully obvious connotation that the light from even this "nearby" galaxy takes about 2 million years to reach the earth!). That this distance is deemed almost inconsequential compared with the most distant objects known in the Universe, which are roughly 10 BILLION light years away (or 5000 times the distance to our "neighbor," M31) should give an idea of the magnitude of the problem.

To provide an inking of what these distances are like, I have used the following description with general audiences to good effect, especially in conjunction with one or more of the above to give it the proper perspective. This has been adapted and updated from a section of an article called "The Incredible Universe," in the May 1974 National Geographic magazine, written by K. F. Weaver and J. P. Blair (no relation!). It is particularly timely given the recent release of a new, very sensitive image obtained with the Hubble Space Telescope showing an essentially "empty" region of sky to be literally littered with galaxies of all types, shapes and colors! Estimates based on this image indicate that there may be 5 (or more) times as many galaxies in the Universe as was thought previously, based on the best available data! Herewith, my adaptation:

Today we know that galaxies are as common as blades of grass in a meadow. The Hubble Space Telescope recently completed a particularly deep (faint) census of a tiny "pencil beam" extending far out into the Universe. This survey, called the "Hubble Deep Field," was targeted on a region of the sky that was nearly devoid of known objects, so as to be (hopefully) representative of conditions in the distant Universe. The resulting images are truly amazing. Strewn across this tiny piece of the sky are perhaps 1500 or more galaxies of all shapes, sizes, and colors! Because this survey pertains to such a small piece of the sky, the implications are staggering: if the region of sky demarked by the "bowl" of the Big Dipper were surveyed to the same depth, it would contain about 32 million galaxies! And the estimate for the entire visible Universe is that there are upwards of 40 BILLION galaxies, each containing tens to hundreds of billions of stars!

But how does one comprehend the size of this galaxy-filled Universe, and grasp the concept that the most distance objects we can see are perhaps 10 billion (or more) light years away? Imagine that the distance from the earth to the sun (93 million miles, or about 8 light minutes) is compressed to the thickness of a typical sheet of paper. On this scale, the nearest star (4.3 light years) is at a distance of 71 feet. The diameter of the Milky Way (100,000 light years) would require a 310 mile high stack of paper, while the distance to the Andromeda galaxy (at 2 million light years one of the most distant objects visible to the naked eye) would require a stack of paper more than 6000 miles high! On this scale, the "edge" of the Universe, defined as the most distance known quasars some 10 billion light years hence, is not reached until the stack of paper is 31 million miles high--a third of the way to the sun on the real scale of things!

If you find this document useful, or if you have suggestions for improving it, please let me know through one of the following channels:

```Telephone: 410-516-8447
Fax: 410-516-8260
E-mail: wpb@pha.jhu.edu
Snail mail: Dept. of Physics and Astronomy, Johns Hopkins University,
3400 North Charles Street, Baltimore, MD  21218-2686
```
William P. Blair