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by Gershom Bradford II
Chapter III: Declination and Right Ascension, Including Precession
76914User:Newmanbe — Chapter III: Declination and Right Ascension, Including PrecessionGershom Bradford II

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 be 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.

It will be readily seen that during the encircling of the sun there must be one position where the northern axis is inclined directly toward that body, another opposite: where it is headed away from him, and two positions midway where the bearing of the axis (projected on the plane of the orbit) is at right angles to the bearing of the sun from the earth; another feature to be “salted down” in the memory.

If the earth revolved on an even keel, the equator and the “waterline” would be coincident, but fortunately this is not the case, and owing to the inclination of the axis another great circle is defined by the “waterline,” called the terrestrial ecliptic, being directly beneath its celestial namesake. The inclination of the northern pole being in a general way toward the perihelion, correspondingly depresses or “submerges” that half of the equator below the plane of the ecliptic, represented by the “water surface,” and at the same time the opposite side rolls the equator above it. At two points (the equinoxes) on opposite sides of the earth, and at right angles to the direction of its inclination, the equator and terrestrial ecliptic cross each other at the “water’s edge.”

The sun is always exactly overhead for that point of the earth which is nearest to it. This is an essential fact to remember in navigation. Bearing in mind that the sun is stationary and ignoring for a time the rotation of the earth, each advance in its orbit brings about a change of bearing of the sun and a new position becomes the nearest point, and thereby directly beneath the sun. The constant changing of the sun’s bearing continues throughout the year, or one revolution, and a circle of these overhead positions is marked upon the earth, which is coincident with the terrestrial ecliptic—the visionary” waterline.” It is obvious that the vertical rays of the sun must apparently follow this line, for it can only be overhead for places that are in the same plane, and this again is the level of the “ocean.”

This circle of overhead positions projected on the celestial sphere marks the ecliptic—the “margin” of the infinite ocean, and the path that the sun seems to follow eastward among the stars.

The above paragraphs show us that the sun in following this line around the earth crosses the equator twice, and twice he attains a distance of 23° 28’ from it, and so must be on the equator twice and reach a declination of 23° 28’ north and 23° 28’ south in the course of one year.

Returning to our imaginary illustration, we will now follow the peregrinations of the earth for a year and note the effect of its inclination in the different parts of the orbit upon the declination of the sun. It will be assumed that it is the 21st of March and from our airy position we see the earth away on our right nearly 90° from the Perihelion. As this is the vernal equinox, there are a number of interesting points to be considered: The direction of the earth’s axis, projected on the plane of the orbit, is at right angles to the bearing ~ of the sun from the earth; the sun is directly over the intersection of the equator and terrestrial ecliptic, and being I overhead for this point on the equator, the declination must be 0°. Moreover, a line drawn from this intersection, or terrestrial vernal equinox, through the center of the sun and extended to the celestial sphere would strike the corresponding intersection of the ecliptic and the~ equinoctial or celestial equator—the celestial vernal equinox. The arrival of the earth at this position is the~~ signal of spring for the northern hemisphere, likewise

announces the advent of autumn to our southern neighbors below the “Line.” The sun this day rises in the east~ (approximately) and passing through the zenith, sets in ~ the west for those living on the equator. The explorer at the north pole is cheered by the first light as the sun appears in the horizon, while the south pole becomes enshrouded in the long Antarctic night. Without lingering for ceremonies over the change of seasons, the earth continues steadily on its way toward the aphelion; the sun’s vertical rays leave the intersection of the equator and the terrestrial ecliptic, and follow along the latter, thus widening its distance from the equator as the earth proceeds. As the ecliptic, in this half of the orbit is above, or north, of the equator the former is in north latitude and the sun, following along it, is thereby also in north declination. A line from any place having the vertical rays, through the sun to the celestial sphere, always terminates on the celestial ecliptic, all being’ in the same plane, and shows the corresponding celestial position of the sun on it. Its declination distance from the celestial equator, in degrees, minutes and seconds, is identical with that of the place on the earth directly beneath it relative to our equator. So by showing the course of the sun’s overhead positions on the earth its celestial positions are, at the same time, indicated. The overhead position of the sun on the terrestrial ecliptic gradually departs from the equator culminating about June 21st, the summer solstice, in a declination of 23° 28’ at a point near the aphelion in the orbit, 90° (approximately) from the equinox.

The positions in the orbit of the summer and winter solstices are reached by the earth several days before the Points of the aphelion and perihelion. These respective Positions would be in conjunction were it not for a slow and remarkable motion of the earth’s axis before spoken of, and later to be described, called the precession of the equinox.

The summer solstice is the great half-way point of the earth’s annual circumnavigation of the sun; it is a matter of moment all over the world, and another great change of seasons is at hand. The sun is overhead for places along the parallel of 23° 28’ N. and bears north 23° 28’ from th zenith at noon from places on the equator.

At the north pole, since its appearance on the horizon on March 21st, the sun has mounted to an altitude o 23° 28’ and to nearly 67° at places on the Arctic circle The earth’s northern axis is, in this position, inclined 23 28’ directly toward the sun, which pours its rays continuously upon the northern regions, uninterrupted eve by the earth’s daily rotation. It is on this day that the whole Arctic zone enjoys the full glory of the midnight sun. The earth’s continuous movement of revolution doe not allow a delay of this favorable season in northern latitudes, but continues to make the sun’s vertical rays folio the terrestrial ecliptic as before on its way toward the intersection with the equator 90° away. On this leg of th journey, the sun is traveling on the upper one of two con verging lines and thereby gradually lessening its distance from the other—the equator—or, in other words, reducing its declination. This continues until September 21st when the autumnal equinox is reached and the sun’s declination becomes 0°. The sun now being overhead at the intersection of the equator and the terrestrial ecliptic, is on the opposite side of the earth from the intersection of March 21st. In fact the conditions are similar, but now earth is on the opposite side of the sun, and the change seasons is the entrance of spring for the dwellers in southern latitudes.

The sun has dropped lower and lower in the sky the north pole since June, until on this day it is in the horizon and it is time for the Esquimos to seek their igloos and prepare to hibernate during the long Arctic night now ushered in.

The sunshine at the time of the equinoxes is equally distributed over the northern and southern zones, and the zenith distance of the sun at noon at any place is, theoretically, equal to the latitude of the place (except a small error due to change of declination accumulated subsequent, or previous, to the instant of the equinox).

The conditions during the next six months are reversed as the earth proceeds into that half of the orbit containing the perihelion. Now the sun following the terrestrial ecliptic enters southern latitudes or south declination, for in this part of the orbit the equator is above (or north) the plane of the ecliptic. The sun’s diverging course from the equator leads it farther and farther southward until on or about December 21st it arrives at the winter solstice with a culmination of 23° 28’ south declination. At this point the earth is but a few degrees from the perihelion as it was from the aphelion at the summer solstice.

The earth’s north pole is now inclined directly away from the sun and its rays have entirely forsaken the Arctic for the Antarctic zone; notwithstanding the earth’s daily rotation, which brings alternating light and darkness to the greater part of the world, the northern polar regions are in a continuous shadow, and no sunlight reaches these remote parts. At this time of the year the northern hemisphere above the tropic of Cancer, is in an unfavorable position relative to the sun, and as a result places situated On parallels less remote than the Arctic are having long nights and short days in proportion to their latitude north.1 On the other hand, in the southern hemisphere the days are longer and the nights shorter, as the southern latitude1 increases until at the Antarctic circle night disappears and the sunshine is uninterrupted. It is seen that this is an exact reversal of the conditions at the summer solstice.