This section is from the book "Scientific American Reference Book. A Manual for the Office, Household and Shop", by Albert A. Hopkins, A. Russell Bond. Also available from Amazon: Scientific American Reference Book.
The seasons are the result of the revolution of the earth in its orbit and the inclination of the ecliptic to the equator. The sun on this account attains different heights above the horizon, giving different lengths of day and night. By reason of its giving to the earth more heat in the day than it loses by radiation in the night, and vice versa, we have summer or winter as the case may be.
The ordinary or tropical year is the period which elapses between two successive appearances of the sun at the vernal equinox. The anomalistic year is the period which elapses between two successive returns of the sun to his perigean point. The sidereal year is the time which elapses between two successive appearances of the same star on the meridian at the same time of day.
The sun and moon attract the protuberant portion of the earth's equator more on that side nearest to them than on that side farthest away, and in this way the differential attraction tends to tilt the axis a little, so that it describes a circle in about 25,800 years. The moon's differential attraction is greater than that of the sun. On account of the moon continually changing its relation to the earth's equator, it causes the axis of the earth to describe a circle with a wavy circumference, to which effect the term nutation, or nodding of the earth's axis, is applied.
Astronomical Symbols and Abbreviations.
° Degrees. ' Minutes of Arc. " Seconds of Arc. N. North. S. South. E. East. W. West.
Aquarius. . .
m Minutes of Time.
s Seconds of Time.
Terrestrial latitude is measured from the equator to the poles, north and south. Terrestrial longitude is, in England, measured from the meridian of Greenwich, but other countries use their own meridians. Right ascension is measured from the first point of Aries. Declination is measured from the celestial equator. Celestial longitude is measured from the first point of Aries. Celestial latitude is measured from the ecliptic.
Variation in the Length of Degrees of Latitude.
Length of Degree in Feet.
Sweden. . .
Cape of Good Hope
The ratio between the radius of a circle and its circumference is always the same, no matter how large or small the circle may be. Thus, an arc of 57.2958° on any circle is equal in length to the radius of that circle; and if this be reduced to seconds of arc, we get 206,265" as the number of seconds in a length of arc equal to radius. The mean angular diameter of the sun, as measured by the micrometer, is a little over 32' of arc. We may consider the sun to form part of the circumference of a circle, with its distance from the earth as radius. There are 1920" in 32', and 206,265 / 1920 = 108 nearly; hence the distance of the earth from the sun is 108 times the diameter of the sun, whatever that may be. But we know the distance of the sun to be 92,885,000 miles; so that the diameter of the sun must be 92,885,000 / 108 = 860,000 miles.
The same method applies to the planets and their satellites as well as to the sun. The angular diameter of the body being measured in seconds of arc, it bears the same ratio to 206,265 (the number of seconds in a length of arc equal to radius) that the diameter in miles bears to the distance in miles; or, calling the actual diameter d, and the real distance D, we have d = D X angular diameter / 206,265 . For example - the moon, in round numbers, is 240,-000 miles distant, and its angular diameter is a little over 31'; hence, by the formula, its diameter is d = 240,000 X 1860 / 206,265 = 2164 miles.
Density of the Earth.
Attraction of leaden ball
The synodic period may be readily observed, and from it the actual time occupied by a planet in completing its revolution round the sun can be calculated. For example, the synodic period of Mercury is 115.9 days; this means that the earth and the planet being in a line with the sun at any time, the latter has progressed in its orbit so quickly as to complete an entire revolution and again overtake the earth during the period of 115.9 days. Now the earth moves360o / 365.25 = 0.9856° in a day, and in the entire period 115.9X0.9856° = 114.2°.
But the planet has moved 360° + 114.2° =
474.2° in the same time, hence the period of the planet is to that of the earth as 114.2° :
474.2°, that is, 114.2oX365.25/474.2o = 88 days nearly.
The names of the principal meteor swarms and the dates of their appearance are as follows: -
Comet having same Orbit.
Comet I. 1861
11 August. . .
Comet III. 1863
The number of stars in the northern hemisphere in Argelander's catalogue is 324,000. The number of known variables is 111, and the suspected variables 381. Roughly, then, there is one variable in every 660 of the known stars. According to Duner, about 1 in 7 of the third type stars is variable.