Earth’s Rotation and Revolution

Earth’s Rotation – Causes daily changes The spinning of earth on its AXIS – the imaginary line through the planet from the North Pole to the South Pole – is its rotation The axis of the earth is tilted 23.5° from a line perpendicular to the plane of its orbit of the sun.

Earth’s Rotation As the earth revolves around the sun, Earth’s axis remains tilted at 23.5° The north end of the axis points toward the north star (Polaris) Earth rotates 360° from west to east (counter clockwise looking down from the north pole) in 24 hours, at an angular rate of l5° per hour (360°/24 hours = 15°/hour)

Tilt of the axis always stays the same

1. Evidence of Earth’s Rotation 1851, Foucault’s pendulum will appear to change in a predictable way. Why is this evidence? There is no force acting on the pendulum to make its plane of oscillation rotate or go around its own axis It would continue to swing in the original path if Earth did not rotate.

No force that makes pendulum rotate – must be earth that is rotating!!! Inertia and gravity make it swing straight out and straight down in a straight arc – not twist.

2. Evidence for Rotation Coriolis Effect – the tendency of objects moving over the earth (air, water, planes, projectiles) to be deflected (curve away) from a straight line path. The French scientist, Gaspard Coriolis, first explained the deflection of objects moving over the surface due to Earth’s rotation The deflection is to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This deflection occurs because Earth’s surface is rotating with respect to the objects.

What are the APPARENT MOTIONS of Celestial Objects An apparent motion is a motion an object appears to make An apparent motion can be real or an illusion For example, the stars appear to move across the sky from east to west However, the apparent motion is caused by Earth’s rotation

Stars in constellations are often very far from one another but we see them in the same direction in the sky. Big Dipper

Pointer Stars point to Polaris

Some Definitions Celestial Sphere: A huge imaginary sphere around the Earth to which the stars appear to be attached. Constellation: An arbitrary grouping of stars in the Sky that are in the same general direction. The modern ones are fixed by international agreement to map the entire Sky. Celestial Equator: Projection of the Earth’s Equator onto the Celestial Sphere.

Imagine all the stars moved down onto a big glass sphere around the Earth. Celestial equator

Stars celestial sphere is stationary Earth Rotates Counterclockwise

Looking upward we see the stars fixed on the celestial sphere Earth’s eastward rotation makes the stars between the equator and north celestial pole appear to move westward Rise in the east and set in the west. Timed photography showing stars rising in the east

Stars appear to be moving from east to west. Stars rising in the east.

Stars appear to be moving from east to west Stars appear to be moving from east to west. Rise in the east and set in the west.

Northern part of the sky around Polaris CCW Moving west to east

Earth’s counter clockwise rotation makes the stars appear to rotate counter clockwise around the north celestial pole (Polaris).

The complete circular path can be seen for stars in the northern part of the sky around Polaris Circumpolar constellations never set. Circumpolar constellations change with latitude… sky changes with latitude

Daily Motions Some of the stars near Polaris appear to move in a complete circle in 24 hours. The paths of all celestial objects moving in the sky are circular or parts of a circle called an arc. All motion occurs at a constant rate of approximately l5° per hour or 360° in 24 hours.

Earth’s Revolution Earth revolves around the sun in a slightly eccentric elliptical orbit or path once a year It takes Earth 365.25 days to revolve 360° in its orbit around the sun. It moves approximately 1° per day. (360°/365.26 days = 1° per day)

Evidence of Earth’s Revolution around the Sun Seasonal Constellations: Because of the Sun’s annual motion, some constellations are visible at night only during certain seasons. Constellations are visible when the dark side of Earth (away from sun) faces toward the constellation.

The 13 constellations the sun appears to travel through during the year

Different constellations at different times of the year

Evidence of Revolution Parallax Shift Because of Earth’s revolution about the sun, near stars seem to shift their position against the farther stars (closer star – greater the shift) If you observe the same star while earth is at 2 different points during its orbit around the sun, the star’s position relative to the more distant background stars will appear to change.

Parallax Shift

Apparent Motion of Sun due to Rotation and Revolution Rotation: Sun – apparent daily path from sunrise to sunset has the shape of an arc moving l5° per hour. Revolution: However, the sun’s arc changes both its position and its length with the seasons

Earth’s Revolution around the Sun – the tilt of Earth’s axis does not change producing a cyclical change of seasons

Because of the tilt of the Earth’s axis, the sun’s rays are only perpendicular (directly overhead) at noon, between 23.5° N and 23.5° S during the year June 21 23.5° N March/Sept. 21 Dec. 21 23.5° S

90° Perpendicular Rays of the Sun aka the ZENITH POSITION The noon perpendicular rays of the sun travel southward from the Tropic of Cancer (23.5° N) on June 21 passing the Equator on September 21 and going to the Tropic of Capricorn (23.5° S) where it turns around and starts going back up passing the Equator on March 21and arriving at the Tropic of Cancer again on June 21.

Zenith Position of the Sun Because of the earth’s spherical shape, on any particular date, there is just 1 place where insolation (incoming solar radiation) is at an angle of 90°. All other places are less than 90°. Does the 90° ever reach the United States? An observer in New York State will never see the Sun directly overhead.

Summer maximum altitude of noon sun is 73°, Winter is 26° Spring/Autumn? (Sun 90 at 23.5 41-23.5 = 17.5 90-17.5=72.5) ( 90-41= 49) (41+23.5 = 64.5 90-64.5 = 25.5)

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Changing Altitude of the Noon Sun LONG ISLAND, NEW YORK

The apparent rising and setting of the sun is due to rotation Changes in the altitude of the path and horizon position of sunrise and sunset are due to revolution Season Sunrise Sunset Summer North of east North of west Equinox Fall/Spring Due east Due West Winter South of east South of west

Summary Rotation: Earth rotates l5° per hour in 24 hours. Revolution: Earth takes 365.25 days to revolve around the sun moving approximately 1° per day.

SHAPE OF ELLIPSES Eccentricity = 0 circle Eccentricity = 0.5 Eccentricity = 1 line

Kepler’s Three Empirical Laws of Planetary Motion 1. The orbital paths of the planets are elliptical, with the Sun at one focus

Kepler’s Three Empirical Laws of Planetary Motion 2. An imaginary line connecting the Sun to any planet sweeps out equal areas in equal time.. Area 1 Area 2

This is the best website for 1st and 2nd laws of Kepler https://solarsystem.colorado.edu/home/lowRes.html