TUNGSTEN VALLEY — So, you’re a castaway on a desert island after a worst-ever three-hour tour. On the upside, you’ve perfected Mary Ann’s coconut cream pie recipe. But now, how to fill your copious spare time?

Find the planets’ distances! Your yardstick will be the earth-sun distance, the Astronomical Unit (AU). Begin by building a three-foot diameter protractor out of palm logs and coconuts, installing it in a clear-sky spot.

Mercury and Venus are easy. Night after night, you measure and record the angle (elongation) between each of these planets and the sun at sunset or sunrise. They each eventually reach a maximum solar elongation, and then they reverse. 

These observations will absorb three or four months for Mercury, and up to 20 months for Venus. Mercury elongates as far as 18 to 28 degrees; its orbit therefore joggles between 0.31 to 0.47 AU, per the sine relation in this month’s picture. Venus’s max elongation, 46 degrees, puts it 0.72 AU from the sun.

The outer planets, Mars through Saturn, are trickier. Although you still measure angles with your protractor, you must now run day counts. For each outer planet, start counting on the day when planet-rise is the same moment as sunset. This is opposition, Day 0, when the earth is exactly between the sun and the planet.

You count days until each planet reaches 90 degrees, quadrature, from the sun. For Mars, Jupiter, and Saturn these will be about 106, 87, and 88 days.

You continue counting days until each planet reaches opposition again. Mars, Jupiter, and Saturn oppositions are every 26 months; 13 months; and 12 months plus 13 days, respectively.

These intervals tell you how long each outer planet takes to orbit the sun: 687 earth days for Mars, 12 years for Jupiter, and 30 years for Saturn. That’s because the excess time beyond one earth year for each opposition is the fraction of the planet’s orbit which it completes in an earth year. For instance, Jupiter gains (13 – 12 months) = 1 earth month, or 1/12 of its orbit per earth year. Therefore, Jupiter takes 12 earth years to go once around the sun.

Finally, you plug your quadrature day counts (Δt) and the earth and planet year lengths in days (T earth, T planet) into the formula in this month’s picture. That’s your solar distance for each outer planet: 1.5 AU, 5.2 AU, and 9.6 AU for Mars, Jupiter, and Saturn.

Now, start that long-delayed remodel of Ginger and Mary Ann’s hut.

The ancient and medieval Babylonians, Greeks, Arabs, and Persians could have done this project if they’d had the nerve to try out a sun-centered planetary system. It only jelled with Copernicus’ 1543 blockbuster hit, De Revolutionibus. A major Copernican advantage was automatic prediction of planetary distances. Earth-centered systems couldn’t do that.

Which brings us to next month’s step-up on the cosmic distance ladder: How big is an AU, anyway?

November Fun Astro Fact: Earth-based radars in the 1960s gave exact distances to Mercury, Venus, and Mars, plus revealing surface features and Mercury and Venus day lengths.

In November Skies:

The sun begins the month in Libra, entering Scorpius on the 26th. At mid-month, days and nights are 9.5 and 14.5 hours, respectively.

The moon’s dates are: Last Quarter November 1; New November 9; First Quarter November 17; Full (Beaver Moon) November 24.

Standard Time began November 1; we gained time as clocks moved backward one hour at 2 a.m.

November Meteors: The North Taurid shower (parent comet Encke) peaks November 11-12. The Leonid shower (parent comet Tempel-Tuttle), one of the year’s best, peaks November 18.

Best Sky Viewing Nights (Minimal Moon): November 1-16.

Sunset (Mid-Month): The Milky Way glistens, southwest to northeast. Fomalhaut rises with the Pleiades and Capella. The Andromeda galaxy is high in the northeast, presenting a nice binocular view. Deneb is directly overhead; Vega a bit westward; Altair southward.

Midnight (Mid-Month): Gemini twins Castor (above) and Pollux (below) are high in the east. Below them and to the right is Procyon. Orion and Sirius are in the southeast. The Great Nebula that births stars in Orion’s sword is naked-eye visible, a terrific binocular view. Andromeda is high in the northwest. Brilliant Capella is nearly overhead; Cassiopeia is high in the northwest.

Sunrise (Mid-Month): Spica is low in the southeast; Arcturus is high in the east; the Big Dipper is overhead. Capella is high in the northwest as Orion sets.

Mercury, in Libra, will give its best dawn viewing of the year in the eastern sky just before sunrise on November 20.

Venus, in Virgo, is the Morning Star, conjuncting spectacularly with Spica November 10.

Mars, rising in Leo at 11 p.m., conjuncts magnificently with Jupiter November 15-16. 

Jupiter, rising in Leo at 11 p.m., conjuncts with Mars November 15-16.

Saturn, in Pisces, is high in the southeast at sunset, setting at 3 a.m. This month gives the best viewing of the year!

Notable Space Missions: The 8-year-old BepiColombo mission drops into orbit around Mercury on November 21. Its two orbiters will observe the planet’s geology, exosphere, and magnetic field.

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