By Jim Kaler

To the north, our eye is drawn to the Big Bear and its iconic asterism, the Big Dipper, or Plough. Given a Big Dipper there ought to be a Little Dipper and also a Little Bear, but in the lights of town, or with moonlight embracing the sky, they (or really it, as the Little Dipper and Bear are pretty much the same thing) are devilishly difficult to see. We are often stuck with making out the end of the Dipper's handle, marked by second magnitude Polaris (Alpha Ursae Minoris), and the top front bowl star, Kochab (Beta), which is almost as bright. Of paramount significance, Polaris is the famed marker of the North Celestial Pole (NCP), about which the sky daily turns. Generations of people have used it as a guide. While lost in the streets of town, you can use it to find north so as to get home. The star is not quite at the Pole, but about 3/4 of a degree off of it. Knowing that the observer's latitude equals the altitude of the NCP above the horizon you can get one of your terrestrial coordinates to within about 85 kilometers or 50 miles, which is admittedly not good enough to get one home from the local pub. While of importance to us, early explorers were surprised to find that Polaris was of little use to the Inuit of the far north. Nearly overhead, it loses its ability to direct. Horizon stars serve better.

In a dark sky, other asterisms abound. Polaris is the bright gem of the "Engagement Ring," a ragged circle of faint stars a couple degrees across that includes rather obvious sixth magnitude HR 286, which pops out nicely in binoculars right next to Polaris. Opposite the North Celestial Pole from Polaris the polymath Robert Hooke (1636-1703) invented a charming though faint and now obscure "constellation" about four degrees across made of sixth to eighth magnitude stars he called "the English Rose." (See Martin Beech's article in the October 2004 issue of the Journal of the Royal Astronomical Society of Canada.) Farther out, Kochab and the other front bowl star, third magnitude Pherkad (Gamma), together make the "Guardians of the Pole" that circulate around and "protect" it.

Polaris was not always the polar marker. As a result of the Earth's 24 hour spin, 1670 kilometers (1040 miles) per hour at the equator, it bulges outward from the center by 20 kilometers (12 miles). You weigh less at the equator than at the poles and pendulum clocks run slower. The Moon orbits not in the Earth's equatorial plane but close to the ecliptic plane (that of Earth's orbit), which is tilted to the equatorial by 23.4 degrees. The pulls of the Moon and, to a lesser extent, the Sun on the terrestrial bulge make the Earth's rotation axis slowly turn about the orbital perpendicular with a period of 25,800 years. As a result, we see the NCP describe a small circle around the North Ecliptic Pole (NEP) in Draco with a radius of 23.4 degrees. Since we are on the moving body, we actually see the reverse, the NEP going about the NCP. The motion, "precession," is so obvious that it was discovered by Hipparchus round 150 BC. In 2500 BC, Thuban, Alpha Draconis, was our pole star, as noted by the ancient Egyptians. The NCP then made a reasonably close pass to Kochab around 1100 BC (the star once called "Polaris"), and here we are with our Polaris, toward which the Pole is still moving. It will glide just under half a degree from Polaris in 2105 and thereafter will pull away. In 2500 years, Gamma Cephei will be a rather poor marker, offset by three degrees. The Pole distantly visits Vega around the year 14,000 and will be back to Polaris in 26,000 years, though it won't be as good as it is today, so enjoy it. Variations in the gravitational pull on the Earth's bulge, caused mostly by the tilt of the lunar orbit to the ecliptic, produce wobbles collectively called "nutation" in the precessional circle of up to 19 seconds of arc. More than a hundred nutational terms are known. The South Celestial Pole has no significant marking star unless you count dim Sigma Octantis in the modern constellation Octans.

If the NCP wobbles, so must the celestial equator. As a result, the equinoxes (the points of intersection between the equator and ecliptic) move westerly through the constellations at a rate of just over 50 seconds of arc a year. Precession thus causes the coordinates of stars (right ascensions and declinations) to change continuously at rates that depend on where they are. The Vernal Equinox is now in Pisces. But earlier than 100 BC it was in Aries, and around 2700 AD it will enter Aquarius, the effect also changing the constellations one sees over the precessional period. The equinoxes as well as the solstices will thus go through all the constellations of the Zodiac. Indeed, the Summer Solstice, traditionally in Gemini, recently crossed the formal border with Taurus. Most astrologers have tied the signs of the Zodiac to the Vernal Equinox. Hence if you are a "Capricorn," the Sun was in Sagittarius when you were born. That is not why astrology does not work.

Given its proximity to the NCP, Polaris is visible almost any time from almost anywhere in the northern hemisphere. In the nineteenth century it therefore made a potentially excellent zero point for the developing magnitude system. Magnitudes are relative, a full magnitude corresponding to a factor of 2.512... in brightness. Polaris anchored the system at magnitude 2.0 and all other stars were compared to it. Unfortunately, Polaris is a variable star, which obviously makes it a rather poor foundation. (Many are the stars that have seemed to be variable because they had variable comparison stars.) And it's not just any variable, but a class F supergiant (highly evolved) Cepheid. That gives one pause, as Polaris seems to be rock solid, not like the classic pulsating Cepheids Delta Cephei, Eta Aquilae, and Zeta Geminorum, which vary by good fractions of a magnitude over respective periods of 5.4, 7.2, and 10.2 days. Luminous and easily-seen Cepheids are of extraordinary importance in establishing the distance ladder of the Universe because of the tight relation between their periods and luminosities, which once known give their distances and the distances of the assemblies in which they lie. Polaris, however, is a singular case. Over the past century it has nearly stopped pulsating, changing only by a few hundredths of a magnitude over an interval of 3.4 days, which is not at all noticeable to the naked eye. It's thought to be changing from an overtone pulsator (similar to the first overtone in a guitar string) to a fundamental mode of 5.7 days. A modern network of other magnitude calibrators then sets the mean magnitude of Polaris at 2.02. It's a big star. At a distance of 430 light years and a temperature of 6000 Kelvin, it radiates with the light of 2200 Suns, giving it a radius of 45 times the solar radius and a mass of six Suns.

An amateur's telescope shows Polaris to be double, with an eighth magnitude F3 dwarf companion 18 seconds of arc (at least 2400 Astronomical Units) from Polaris proper. Spectroscopic and recent Hubble studies reveal a third component, a dimmer F7 dwarf just over a tenth of a second of are away, giving us three F stars in one basket. Close companions are a bane of Cepheid studies as they can contaminate the Cepheid's light and skew the distance.

Beyond this richness, Ursa Minor does not have much more to offer. Kochab is a K4 orange giant, one of many that flock the sky, while Pherkad is a rapidly rotating white A3 giant. In the Little Dipper's handle, Epsilon UMi is a G5 eclipsing binary that changes by just 0.04 of a magnitude with a period of 39.48 days. It spins so fast thanks to interaction with its partner that it generates magnetic activity and X-rays. Of interest, but with little attention paid, is the semi-regular class M5 red giant variable RR Ursae Minoris, which lies 34 degrees south of the pole and changes by a few tenths of a magnitude over an uncertain period. But we don't really these when we have Polaris, which teases us with the mysteries of its evolutionary changes and guides our way in the dark.

Copyright © James B. Kaler, all rights reserved. These contents are the property of the author and may not be reproduced in whole or in part without the author's consent except in fair use for educational purposes. First published in the January 2015 Newsletter of the Lowestoft and Great Yarmouth Regional Astronomers, who are gratefully acknowledged.