A Text-Book of Astronomy

by George C. Comstock

But it is only in appearance that the pole maintains its fixed position among the stars. If photographs are taken year after year, after the manner of [Exercise 7], it will be found that slowly the pole is moving (nearly) toward Polaris, and making this star describe a smaller and smaller circle in its diurnal path, while stars on the other side of the pole (in right ascension 12h.) become more distant from it and describe larger circles in their diurnal motion; but the process takes place so slowly that the space of a lifetime is required for the motion of the pole to equal the angular diameter of the full moon.

Spin a top and note how its rapid whirl about its axis corresponds to the earth's diurnal rotation. When the axis about which the top spins is truly vertical the top "sleeps"; but if the axis is tipped ever so little away from the vertical it begins to wobble, so that if we imagine the axis prolonged out to the sky and provided with a pencil point as a marker, this would trace a circle around the zenith, along which the pole of the top would move, and a little observation will show that the more the top is tipped from the vertical the larger does this circle become and the more rapidly does the wobbling take place. Were it not for the spinning of the top about its axis, it would promptly fall over when tipped from the vertical position, but the spin combines with the force which pulls the top over and produces the wobbling motion. Spin the top in opposite directions, with the hands of a watch and contrary to the hands of a watch, and note the effect which is produced upon the wobbling.

The earth presents many points of resemblance to the top. Its diurnal rotation is the spin about the axis. This axis is tipped 23.5° away from the perpendicular to its orbit (obliquity of the ecliptic) just as the axis of the top is tipped away from the vertical line. In consequence of its rapid spin, the body of the earth bulges out at the equator (27 miles), and the sun and moon, by virtue of their attraction (see [Chapter IV]), lay hold of this protuberance and pull it down toward the plane of the earth's orbit, so that if it were not for the spin this force would straighten the axis up and set it perpendicular to the orbit plane. But here, as in the case of the top, the spin and the tipping force combine to produce a wobble which is called precession, and whose effect we recognize in the shifting position of the pole among the stars. The motion of precession is very much slower than the wobbling of the top, since the tipping force for the earth is relatively very small, and a period of nearly 26,000 years is required for a complete circuit of the pole about its center of motion. Friction ultimately stops both the spin and the wobble of the top, but this influence seems wholly absent in the case of the earth, and both rotation and precession go on unchanged from century to century, save for certain minor forces which for a time change the direction or rate of the precessional motion, first in one way and then in another, without in the long run producing any results of consequence.

The center of motion, about which the pole travels in a small circle having an angular radius of 23.5°, is at that point of the heavens toward which a perpendicular to the plane of the earth's orbit points, and may be found on the star map in right ascension 18h. 0m. and declination 66.5°.

Exercise 20.—Find this point on the map, and draw as well as you can the path of the pole about it. The motion of the pole along its path is toward the constellation Cepheus. Mark the position of the pole along this path at intervals of 1,000 years, and refer to these positions in dealing with some of the following questions:

Does the wobbling of the top occur in the same direction as the motion of precession? Do the tipping forces applied to the earth and top act in the same direction? What will be the polar star 12,000 years hence? The Great Pyramid of Egypt is thought to have been used as an observatory when Alpha Draconis was the bright star nearest the pole. How long ago was that?

The motion of the pole of course carries the equator and the equinoxes with it, and thus slowly changes the right ascensions and declinations of all the stars. On this account it is frequently called the precession of the equinoxes, and this motion of the equinox, slow though it is, is a matter of some consequence in connection with chronology and the length of the year.

Will the precession ever bring back the right ascensions and declinations to be again what they now are?

In what direction is the pole moving with respect to the Big Dipper? Will its motion ever bring it exactly to Polaris? How far away from Polaris will the precession carry the pole? What other bright stars will be brought near the pole by the precession?

47. The warming of the earth.—Winter and summer alike the day is on the average warmer than the night, and it is easy to see that this surplus of heat comes from the sun by day and is lost by night through radiation into the void which surrounds the earth; just as the heat contained in a mass of molten iron is radiated away and the iron cooled when it is taken out from the furnace and placed amid colder surroundings. The earth's loss of heat by radiation goes on ceaselessly day and night, and were it not for the influx of solar heat this radiation would steadily diminish the temperature toward what is called the "absolute zero"—i. e., a state in which all heat has been taken away and beyond which there can be no greater degree of cold. This must not be confounded with the zero temperatures shown by our thermometers, since it lies nearly 500° below the zero of the Fahrenheit scale (-273° Centigrade), a temperature which by comparison makes the coldest winter weather seem warm, although the ordinary thermometer may register many degrees below its zero. The heat radiated by the sun into the surrounding space on every side of it is another example of the same cooling process, a hot body giving up its heat to the colder space about it, and it is the minute fraction of this heat poured out by the sun, and in small part intercepted by the earth, which warms the latter and produces what we call weather, climate, the seasons, etc.