The following is a simple classroom demonstration I have developed to illustrate the true scale of the universe. My original audience was 6th grade students (at Queensland Downs Elementary School in Calgary, Alberta, Canada), but the material is suitable for any age group.
The demonstration employs a few simple props and the imagination of the audience on three different but interlocking scales. The universe is too big to convey on a single scale -- the distance to the furthest objects we can see is about 10 million million million (1019) times greater than the diameter of the Earth, while the human mind has difficulty directly visualizing numbers larger than one million. (By coincidence, the number of air molecules in a cubic centimeter at sea level is of similar magnitude, around 2.5 x 1019; the microscopic realm is vast in its own way.)
More information is given in the notes below than any single demonstration would probably need. This is intended as reference material; the instructor is free to choose what to include and what to leave out.
The minimum time for the demonstration is 10 minutes, which requires leaving out most of the material after parts 1 and 2. If the time is less than 10 minutes, the reality of the scales discussed may not be made clear. But the time can easily be lengthened for greater impact by using more detail in the later sections, or discussing particular planets, stars, or galaxies in more depth.
There are other exercises like this on the web. For an example focusing on the Solar system in more detail, see Guy Ottewell's Thousand Yard Model. A computer model of some different planets and stars illustrating relative sizes is also available online, although I haven't been able to find any official website, just copies of an email that circulated in June 2007. For a more general graphic overview, movies like ``The Powers of Ten'' or this web adaptation are worth checking out. Lastly, for a single log-scale chart of cosmic distance scales, see Figure 8 of Gott et al. (2005, ApJ, 624, 463).
I use metric units in the models below, but these can be converted to English units easily: 1 centimeter (cm) = 0.39 inches; 1 meter (m) = 39.4 inches = 3.28 feet; 1 kilometer (km) = 0.62 miles. Some other units in use are the Astronomical Unit (AU) and light year (ly), which sometimes appear with metric prefixes (e.g. mAU = milli-AU = 0.001 AU, Mly = mega-ly = 1,000,000 ly).
Some numbers below have been rounded slightly for convenience, but most are accurate to within a few percent unless otherwise noted. Interstellar and extragalactic distances on larger scales may be somewhat more uncertain.
Scale 1: 1 / 31.9 million (1 cm = 319 km)
On this initial scale, the Earth is the size of the globe. The Moon is about the size of the grapefruit. The distance between the two is 12 meters. Have two students hold the globe and grapefruit on opposite sides of the room to illustrate this. Some may know that the Moon is only 1/4 the diameter of the Earth, but few will have realized before how far apart the two are -- about 30 times the diameter of the Earth! The Apollo astronauts took three days to travel this distance, the farthest that humans have yet traveled from the Earth. A beam of light or a radio signal takes about 1.3 seconds to cover the same distance.
| Object | Measurement | Actual | Light Travel | Scaled | Model |
|---|---|---|---|---|---|
| Moon | Diameter | 3,476 km | 0.01 second | 11 cm | grapefruit |
| Earth | Diameter | 12,756 km | 0.04 second | 40 cm | large globe |
| Jupiter (Equator) | Diameter | 142,984 | 0.48 second | 4.8 m | 40% of classroom |
| Earth-Moon | Separation | 384,400 km | 1.28 seconds | 12 m | classroom |
| Sun | Diameter | 1,392,000 km | 4.64 seconds | 44 m | 14-floor building |
| Earth-Sun | Separation | 149,600,000 km | 8.33 minutes | 4.7 km | 1-hour walk |
The sizes of Jupiter and the Sun, and the distance to the Sun are shown here for reference but need not be part of the discussion.
| Here and in the following sections, data not essential to the presentation are in this color. |
Scale 2: 1 / 15.4 billion (1 cm = 154,000 km = 0.001 AU)
[483 times
smaller than Scale 1]
Stick the two pins into the eraser, about 2.5 cm (1 in) apart. These now represent the Earth and the Moon (both of which are actually smaller than the heads of the pins). With a 5 cm long eraser, if one pin is near the center and the other at one end, the full length of the eraser represents the diameter of the Moon's orbit. On this same scale, the Sun can now be represented by the grapefruit (see table below). The Sun is almost twice as large as the diameter of the Moon's orbit around the Earth! The distance between the Earth and the Sun is 9.7 meters, or about 400 times the Earth - Moon separation. Since the Moon and Sun appear to be the same size in our sky (as in a Solar eclipse), this means the Moon is 1/400th the diameter of the Sun, and the Earth is 1/100th the diameter of the Sun. Have someone hold the eraser with the two pins representing the Earth and Moon 10 meters from the grapefruit (a little closer than the person with the globe was before).
The average distance between the Earth and the Sun is 1 Astronomical Unit (AU). The AU is a convenient yardstick for measuring distances in our own Solar system. Interplanetary space probes take months or years to travel across the Solar System. By comparison, light takes about 500 seconds (8.3 minutes) to travel 1 AU. At our current scale, Solar-system and comparable sizes are:
| Object | Measurement | Actual | Light Travel | Scaled | Model |
|---|---|---|---|---|---|
| Earth | Diameter | 0.085 mAU | 0.04 second | 0.83 mm | pin width (no head) |
| Jupiter (Equator) | Diameter | 0.96 mAU | 0.48 second | 9.28 mm | fingernail width |
| Earth-Moon | Separation | 2.57 mAU | 1.28 seconds | 2.50 cm | pinhead spacing |
| Sun | Diameter | 9.31 mAU | 4.65 seconds | 9.28 cm | grapefruit |
| Sun-Mercury | Separation | 0.39 AU | 3.25 minutes | 3.79 m | 32% of classroom |
| Sun-Venus | Separation | 0.72 AU | 6.00 minutes | 6.99 m | 58% of classroom |
| Sun-Earth | Separation | 1.00 AU | 8.33 minutes | 9.71 m | 81% classroom |
| Sun-Mars | Separation | 1.52 AU | 12.7 minutes | 14.8 m | 123% of classroom |
| Sun-Jupiter | Separation | 5.20 AU | 43.3 minutes | 50.5 m | 1/2 football field |
| Betelgeuse | Diameter | 8.84 AU | 1.23 hours | 85.9 m | 28-floor building |
| Sun-Saturn | Separation | 9.54 AU | 1.32 hours | 92.7 m | 1 football field |
| Sun-Uranus | Separation | 19.2 AU | 2.66 hours | 187 m | 2 football fields |
| Sun-Neptune | Separation | 30.1 AU | 4.17 hours | 292 m | 3 football fields |
| Sun-Pluto | Separation | 39.4 AU | 5.46 hours | 383 m | 4 football fields |
| Outer Kuiper Belt | Distance | 55 AU | 7.62 hours | 534 m | 5 football fields |
| Inner Oort Cloud | Distance | 2,000 AU | 11.6 days | 19.4 km | nearby towns |
| Outer Oort Cloud | Distance | 50,000 AU | 289 days | 486 km | medium US state |
| Alpha Centauri | Distance | 4.36 ly | 4.36 years | 2680 km | 24 degrees of latitude or New York to Denver or Bowling Green to Calgary |
On this scale, the largest planet, Jupiter, has a diameter of 0.93 cm. This is 1/10th the size of the Sun and 11 times the size of the Earth. These planetary distances from the Sun are averages, since planetary orbits are elliptical rather than circular. For an extended demonstration, this part could be held outdoors, with one student volunteer standing at the appropriate distance for each planet out to some reasonable limit (Saturn?), holding some appropriately-sized small object.
On the same scale, Alpha Centauri, the nearest star system to the Sun, is about 2,700 kilometers away, or over 9,000 times the distance to Neptune! Pick a prominent geographical reference to illustrate this (e.g., distance to a major city). The diameters of the stars relative to the distances between them are illustrated by considering one student holding the grapefruit in the classroom, and another student holding another grapefruit half a continent away.
Scale 3: 1 / 5.984 trillion (2.5 cm = 149,600,000 km = 1 AU = 500 light
seconds)
[400 times smaller than Scale 2]
This is an optional intermediate scale between Scale 2 (inner Solar system) and Scale 4 (interstellar space). It overlaps with both but may be useful in an extended presentation.
Now make the separation of the two pins the distance between the Earth and the Sun, or 1 Astronomical Unit. On this scale, the Sun's diameter is 0.01 inch = 0.25mm, smaller than the width of 1 pin! (Betelgeuse, one of the biggest stars known, is about 22cm = 8.7 inches in diameter.) Pluto's mean orbital distance from the Sun is about 40 inches = 1 meter. The Kuiper Belt is a bit outside this, and the outer Oort comet cloud extends out to about 1 km from the Sun. The nearest star, Alpha Centauri, is 6.9 km away, and Deneb, one of the most distant stars visible to the naked eye, is 2,300 km away.
| Object | Measurement | Actual | Light Travel | Scaled | Model |
|---|---|---|---|---|---|
| Sun-Mercury | Separation | 0.39 AU | 3.25 minutes | 0.98 cm | |
| Sun-Venus | Separation | 0.72 AU | 6.00 minutes | 1.80 cm | |
| Sun-Earth | Separation | 1.00 AU | 8.33 minutes | 2.50 cm | pinhead spacing |
| Sun-Mars | Separation | 1.52 AU | 12.7 minutes | 3.80 cm | |
| Sun-Jupiter | Separation | 5.20 AU | 43.3 minutes | 13.0 cm | hand width |
| Betelgeuse | Diameter | 8.84 AU | 1.23 hours | 22.1 cm | |
| Sun-Saturn | Separation | 9.54 AU | 1.32 hours | 23.9 cm | |
| Sun-Uranus | Separation | 19.2 AU | 2.66 hours | 48.0 cm | |
| Sun-Neptune | Separation | 30.1 AU | 4.17 hours | 75.3 cm | |
| Sun-Pluto | Separation | 39.4 AU | 5.46 hours | 98.6 cm | meter stick |
| Outer Kuiper Belt | Distance | 55 AU | 7.62 hours | 1.38 m | |
| Inner Oort Cloud | Distance | 2,000 AU | 11.6 days | 50.0 m | |
| Outer Oort Cloud | Distance | 50,000 AU | 289 days | 1.25 km | small town |
| Alpha Centauri | Distance | 4.36 ly | 4.36 years | 6.90 km | medium city |
| Deneb, Alpha Cygni | Distance | 1,440 ly | 1,440 years | 2,270 km | distant major city |
Scale 4: 1 / 1.627 quintillion (2.5 cm = 41,300,000,000,000 km = 4.36 light
years)
[276,000 times smaller than Scale 3, or 107 million times
smaller than Scale 2]
[Note: many distances in this section are uncertain at the 10-20% level, because they become progressively harder to measure. Consequently, the precision (number of significant digits) used below is misleading, and should not be taken seriously -- a lot of distances below, especially for dimensions of the parts of the Milky Way galaxy, are based on more rounded figures in parsec units and then converted to light years (1 pc = 3.26 ly) without re-rounding!]
Now we must make a much larger conceptual leap in order to consider interstellar and galactic distances. The 4.3 light year separation between the Sun and Alpha Centauri, which was near the top of Scales 2 and 3, is shrunk down to the bottom of the new scale: the 2.5 cm separation of the two pins on the eraser used to illustrate the Earth-Moon system with Scale 1. The two pin heads are much, much bigger than the actual stars would be if shrunk to this scale.
The distance of a few light years between the Sun and Alpha Centauri is typical of many stars in our part of space. Hold the eraser and pins up for everyone to see, and ask them to imagine the room is filled with such pins, all about the same distance apart, from wall to wall and floor to ceiling. These are the stars within a few hundred light years of the Sun, a region sometimes called the Solar Neighborhood (though its exact definition varies). Most are faint stars which cannot be seen without a telescope, but the brighter ones shining here and there are visible to the naked eye from Earth. Of the millions of stars in this volume, a few thousand are bright enough for us to see in our skies. We group them into patterns we call constellations, which are often chance alignments of perspective -- many stars in the same constellation lie at radically different distances from us. The nearest star we can see (Alpha Centauri) is only 2.5 cm away, while one of the most distant (Deneb) is 8 meters away! Other bright stars, like those in Orion and the Big Dipper, lie at intermediate distances.
| Object | Measurement | Actual | Scaled | Model |
|---|---|---|---|---|
| Alpha Centauri (nearest visible star) | Distance | 4.36 ly | 2.50 cm | pinhead spacing |
| Vega, Alpha Lyrae | Distance | 25.3 ly | 14.5 cm | |
| Aldebaran. Alpha Tauri | Distance | 65.2 ly | 37.4 cm | |
| Big Dipper (Ursa Major) Cluster | Distance | 81.5 ly | 46.8 cm | |
| Milky Way Star-forming Disk | Thickness | 326 ly | 1.87 m | tall human |
| Local Interstellar Bubble Edge | Distance | 326 ly | 1.87 m | |
| Pleiades Cluster (M45) | Distance | 440 ly | 2.52 m | |
| Betelgeuse, Alpha Orionis | Distance | 652 ly | 3.74 m | |
| Orion Nebula (M42) | Distance | 1,270 ly | 7.27 m | |
| Deneb, Alpha Cygni | Distance | 1,440 ly | 8.23 m | 68% of classroom |
| Milky Way Thin Stellar Disk | Thickness | 2,120 ly | 12.2 m | 3-floor building |
| Double Cluster (next spiral arm) | Distance | 7,500 ly | 43.0 m | |
| Milky Way Thick Stellar Disk | Thickness | 9,130 ly | 52.4 m | 17-floor building |
| Milky Way Galactic Center | Distance | 26,100 ly | 150 m | |
| Hercules Globular Cluster (M13) | Distance | 34,200 ly | 196 m | |
| Milky Way Stellar Disk | Diameter | 97,800 ly | 561 m | 5-minute walk |
| Milky Way Gas Disk | Diameter | 163,000 ly | 935 m | |
| Large Magellanic Cloud | Distance | 163,000 ly | 935 m | 10-minute walk |
| Andromeda Galaxy (M31) | Distance | 2.54 Mly | 14.6 km | nearby town |
| Ursa Major Group (M81, etc.) | Distance | 11.7 Mly | 67.3 km | |
| Virgo Cluster (M87, etc.) | Distance | 52.2 Mly | 299 km | 3-hour drive |
| CfA2 Great Wall | Distance | 196 Mly | 1,120 km | |
| Sloan Great Wall | Distance | 978 Mly | 5,610 km | width of North America |
| 3c273 Quasar | Distance | 2.45 Gly | 14,000 km | 1.09 times Earth diameter |
| 0957+561 Lensing Cluster (z=0.355) | Distance | 3.70 Gly | 21,200 km | |
| 0957+561 Lensed Quasar (z=1.41) | Distance | 8.70 Gly | 49,900 km | |
| Light speed * age of Universe | Distance | 13.7 Gly | 78,600 km | 20% of Moon distance |
| Evolved microwave background | Distance | 45.7 Gly | 262,000 km | 68% of Moon distance |
The Solar Neighborhood is only part of a much larger system of many billions of stars called the Milky Way Galaxy. The Milky Way is shaped like a disk with a bulge near the center (think of a fried egg), and with spiral-shaped concentrations of brighter stars and clouds of interstellar gas within the disk (in the "white" of the egg) which sweep out from the center like the arms of a whirlpool. Dimensions of various components are listed above, including the distance to the Galactic center (150 m), stellar disk diameter (560 m), and disk thickness (50 m for the oldest disk stars, 12 m for Solar-age stars, and 2 m for the youngest stars and the dense interstellar clouds from which they form). Spiral arms in the disk are spaced about 30-50 meters apart, and they gradually turn with the disk as all the stars orbit Galactic center. The star Deneb, in the constellation of Cygnus, marks the direction in which our Sun is moving in its 200 million year orbit. We will reach Deneb's position in a little under 2 million years.
The Milky Way is, in turn, only one galaxy in a universe of many billions of galaxies. The nearest naked-eye galaxy to our own is the Large Magellanic Cloud, a small satellite galaxy about 1 km away. Our sister spiral galaxy, Andromeda, is 15 km away; our small Local Group of galaxies has a diameter about twice this distance. There are many other groups of galaxies, as well as denser, more populous clusters. The nearest is the Virgo Cluster, which contains perhaps two thousand galaxies in a volume a few times that of the Local Group, and which lies some 300 km away. The scatter of clusters, groups, and occasional isolated galaxies continues on as far as we can see -- an area limited by the speed of light, the age of the Universe, and the curvature of spacetime, but which is somewhat smaller than the distance to the Moon. Remember how far away the moon was on the first scale?
Scale 5: 1 / 92.5 sextillion (1 cm = 925,000,000,000,000,000 km = 97,800
light years)
[56,100 times smaller than Scale 4]
This last section is also optional, and uses no props, just imagination. But it gives a quick way to visualize the entire known universe!
Imagine each galaxy as a snowflake 1 centimeter across; the universe is a heavy ``blizzard'' in which the ``snowflakes'' are about 20 centimeters apart on average, although eddies in the blizzard cause some snowflakes to be closer together than this, and others to be farther apart, depending on location. We can see a distance of about a kilometer in any direction, because this is as far as light has traveled during the 13.7 billion years since the storm began (the Big Bang). For this reason, we don't actually know how big the whole blizzard is! Because of the slowness of light travel on these large scales, when we look out into the storm, we are also looking backward in time to when it was younger. If we look as far as we can, we see that the snowflakes used to be smaller on average, indicating that perhaps they have stuck together as the storm evolved, forming the bigger, heavier snowflakes we have now. The snowflakes were also once closer together than they are now; the storm has grown in size. This Hubble Space Telescope image of NGC 4921 gives a nice close-up of one galactic ``snowflake'' with the rest of the cosmic ``blizzard'' visible in the distant background.
On this scale, we have:
| Object | Measurement | Actual | Scaled | Model |
|---|---|---|---|---|
| Earth (ordinary rocky planet) | Diameter | 1.35 nly | 0.14 fm | 1/7 proton diameter |
| Jupiter (ordinary gas giant) | Diameter | 15.1 nly | 1.55 fm | 1.5 proton diameters |
| Sun (ordinary star) | Diameter | 147 nly | 15.0 fm | 15 * proton diameter |
| Betelgeuse (large evolved star) | Diameter | 140 uly | 14.3 pm | 1/70 hydrogen atom |
| Alpha Centauri (nearest star) | Distance | 4.36 ly | 0.45 um | blue photon |
| Milky Way Thick Stellar Disk | Thickness | 9,130 ly | 934 um | 1 mm |
| Milky Way Stellar Disk | Diameter | 97,800 ly | 1.00 cm | large snowflake |
| Milky Way Gas Disk | Diameter | 163,000 ly | 1.67 cm | |
| Large Magellanic Cloud | Distance | 163,000 ly | 1.67 cm | |
| Andromeda Galaxy (M31) | Distance | 2.54 Mly | 26.0 cm | 1/4 m = 10 in |
| Ursa Major Group (M81, etc.) | Distance | 11.7 Mly | 1.20 m | |
| Virgo Cluster (M87, etc.) | Distance | 52.2 Mly | 5.34 m | 1/2 classroom |
| CfA2 Great Wall | Distance | 196 Mly | 20.0 m | |
| Sloan Great Wall | Distance | 978 Mly | 100 m | football field |
| 3c273 Quasar | Distance | 2.45 Gly | 250 m | |
| 0957+561 Lensing Cluster (z=0.355) | Distance | 3.70 Gly | 378 m | |
| 0957+561 Lensed Quasar (z=1.41) | Distance | 8.70 Gly | 890 m | |
| Light speed * age of Universe | Distance | 13.7 Gly | 1.40 km | 15-minute walk |
| Evolved microwave background | Distance | 45.7 Gly | 4.67 km |
As noted for Scale 4, our estimate of the scale of the visible Universe depends on the curvature of spacetime. The two largest distances above are limit cases only. One neglects the expansion of space entirely, while the other projects that expansion to predict how far away features we see in microwave background images of the early Universe may be from us today, even if we cannot observe them as they are ``now''.