TUNGSTEN VALLEY — Last month we saw how to measure the earth’s size with just an odometer and a pair of sticks at two locations, and that a Greek scientist pulled it off 2,300 years ago. This month we ascend the next rung on the cosmic distance ladder: to the moon.

Just as the Greeks resolved the earth’s size without benefit of any modern (post-1600) technology, so they also measured the moon’s distance to within a few percent with only the simplest of tools but the sharpest of brains.

Three Greek mathematical astronomers, working between 250 B.C. to 150 A.D., independently sorted out Luna’s distance with progressively better accuracy.

First at bat, around 250 B.C., was Aristarchus of Samos. He wrote a book, now lost, where he became history’s first person to argue for the earth’s movement around the sun. In another book, still extant, he used observations of the earth’s shadow on the moon’s face during a total lunar eclipse to derive relative distances for the sun and the moon.

He missed on the sun’s distance but his value for the moon’s distance, 67 earth radii, was only off by about eleven percent from the true value of 60 earth radii.

About three generations later came Hipparchus, who worked at Rhodes. 

He noted that a solar eclipse (either March 14, 189 B.C. or November 20, 128 B.C.) was total near what’s now Istanbul, but that only 4/5 of the sun’s face was covered at Alexandria. Applying the separation between the two observation points, the angular difference of the moon at those places, and the uncertainties in the observational data, he bracketed the lunar distance between 59 to 67 earth radii.

If you think this month’s diagram, a schematic of Hipparchus’s method, looks complicated, it is actually substantially simplified from the geometry he had to address. In order to complete his work, he had to invent a new branch of mathematics, trigonometry.

Batting clean-up was Ptolemy of Alexandria around 150 A.D. Like Hipparchus, Ptolemy used parallax measurements of eclipses and of the moon’s location against background stars. In his Almagest (from the Arabic al-Majisti), which would be translated from Greek to Syriac to Arabic and eventually into Latin in Spain after having been lost in Europe for a millennium, he arrived at a lunar distance of 59 earth radii, accurate to 1.7 percent. That number would not be improved upon until 1751.

The rapid progress made on the problem of lunar distance between 250 B.C. to 150 A.D. was emblematic of the bright light that Greek science was, until it flickered out in a Mediterranean world that found no particular value in knowledge for its own sake after the First Century.

For the next thousand years, European intellectual achievement would remain stunted.

Not until 1543 would Aristarchus’s old, discarded idea that the earth orbits the sun be reborn and revitalized in Copernicus’s De Revolutionibus. Next month, we’ll use that intellectual breakthrough to ascend the third rung of the cosmic distance ladder—the distance of the earth from the sun.

October Fun Astro Fact: The moon’s size in the sky is the same when it’s at the horizon as when it’s high overhead. You can check that yourself, by sighting it through the visual gap of a threaded C-clamp braced on a tripod. The moon seems larger when it’s rising or setting because we see it juxtaposed with terrestrial objects.

In October Skies:

The sun begins the month in Virgo, entering Libra on the 25th. At mid-month, days and nights are 11 and 13 hours long, respectively.

The moon’s dates are: Last Quarter October 3; New October 10; First Quarter October 18; Full (Hunter’s Moon) October 25.

October Meteors: Camelopardalids October 6; Draconids, southern Taurids, and delta Aurigids October 7; epsilon Geminids October 18; Orionids (Halley’s Comet debris) October 21-22; and Leonis Monorids October 25.

Best Sky Viewing Nights (Minimal Moon): October 1-17.

Sunset (Mid-Month): Pegasus is low in the east; the Navigator’s Triangle of Vega, Deneb and Altair is high overhead; Arcturus is setting in the west.

Midnight (Mid-Month): Capella is high in the northeast in Auriga. Just above it is brilliant Perseus with Algol. Andromeda is directly overhead. Cetus, the Whale, is in the south. Orion rises in the east.

Sunrise (Mid-Month): Leo is high in the southeast. Orion is in the southwest. Sirius, in Canis Major, is low in the south.

Mercury, in Libra, gives its best viewing for the fall on the 12th, low in the west at sunset.

Venus, in Libra, is lost in the sunset.

Mars, in Cancer, rises at 1 a.m. Halfway between Jupiter and Castor and Pollux, it is high in the ESE at sunrise.

Jupiter, in Hydra, rises at 2 a.m. and is high in the east at sunrise. It and its moons will pass behind (be occulted by) the moon between 2:15 to 3:45 a.m. in Nederland on October 6.

Saturn, in Pisces, is at its brightest apparition of the year at opposition (directly opposite the sun) on the 4th. It rises at sunset and sets at sunrise.

Notable Space Mission Being Ripped: NASA’s Heliophysics Division is slated to pull the plug on the New Horizons (visited Pluto in 2016) solar wind and interstellar dust measurements. This is due to $2 million having been cut from its mission for the next year. Put in perspective, that’s what the DoD’s Inspector General says the US has been spending on its Iran War every 15 minutes since February 28. That’s the humiliating level of degradation that this country has come to under this administration.

Frank Sanders, a spectrum scientist, takes astronomy-related inquiries at backyardastronomy1@gmail.com.