The whys and wherefores of navigation

by Gershom Bradford

The interval between two successive transits of the sun across the meridian constitutes a solar day, and likewise the period required for a certain star to return to the same meridian is a sidereal day, but these two days are not of the same length. The solar day we know is 24 hours long, but its sidereal contemporary has a length of only 23 hours, 56 minutes (approximately) solar time. The sidereal clocks, however, are geared to show 24 hours, sidereal time, in 23 hours, 56 minutes, solar time. By this it will be seen that in any given period the face of the sidereal clock will show more hours than the solar clock.

Both the solar and sidereal clocks start even at the vernal equinox, about March 21st, but from then on, the sidereal clock gains on the solar time clock about 4 minutes a day until in a year it is a full 24 hours ahead, showing that there is one more day in a sidereal year than in a solar year. The approximate relation of the times shown by these clocks is readily calculated by allowing a gain in the sidereal clock of one hour for each 15 days after March 21st, or two hours for each month.

In order to aid in a simpler explanation, let us again follow the earth around its orbit and note the conditions that distinguish sidereal from solar time. Let us once more assume it to be the time of the vernal equinox, the clocks, both sidereal and solar, now show 0 hours, and the sun, the earth and the First Point of Aries are in range. The earth immediately moves out of line by virtue of its onward motion, and the sun correspondingly appears to move eastward; this is imperceptible at first, however, and not noticeable without a careful measurement, as it seems to be swallowed up in the contrary (westward) diurnal movement.

After 24 hours of rotation from the instant of the equinox the earth turns the meridian until it causes the First Point of Aries to transit, marking sidereal noon of the first day. The sidereal clock at this moment reads 24 hours, but a glance at the solar clock shows 11 hours 56 minutes A.M., about 4 minutes short of (solar) noon. An observation will show that the sun has apparently moved about a degree eastward of the hour circle passing through the First Point of Aries since the preceding noon, and the earth must turn this extra degree before the sun will be brought to the meridian, thus occupying the 4 minutes mentioned above. In other words, the earth turns 360° in a sidereal day but must turn about 361° in a solar day.

Three months after the vernal equinox, the angle between the First Point of Aries and the sun becomes, in round numbers, 90°, and it requires 6 hours for the earth to bring the sun to the meridian after the passage of the First Point of Aries. In plainer language, when the First Point of Aries crosses the meridian (sidereal noon) the sun is about 90° to the left—about rising in the eastern sky; the earth must make a quarter turn, or 6 hours, before it will be solar noon. Thus it will be seen that at this point sidereal time is 6 hours ahead of solar time.

In six months, when the First Point of Aries is on the meridian the noonday sun is shining on the antipodes, and it lacks 12 hours of solar noon. The difference between the sidereal and solar clocks has now reached 12 hours and through a continuation of the same process the interval between their readings, widens throughout the remainder of the year.

When the 21st of March comes around again, and the meridian presents itself to the sun and the First Point of Aries in range, a careful count of the number of times this latter point has crossed the meridian during the year, discloses 366¼ transits. That is, the earth has actually turned about its axis 366¼ times. The sun is found to have passed the meridian only 365¼ times. Counting the rotations of the earth by the number of the sun’s transits while we are revolving around him, causes the apparent loss of a day due to the earth unwinding itself once, so to speak, during the year. The accumulated difference amounts to one sidereal day. Hence it will be seen that a year contains 366¼ sidereal days of 23 hours, 56 minutes each, and 365¼ solar days of 24 hours each.

Now for a recapitulation of the subject of time.

The rotation of the earth is the real standard of measuring time intervals; the period required for this rotation does not vary. It has been suggested that the tide waves have a minute effect on the regularity of this movement, but the construction of our clocks is such, that if any variation exists we are unable to detect it. Whether we use the passages of the stars, or the transits of the sun to reckon our time, it falls back in either case upon the diurnal rotation of the earth.

Apparent time is measured by the seeming progress of the actual sun. The time of its transit of the meridian is irregular, but is always shown by its “dip,” culmination, with the sextant.