The angle formed at the pole by the hour circle passing through a body and a local meridian is the hour angle of that body, and is measured westward through 24 hours, although A.M. hour angles of the sun are reckoned eastward through 12 hours.
At the north pole where the zenith is identical with the celestial pole, the vertical circles, parallels of altitude and rational horizon are coincident with the hour circles, parallels of declination and the equator, respectively; but departing from this point they form angles with each other corresponding to the degrees of latitude from the pole; at the equator the angle reaches 90°.
The system of circles described above is by far the most extensively used, and positions determined by its coordinates are comparatively constant, but there is still a third system of circles which was used and handed down to us by the ancients. In the place of the celestial equator, a similar great circle is used, known as the ecliptic. This circle is determined by the extension of the plane of the earth’s orbit to the celestial sphere. The poles of the ecliptic everywhere 90° from this circle are the points from which meridians depart as upon the earth. The prime meridian of this system passes through the intersection of the celestial equator, and the ecliptic—the vernal equinox or First Point of Aries. Celestial latitude and longitude are the coordinates used with this system, but navigators universally prefer to use the well-known declination and right ascension. Hence the path of usefulness of the former seldom leads beyond the observatories.
CHAPTER III
Declination and Right Ascension
Owing to the important place that declination holds in nautical astronomy, a detailed explanation will appropriately follow closely in the wake of the preceding remarks. It must be made clear, before getting under way, that declination is the distance, in degrees, minutes and seconds, of a body north (+) or south (-) of the celestial equator measured on the hour circle passing through the body. This distance is identical with the latitude of the place in the zenith of which the body happens to be. What declination is to a body in the heavens, latitude is to the place on the earth directly beneath it.
The declination of fixed stars changes very slowly from month to month, but the planets meander about on the celestial sphere in a way that is liable to puzzle anyone other than an astronomer. This element, however, is worked out in the observatory and given in the nautical almanac in a way that relieves the navigator of worry concerning the complex movements of these latter bodies. The same may be said of the moon, but the subject will be treated, somewhat superficially though sufficiently for the needs and desires of the practical mariner, in a special talk on the moon. This eliminates all the celestial bodies except the sun, the most important; and for this reason the facts relative to its declination will be considered at some length.
As has already been stated, the sun is stationary, but our movements around it to the right causes it to appear to move to the left; precisely as you see, when under way, an anchored vessel’s masts move to the left along the land behind her, while you move on to the right. We have no landmarks behind the sun by which to observe his apparent movements, so in lieu of such ranges, we resort to the fixed stars, which serve as excellent marks to get a bearing on Old Sol and keep tab on him as he moves eastward among them. This movement must in no way be confounded with his apparent daily motion westward. As an illustration, we may see Orion—a familiar friend—swinging high in the western sky in the early evening; some weeks later he is riding low, and yet a little later still, he is swallowed up in the brilliancy of the setting sun. In other words, the sun and Orion have approached and passed each other. We know Orion does not move, for he is composed of fixed stars, and this seeming westward movement of his is in reality the apparent eastward marching of the sun, which is due to the earth’s movement of revolution. The sun in this apparent movement eastward follows a course at a rate equal to that of the earth, along a great circle of the celestial sphere called the ecliptic, a circle that plays an important part in the explanation of declination, particularly that of the sun. The ecliptic is marked by the extension of the earth’s orbit to the celestial sphere.
A few more words concerning great circles will be introduced here, and the following statements, while they apply to great circles in general, especially fit the relationship of the equinoctial or celestial equator to the ecliptic. These two great circles cut each other at an angle of 23° 28´. Great circles always bisect each other, and hence any two great circles of the celestial sphere, regardless of the angle they may take with the celestial equator, must intersect each other at exactly opposite points, 180° apart. What is true in this regard of the celestial sphere is equally true of the great circles of the earth. A vertex of a great circle is the point which departs the greatest distance from the equator—the highest point of the circle reached in declination. There are two vertices 180° apart with the two points of intersection 90° in either direction. The declination or latitude of either vertex is equal to the angle at which the circles intersect each other. The intersections are called the equinoxes, and it may be well to say here that the word equinox has several meanings in navigation, often rendering it necessary to judge by the text which is intended. The vernal equinox, for instance, refers to a certain time of year—March 21st. The sun is that day directly overhead at the intersection of the equator and the terrestrial ecliptic and this point is sometimes called the vernal equinox. Again, the sun at the same time occupies a point on the heavens also known as the vernal equinox, which is at the intersection of the celestial equator and the ecliptic. The point in the orbit occupied by the earth at this time is also spoken of as the vernal equinox.
The reader is now asked to arouse his imagination and if possible to conceive himself a passenger in an aeroplane equipped with some remarkable power capable of carrying him to a position in space, above, yet a little outside, the earth’s orbit, near the Perihelion, and there to heave to and view awhile an astronomical picture. Spread out before his unrestricted vision will be the earth, its orbit, and the sun. It is to be hoped that the imagination of the reader is still sufficiently supple to suppose the plane of the orbit to be the surface of an infinite ocean stretching away beyond human conception of distance and “breaking” against the celestial sphere; the “surfline” there marks the ecliptic; the “ocean’s” surface representing the great plane of the ecliptic. The sun will be seen as if at anchor in his proper place within the orbit. The earth is “underway,” half submerged, and listed 23° 28´ toward our point of vantage. This inclination, or direction of the axis, is in a general way toward the perihelion, and within a few degrees of being parallel with the long diameter of the orbit. The earth maintains this nearly parallel position of its axis with the long diameter throughout the period of its revolution; a fact of importance to remember.