The whys and wherefores of navigation

by Gershom Bradford

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 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 it 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 equinoxes.

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 the 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 of 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 even 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 does not allow a delay of this favorable season in northern latitudes, but continues to make the sun’s vertical rays follow the terrestrial ecliptic as before on its way toward the intersection with the equator 90° away. On this leg of the journey, the sun is traveling on the upper one of two converging 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 the earth is on the opposite side of the sun, and the change of seasons is the entrance of spring for the dwellers in southern latitudes.