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Scale of the Galaxy Near the Sun from 1901

-- | July 15, 2012

Question: I am reading a very interesting book called, ‘Astronomy for Everybody’, published in 1901. I was wondering if the following scale model of the universe is in agreement with what has been learned by scientists since the publication of the book. The author says; The earth is represented by a mustard seed, the moon a particle one fourth of that size placed at about an inch from the earth. The sun is represented by a large apple, placed at a distance of forty feet. Other planets, ranging in size from an invisible particle to a pea, vary in distance from the sun from ten feet to a quarter of a mile. On this scale the whole solar system can be laid down in a field half a square mile. Outside of this field would be a tract broader than the whole continent of America without a visible object in it unless perhaps comets scattered around its border. ‘Far beyond the limits of the American continent we would find the nearest star, which, like our sun, might be represented by a large apple. At still greater distances, in every direction, would be other stars, but, in the general average, they would be separated from each other as widely as the nearest star is from the sun. A region of the little model as large as the whole earth might contain only two or three stars.'”… I’m doing research on the subject and found the authors scale astounding and would like to reference it but am not sure if his information is outdated. Can you help me? Thanks, — EB

Answer: First lets figure out what the scale is for this model. The distance from the Earth to the Sun is described as being 40 feet. The measured distance from the Earth to the Sun is one Astronomical Unit, which is about 1.5×10^(11) meters. So, let’s use 1 inch = 3×10^(8) m for our model scale. Using this scale I derive the following from the author’s descriptions:

Earth = mustard seed = 0.05 inch = 1.5×10^(7) meter
Earth to Moon = 1 inch = 3×10^(8) meter
Moon = 1/4 Earth = 0.0125 inch = 4×10^(6) meter
Sun = large apple = 4 inch = 1.2×10^(9) meter
Other Planets = invisible to pea = < 0.25 inch = 7.5×10^(7) meter
Other Planets Distance = 10 ft to 1/4 mile = 120 to 15840 inch = 3.6×10^(10) to 4.8×10^(12) meter
Solar System Size = 0.5 mile = 31680 inch = 9.5×10^(12) meters
Nearest Star = American Continent = 3000 miles = 1.9×10^(8) inch = 5.7×10^(16) meter

Now, let’s compare these calculated distances to their actual values:

Earth = 4×10^(7) meter
Earth to Moon = 4×10^(8) meter
Moon = 3.5×10^(6) meter
Sun = 1.4×10^(9) meter
Other Planets = 5×10^(6) (Mercury) to 1.5×10^(8) (Jupiter) meters
Other Planets Distance = 5×10^(10) (Mercury) to 6×10^(12) (Pluto) meters
Solar System Size = 1.5×10^(13) meter
Nearest Star = 4×10^(16) meter

It appears to me that the rough scale described by this author is pretty close to the measured scale of our galaxy near the Sun. The only thing I think the author might not have quite right is the last comment about the number of stars within the scale of the size of the Earth in their model, which would be an actual size of about 10^(17) meters. This is a size of about 4 parsecs. There are about 64 known stars within 5 parsecs of the Sun, so the estimate of “only two or three stars” within the scaled size of the Earth in their model is a bit of an underestimate.

Jeff Mangum

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