The Earth as a Peppercorn

by Victor Davis

The Earth as a Peppercorn

Seeking a “Gee Whiz” Moment
With spring comes an upwelling in our club’s outreach activities, from Friday night star parties at the observatory to on-site presentations at schools, libraries, and other venues. How can we make these encounters memorable to a public accustomed to experiencing the cosmos superficially? How can we provide experiences like the ones that got us hooked on astronomy lo, those many years ago? Certainly a firstlook at Saturn through a telescope eyepiece qualifies as a transcendental experience. Or a look at the detail-rich Moon or solar prominences or (per David Zahler) “original photons” from a faraway galaxy. With experience, the list grows. Getting an “OMG” from a grownup or a “Sick!” from a younger visitor feels pretty good.

An Outdoor Nature Activity
Sky and Telescope describes amateur astronomy as an “outdoor nature activity,” and my favorite outreach activities exemplify that view. So, here’s a hands on activity that I heartily recommend as an introduction to astronomy for people of all ages. It’s a perspective-altering exercise that helps to visualize the sizes of astronomical objects—and the spaces between them—beginning with the Solar System. This solar system model, or planet walk, or cosmic hike was developed by Guy Ottewell and published as “The Thousand Yard Model.” I have added a few refinements of my own, and indeed, the level of appropriate detail to convey will vary depending on the interest level and sophistication of the hikers. Ottewell points out that there’s a big difference between knowing something and apprehending it, and so reading this description of the planet walk will not substitute for performing it. It will not fail to impress even the most jaded participant.

A Matter of Scale
Science writers often try to incorporate a sense of scale in their descriptions. Books sometimes contain fold-out illustrations of the planets to scale. Often the Sun is represented as an arc segment that runs off the edge of the page. Rarely are the spaces between them shown to the same scale. Then, there is the challenge of choosing a convenient and pedagogically effective scale. Ottewell suggests a scale of 1:6,336,000,000, or one inch equals one hundred thousand miles. On this scale, the Sun, a star roughly 864,000 miles in diameter, is represented by a ball approximately 8.64 inches wide—almost exactly the size of a regulation soccer ball. On this same scale, model Mercury’s diameter is 0.03 inch and represented by a pinhead. Venus and Earth, similar-sized planets with scale-model diameters of about 0.08 inch, are represented by—you guessed it—peppercorns. The table summarizes the scale-model objects and distances:

Solar System Object Scale Model Size Represented by Incremental distance
Sun 8.64 inches Soccer ball
Mercury 0.03 inches Pinhead 10 paces
Venus 0.08 inches Peppercorn 9 paces
Earth 0.08 inches Peppercorn 7 paces
Moon 0.02 inches Pinhead 2.4 inches
Mars 0.04 inches Pinhead 14 paces
Jupiter 0.9 inches Pecan 95 paces
Saturn 0.7 inches Hazelnut 112 paces
Uranus 0.3 inches Pistachio 249 paces
Neptune 0.3 inches Pistachio 281 paces
Pluto 0.02 inches Pinhead 242 paces

The choice of representative objects is somewhat arbitrary, and the dimensions are inexact. It does not matter that they are not particularly spherical. What matters is that they are common objects the learner associates with a rough size. A pecan conjures up a lasting size impression that a ball of Play-Doh exactly 0.869 inch in diameter does not.

You may want to mount the planets on tongue depressors or popsicle sticks so that they are easily used and found. This provides the opportunity to glue the Earth and Moon models on a popsicle stick about 2.4 inches apart.

You can begin the exercise by talking about the planets, their relative sizes, and their distance order from the Sun. It’s fun to have youngsters guess how far apart the planets need to be in the scale model solar system. It’s a good idea to fasten the soccer ball to a traffic sign or a tree so it can be seen as the walk progresses. Another of the million uses for duct tape. Recently, I created photo data tables for each planet, mounted on thin fiberglass rods that can be stuck into the ground. I can discuss with fellow walkers planet vital statistics such as rotation rate, orbital period, atmospheres, and other, sometimes surprising, facts as time and attention allow.

A view from the Earth

A view from the Earth

Walking It Off
The mind-bending part of the planet walk is to pace off the spaces between the model objects. At our scale of 1” = 100,000 mi., the average teenager’s pace (increment the count each time the same foot hits the ground) is about 36 inches, representing the enormous distance of 3,600,000 miles. I assign each planet to a hiker, and have helpers join him in counting abridgment off the paces to the spot where he will place his planet. Walking at a normal speed, we traverse our miniature solar system at the scale speed of 20 times the speed of light (Warp 20)!

After 10 paces, put down Mercury.
Another 9 paces; Venus
Another 7 paces; Earth/Moon

Already, the model is starting to freak people out. Who can believe that our planet can be warmed by something so far (93 million miles / 8 1/3 light-minutes) away? To convince ourselves that the scale is correct we can look back at the soccer ball from Earth’s position and notice (cautiously) that it subtends the same angle as the real Sun in the sky.

Then, the distance intervals increase greatly, astonishment sets in, and grumbling begins in earnest.

Another 95 paces to Jupiter.
Another 112 paces to Saturn.
Another 249 paces to Uranus.
Another 281 paces to Neptune.

When I began doing this exercise with schoolchildren in the 1990’s, I often ended the hike at this point, invoking the convenient excuse that, due to Pluto’s eccentric orbit, Neptune was temporarily the Solar System’s most distant planet. More recently, the IAU’s demotion of Pluto provided a more official abridgment opportunity. Nevertheless, at its furthest extent

Another 242 paces to Pluto.

Extending the Model
If we have the fortitude to complete the model, we will have walked about one thousand yards–about half a mile. To appreciate cosmic distances, that’s just the beginning. Using the scale 1” = 100,000 mi.:

  • 1 AU: 78 feet
  • Extent of Kuiper Belt (30 – 50 AU): ~0.7 miles
  • Furthest reaches of Oort Cloud (100,000 AU): ~1,800 miles
  • One light-year: 928 miles Distance to nearest star (Proxima Centauri): 4,000 miles
  • Diameter of Milky Way galaxy: 91,000 miles
  • Distance to Andromeda galaxy: 2.3 million miles

At the cosmically modest distance to our nearest galactic neighbor, even the model becomes too large to comprehend.

Limitations of the Model
As with all models, this one helps to visualize some aspects of reality, and misleads in others. Most obviously, the real planets do not line up in a straight line on one side of the Sun as the model would have it. As the planets orbit the Sun, the distance between two planets can be anywhere from the differences of their distances from the Sun to the sum of their distances. Seen from above (north of) the ecliptic plane, the planets excepting Pluto all travel counterclockwise in their approximately circular orbits with periods ranging from about 3 months to 165 years.

The Solar System is not as flat as the model depicts. Pluto, for instance, has an orbit inclined to the ecliptic by around 17 degrees. This means that part of its orbit would 600 feet up in the air, and part would be in a hole that is equally deep.A

Sense of Emptiness
How can galaxies interact gravitationally without stars crashing into each other? This model helps provide the sense of emptiness to help visualize vast star clouds passing through each other. A 100,000 mile-wide disk containing on average soccer ball sized objects spaced 4,000 miles apart begins to seem pretty unsubstantial. Why are dim or distant objects so hard to detect? Why do near-earth objects sneak up on us with some regularity? What are the complications and time scales for sending a robot to Ultima Thule? Anyone experiencing this planet walk has taken a fun and important first step (1,019 paces, actually) towards appreciating these kinds of questions.

Guy Ottewell’s publications are available at http://www.universalworkshop.com

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This entry was posted in April 2019, Sidereal Times and tagged . Bookmark the permalink.

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