Other models

Since devising the thousand-yard model, I have learned of similar ones by other people. The idea, after all, is obvious; what is crucial to its workability is the choice of scale.

Sir John Herschel, a wonderful scientist and son of Sir Williiam Herchel who discovered Uranus, proposed in his book Outlines of Astronomy (1849) a model of the solar system using peas, oranges, plums and the like. The scale he chose was too large, so that from the Sun to Pluto would have been 3 miles.

In the World Book is depicted another model, with the Sun reduced to the size of a quarter, so that the solar system fits within a baseball stadium. Here the scale is too small: the lesser planets would be almost invisible, and could not be represented by objects more memorable than variously sized grains of sand.

At least one modern education film shows a teacher making a model, with a weather-balloon as the Sun and steel globes of various sizes as the planets. Here again the objects are not memorable and the scale is too large. The Sun and Earth have to be at opposite ends of a football-field; after that the making of the model ends, and we are told that Jupiter would be 4 more football-fields away, etc.

Any model whose scale is much larger than that of the Thousand-Yard Model (such as Herschel's and the film's) results in distances of a mile or more, which people cannot be asked to walk during a lesson. Any model whose scale is smaller (such as those of orreries, ceiling models, the World Book, and all pictures) results in planets too small to see (unless the scale is falsified).

In both cases, therefore, the model remains something to be contemplated only in the head. And it is the real doing and seeing that are indispensable to the effect.

Head and pupil

If, instead of taking people for a walk, you are merely talking to them, it can be useful to say that if the Sun is shrunk to the size of your head, then the Earth will be the size of the pupil of your eye. These have about the same width as the eight-inch ball and the peppercorn.

Light-time

Light travels 186,283 miles (or 299,793 kilometers) per second. It could travel, for instance, 7 1/2 times around the Earth in one second. A "light-year" is the distance light travels in a year, and similarly we can call the distance light travels in a second a "light second," etc.

							in model
Moon to Earth			1.28 light-seconds	2.4 inches
Sun to Earth			8.3 light-minutes	26 yards
Sun to Jupiter			43.27 light-minutes	132 yards
Sun to Pluto			5 1/2 light-hours	1019 yards
Sun to Proxima Centauri		4.22 light-years	4000 miles

Tabulation

Our scale is 1: 6,336,000,000. This means that:

1 inch		represents	100,000     miles
1 foot		    "		1,200,000      "
1 yard		    "		3,600.000      "
1 mile		    "		6,336,000,000  "
928 miles	    "		5,880,000,000,000  miles   or light-year

To carry out the exercise with a group, and to be able to answer questions promptly; you may make a copy of this tabular summary and take it with you. (Another way, especially if you do the exercise several times, it to memorize the successive numbers of paces-10, 9, 7, 14, 95, 112, 249, 281, 242. I do it by means of a private mnemonic with letters for numbers, but that is another subject.)

							  in the model
						miles	  yards inches
	diameter of Sun			       800,000		   8.0	(ball)
distance from Sun to Mercury		    36,000,000	    10
	diameter of Mercury			 3,000		   0.03 (pinhead)
distance from orbit of Mercury to Venus	    31,000,000	     9
	diameter of Venus			 7,500		   0.08 (peppercorn)
distance from orbit of Venus to Earth	    26,000,000	     7
	diameter of Earth			 8,000		   0.08 (peppercorn)
distance from orbit of Earth to Mars	    49,000,000	    14
	diameter of Mars			 4,000		   0.04 (pinhead)
distance from orbit of Mars to Jupiter	   342,000,000	    95
	diameter of Jupiter			90,000		   0.90 (chestnut)
distance from orbit of Jupiter to Saturn   403,000,000 	   112
	diameter of Saturn			75,000		   0.75 (filbert)
distance from orbit of Saturn to Uranus	   896,000,000	   249
	diameter of Uranus			32,000		   0.30 (peanut)
distance from orbit of Uranus to Neptune 1,011,000,000	   281
	diameter of Neptune			30,000		   0.30 (peanut)
distance from orbit of Neptune to Pluto	   872,000,000	   242
	diameter of Pluto			 1,400		   0.01 (pinhead)
		total of distances	 3,666,000,000	 1,019

distance from Earth to Moon		       240,000		   2.40
diameter of Moon				 2,000		   0.02 (pinhead)

In my earlier versions the total distance in the model happened to come out at exactly 1,000 yards. This had no real signifcance, but was convenient since it made the complete model easy to remember. Unfortunately it was based on some- what incorrect distances for the planets from Mars outward. Mile orginally meant "thousand paces" (Latin mille passuum) but grew to be 1,760 yards.

Metric version

One day presumably the metric system will complete its hold on the English speaking countries as it has on most of the others. To me that will be a sad day because the lumpish term kilometer can never subsitute for the fine old monosyllable mile. But, in case this planet-walk is still in use, it will need a decimal translation.

Our basic unit of the yard will have to be translated into the meter. A yard, in origin a pace (a fairly long one), is 36 inches; a meter, in origin 1/40,000,000 of the circumference of the Earth, is 39.27 inches, so we are fairly lucky. The Pacer's legs should stretch a bit more.

For our scale, instead of 1: 6,336,000,000, we'll choose the rounder number of 1: 6,000,000. Thus, in pacing between the planets, 1 meter (pace) represents 6,000,000 kilometers. In the sizes of the bodies, 1 centimeter represents 60,000 kilometers.

							 in the model
						km	   m	 cm
	diameter of Sun			     1,400,000	   23	     (ball)
distance from Sun to Mercury		    58,000,000	   10
	diameter of Mercury			 5,000		0.08 (pinhead)
distance from orbit of Merury to Venus      50,000,000	    8
	diameter of Venus			12,000		0.20 (peppercorn)
distance from orbit of Venus to Earth	    41,000,000	    7
	diameter of Earth			13,000		0.20 (peppercorn)
distance from orbit of Earth to Mars	    78,000,000	   13
	diameter of Mars			 7,000		0.10 (pinhead)
distance from orbit of Mars to Jupiter     550,000,000	   92
	diameter of Jupiter		       143,000		2.40 (chestnut)
distance from orbit of Jupiter to Saturn   649,000,000	  108
	diameter of Saturn			120,00		2.00 (filbert)
distance from orbit of Saturn to Uranus	 1,443,000,000	  240
	diameter of Uranus			51,000		0.90 (peanut)
distance from orbit of Uranus to Neptune 1,627,000,000	  271
	diameter of Neptune			49,000		0.80 (peanut)
distance from orbit of Neptune to Pluto	 1,404,000,000	  234
	diameter of Pluto			 2,300		0.04 (pinhead)
total of distances			 5,900,000,000	  983

distance from Earth to Moon		       384,000		6.40
	diameter of Moon			 3,500		0.06 (pinhead)

This makes the total walk slightly less than a kiloneter (1000 meters). You can call it "about a kilometer." Then a light-year (9,460,530,000,000 kilometers) because in the model 1,600 kilometers, and the nearest star, at 4.22 light-years, is about 6,700 kilometers away.

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