Revolution Of The Earth In Its Orbit

The stars which are seen nearest to the sun after sunset at different times of the year are not the same, but belong to different signs of the zodiac. This change of position of the sun with respect to the stars takes place at the rate of about 1° a day, so that the whole heavens appear to revolve once in a year independent of their diurnal revolution. This is due to the real revolution of the earth in its orbit. The stars appear to describe little ellipses in the course of a year, but, as a matter of fact, it is the light coming from the stars that is displaced by the motion of the earth in its orbit, the form of this orbit being elliptical, so that the star's position is changed in such a way as to project an ellipse similar to that which the earth traces out. This phenomenon is known as the aberration of light, and was discovered by Bradley.

Velocity Of Light

Fizeau determined the velocity of light by reflecting a spot of light from a mirror at one station to a second mirror at a distant station. The light was brought to a focus at the required points by means of lenses. A toothed wheel whose revolutions could be registered was so placed that its teeth revolved in the focus, and the spot of light could be seen between two teeth. It was possible to turn the wheel so quickly that the spot of light was stopped by a tooth coming up before it could pass through. The distance between the stations being known, and the rate at which the wheel turned, the velocity of light could be found. Foucault's method consisted of a rapidly rotating mirror, on which a beam of light was admitted through a slit. It was then reflected on to a lens, after which it was brought to a focus on a concave mirror at some distance. It was found possible to turn the mirror so quickly that it moved through a small angle before the spot of light returned. The distance between the mirrors, the rate of rotation of the mirror, and the amount of displacement being known, the velocity of light could be estimated. The velocity of light and the aberration angle being known the sun's distance can be found.

(1) The ratio of the velocity of light and the earth in its orbit as determined by observation is as 10,089 : 1.

(2) The earth completes its orbit in 365 days.

(3) Light would do the same journey in 365 / 10,089 days.

(4) Knowing the time it would take to complete the revolution we can find how long it would take to cross the diameter, and therefore the radius.

(5) We multiply the number of seconds taken by light to cross the radius of the earth's orbit by the velocity of light, and it gives us 92,628,000 miles as the sun's distance.

The Sun Not Always At The Same Distance From The Earth

In the Nautical Almanac the sun's apparent diameter is given for every day in the year. The apparent diameter was 32'35.2" on January 3rd, 1904, and on July 4th of the same year it was only 31'30.7". This proves the sun is farther away from us in summer than in winter.

Perihelion And Aphelion

When the earth is nearest to the sun it is said to be in Perihelion, and when farthest from the sun it is said to be in Aphelion.

The Earth Moves With Varying Velocity In Its Orbit

This is ascertained by measuring the sun's longitude for two successive days at different times of the year, by which means it is found in December to move over 61'10.0" within a period of twenty-four hours, while in June it only moves over 57'10.8" in the same time.

Kepler's Law Of Equal Areas

Kepler found that the line joining the center of the sun with the center of the earth moved over equal areas in equal times, that is, the greater distance of the earth from the sun in June compensated for the smaller arc of motion in longitude, so that lines drawn from the sun to the extremities of the arcs moved over make equal triangles.

How The Inclination Of The Ecliptic To The Plane Of The Earth's Equator Is Determined

The elevation of the sun above the horizon is measured by the shadow cast by the gnomon, or the north polar distance is ascertained by the transit instrument for each day in the year. In either case the sun will be found to oscillate backwards and forwards over an arc of about 47°, half of which arc is the inclination of the ecliptic to the equator.

Nodes

The two points where the plane of the ecliptic crosses the plane of the celestial equator or equinoctial are called nodes, that point at which the sun appears to come up from below the equator being called the ascending node, and that at which the sun appears to descend from above the same plane being called the descending node.

The First Point Of Aries

The ascending node above referred to is the first point of Aries. It is universally used by astronomers for fixing the longitudinal and right ascension of celestial bodies.

The Sidereal, Solar, And Mean Solar Day

The sidereal day is the interval which elapses between two successive appearances of the same star on the meridian. The solar day is the interval which elapses between two successive appearances of the sun on the meridian, but these are not of the same length. The mean solar day is the interval of time obtained by adding all the solar days in a year together, and then dividing by the number of days in a year.

Equation Of Time

The inequality of the solar days arises from two causes, namely, the obliquity of the ecliptic to the equator, and the unequal velocity of the earth in its orbit. The equation of time is the algebraic sum of these two variables - that is to say, sometimes they both cause the sun to come too soon to the meridian; at other times one causes the sun to come up too soon and the other too late. In the former case the sum of the two corrections, and in the latter case the difference of the two corrections, is the equation of time, and so on.