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LECTURE 2

Earth-Sun Relationships and Illumination of the Globe

I. Earth-Sun Relationships:

Why we have to understand? Because by understanding earth-sun relationships one will be able to determine the apparent path of the sun in the sky, the angles at which sun's ray (light) strike, the lengths of day and night, and the occurence of seasons.

The earth is turning on its axis at the same time that it is moving in a path about the sun, and because the earth's axis is tilted with respect to the plane of its orbit, therefore, it will be much easier for us to view these relationships in 3-dimension, or to view the earth from space.

II. Motion of the Earth: Rotation and Revolution

A. Rotation: The spinning of the earth on its polar axis.

Direction of Rotation: is from west to east (eastward), eastward rotation of the earth. Looking down upon the North Pole - it is counterclockwise rotation; clockwise movement on the South Pole.

Time of Rotation: Mean Solar Day - consisting of 24 mean solar hours, it is the average time required for the earth to make one complete turn (rotation) in respect to the sun.

Velocity of Rotation: rate of travel of a point on the earth's surface in a circular path due to rotation.
Angular velocity (constant on earth) and linear velocity.

Equator: 25,000 miles / 24 hrs = 1050 miles / hr 40,000 km/24 hrs = 1700 km/ hr 60 N & S = 525 miles / hr = 850 km / hr 90 N & S = 0 mile / hr

We are unaware of this motion because the rotation is at an almost perfectly constant rate. All the objects and atmosphere are moving together.

Proof of the Earth's Rotation: the Faucault experiment (1851), French physicist M. Leon Faucault suspended a heavy ball by wire of 200 feet long from a suspended dome, he observed either the pendulum changed its plane or the building was gradually turned around.

d = 15 Sin L

d: number of degree of turning/hr L: Latitude

Oblate ellipsoidal form of the earth is another proof of rotation: centrifugal force caused by rotation on an axis.

B. Revolution of the Earth:

Revolution: The motion of the earth in its orbit around the sun

Direction of Revolution: Looking down upon the North Pole of the Earth, the Earth is traveling counterclockwise around the sun, and clockwise revolution when you look at the South Pole.

Time of Revolution: Period of revolution (year) is the time required for the earth to complete one circuit around the sun.

Sidereal year: Time required for the earth to return to a given point in its orbit with reference to the fixed stars.

Tropical year: The period of time from one vernal equinox to the next. Usually it takes 365 days 5 hours 48 minutes 45.68 seconds (365 1/4 days)

Calendar year: 365 days.

Leap year: 366 days. Feb. 29, every 4 years.

Velocity of Revolution: Earth is revolving around the sun on earth's orbit. and the distance is approximately 583 million miles.

Earth Orbit: It is an ellipse rather than a circle. The ellipticity or degree of flattening of the ellipse is very slight. The mean distance between earth and sun is about 93 million miles (150 million km) but because of the ellipicity of the orbit the distance may be 1.5 million miles greater or less than this figure.

Perihelion (around or near, helios: Sun): the least distance from earth to sun is about 91.5 million miles (147 million km) happen on about January 3.

Aphelion (Ap: away from; helios: sun): on July 4, the earth is at its fartherest point from the sun at a distance of 94.5 million miles (152 million km).

The mean velocity of the earth in its orbit is about (583,000,000 miles / 365 days) 66,600 miles (107,000 km) per hour or 18.5 miles/second. The velocity is greatest at perihelion, least at aphelion.

III. Inclination of the Earth's Axis

This is the most important fact of Earth-sun Relations.

A. Plane of the Ecliptic: For tilted globes the plane in which the earth's orbit and the sun lie is imagined to be horizontal and to pass through the center of the globe. The plane of the equator is inclined 23.5 degrees with the plane of the ecliptic. 23 degrees 27 minutes more exactly. The earth's axis makes an angle of 66.5 degree with the plane of the ecliptic, and is tilted 23.5 degrees from a line perpendicular to that plane.

(1) The earth's axis keeps a fixed angle with the ecliptic plane.
(2) The axis always points to the same place among the stars.

The seasons result because the tilted earth's axis keeps a constant orientation in space as the earth revolves about the sun.

B. Solstice and Equinox:

Summer Solstice: On June 21 or 22, the North Pole end of its axis leans at the maximum angle 23.5 degrees toward the sun.

Winter Solstice: On December 21 or 22, the southern hemisphere tipped toward the sun. Circle of illumination tangent to the arctic and antarctic circles.

Vernal Equinox: March 20 or 21.

Autumnal Equinox: September 22 or 23.

C. Circle of Illumination: The great circle that marks the boundary between sunlight and shadowed halves of the earth. Winter solstice characteristics:

(a) Night is longer than day in the northern hemisphere
(b) Day is longer than night in the southern hemisphere
(c) Inequality between day and night increases from the equator poleward.
(d) At corresponding latitudes north and south of the equator the relative length of day and night are in exact opposite relation.
(e) Between the Arctic Circle and the North Pole, night lasts the entire 24 hours.
(f) Between the Antarctic Circle and the South Pole, day lasts the entire 24 hours.

D. Altitude of Noon Sun (ANS) at Winter Solstice

Noon occurs simultaneously at all points having the same longitude, therefore, noon is often termed the meridian passage of the sun. The vertical angle of the sun above the horizon at noon is designated the altitude.

(a) At 23.5 S latitude, the sun's rays strike the earth at an angle of 90 degree above the horizon at noon.

Zenith: the sun is exactly in the center of the sky. At the winter solstice, the sun's declination is 23.5 degree south.

(b) At the equator, the sun's noon altitude is 90 - 23.5 (s) = 66.5 above the southern horizon.
(c) At the Arctic Circle, the sun at noon is on the horizon. 90 - 23.5 (s) - 66.5 = 0 -- horizon.
(d) At the Antarctic Circle, the sun at noon has an altitude of 90 + 23.5 - 66.5 = 47 degrees above the northern horizon.
(e) At the South Pole, the noon sun has an altitude of 90 + 23.5 - 90 = 23.5 degrees above the horizon.

General rule of sun's noon altitude or declination is: The sun's noon altitude at a place is equal to 90 degrees minus the arc of meridian between the place and the parallel where the sun's rays strike vertically.

In different hemispere + In the same hemisphere -

ANS = 90 - Z Z = (LP +- LS) Therefore, ANS = 90 - (LP +- LS)

E. Path of Sun in Sky:

The plane of the sun's path at all times makes an angle with the plane of the horizon equal to 90 degrees minus the latitude. See Figure 4.9, P.66 in Text.

F. Direction of Sunrise and Sunset:

On the December solstice, sunrise and sunset between Antarctic Circle and Arctic Circle is at some point between south-east and south-west.

Solstice conditions at the poles: The sun's path follows a horizontal circle, remaining parallel with the horizon throughout the day. The path is spiral. The shadow of an object on December solstice would always point due north no matter what the hour of the day.

Summer solstice: On June 21 or 22: Summer solstices are the exact reverse of winter solstice conditions.

The equinoxes: Vernal equinox : March 20 or 21. Autumnal eqinox: September 22 or 23.

The earth's axis is always inclined 66.5 degrees to the ecliptic plane, it is neither toward nor away from the sun. The sun's rays make an angle of 90 degrees with the earth's axis.

The circle of illumination at the equinoxes passes through the poles. The parallels are divided into equal halves by the circle of illumination. Hence day and night are of equal length. The altitude is always the colatitude, or 90 - latitude.

G. Length of Day and Night and times of Sunrise and Sunset

Intermediate dates: The exact amount of the sun's declination may be found for everyday of the year in the air Almanac.

1. For the equinoxes, lengths of day and night are equal
2. Winter solstice, See Figure 4.13, Page 70.
Rubber band placed to represent circle of illumination - cross equator at 90 W & E, tangent to Arctic and Antarctic.
3. Summer solstice, use Pacific side.
4. Other times of the year: Determine the sun's declination from the Analemma (Figure 5.7, P.83) then adjust rubber band.

Local apparent solar time vs. standard time system: See Figure 4.14, P.71 and sunrise and sunset diagram.

H. Twilight:

Twilight: a diffuse illumination that follows sunset and precedes sunrise, and is attributed to scattering action of air molecules and to the presence of dust and moisture; reflect the sun's rays back to the earth's surface.

Again, twilight is a diffuse reflection from atmospheric molecules, dust, and moisture particles. The duration of twilight depends on the thickness of the earth's atmosphere and the rate at which sun sinks below the horizon. It usually last longer in higher latitude. See Figure 4.16, P.72.

Three kinds of twilight:
1. Astronomical twilight: is the period during which any detectable glow exists in the sky, last while the sun is between the horizon and a point 18 degrees below the horizon.
2. Nautical twilight: sun is between the horizon and a point 12 degrees below the horizon.
3. Civil twilight: normal outdoor activities can be carried on without the aid of lights. The sun is between the horizon and a point 6 degrees below the horizon.

See twilight diagram Figure 4.17, P.72.

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