The motion of Earth
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Transcript of The motion of Earth
r
R = rotation
r = revolution
P = precession
N = nutation
Earth Motion
•The spin of the Earth on its axis. It takes one day for the Earth to complete one rotation. The daily motion of the Earth is called diurnal motion
•The apparent westward motion of the Sun, Moon, and stars across our sky each day is caused by Earth’s rotation
•We generalize this motion to make statements such as, “The Sun rises in the east and sets in the west.”
•The same is true for the Moon, planets and the stars.
Earth Rotation
•At middle latitudes, we see the Sun, Moon, and many of the stars first come into view moving upward, rising at some point along the eastern horizon. Then, they appear to arc across the sky, gaining greatest altitude at the local meridian. Finally, they disappear somewhere along the western horizon. •Each day we see the Sun’s path across our sky, it is a snapshot of a series of 365 separate paths that occur throughout the year.•Each daily “snapshot” of the Sun is just one position of the Sun along the ecliptic plane (as seen from the Earth).
Earth Rotation
The Sun rises at different points along the horizon at different times of the year and also peaks at different heights.
Earth Rotation
Different parts of the world experience different times of day as the Earth rotates..
Earth Rotation
Variations in the Earth rotation•Earth averages one rotation every 24 hours, which means that some days are slightly longer or shorter than the average.
•Earth’s rotational speed throughout geologic time has slowed due to it’s gravitational (tidal) interaction with the Moon.
Ecliptic If the sun's path is observed from the Earth's reference frame, it appears to move around the Earth in a path which is tilted with respect to the spin axis at 23.5°. This path is called the ecliptic. It tells us that the Earth's spin axis is tilted with respect to the plane of the Earth's solar orbit by 23.5°.
Vernal equinox The points where the ecliptic crosses the equatorial plane of the celestial sphere are called equinoxes. On those dates there are 12 hours each of daylight and dark. The most northern excursion of the sun is called the summer solstice and will have the longest amount of daylight. The winter solstice opposite it is the shortest period of daylight.
The point of the Sun’s path farthest north on the celestial sphere is called the summer solstice (JUN 21), while the point of the ecliptic farthest south is called the winter solstice (DEC 21).
The two points on the ecliptic where the Sun crosses the celestial equator are called equinoxes. During the vernal equinox (MAR 21), the Sun is moving north, while during the autumnal equinox (SEPT 21), the Sun is moving south.
Vernal equinox
Earth Revolution
•The movement of the Earth in orbit around the sun. It takes one year for the Earth to complete one revolution.
•Zodiac constellations appear to shift along the ecliptic slightly less than 1 degree per day. Eventually, constellations visible at night become invisible during the day.
•The altitude of the Sun in the sky at local meridian changes daily. This alters the Sun’s path across the sky
Earth revolution•The Earth’s orbital speed varies because its orbital path is not a perfect circle; it is elliptical. •The Earth orbits fastest when it is furthest away from the Sun and slowest when it is closest .
The Earth also revolves around the Sun, which changes our view of the stars.
Earth Revolution
Seasons are caused because the Earth’s axis is tilted and as the Earth revolves around the Sun, different parts of the Earth receive more direct sunlight (summer), while other parts of the Earth receive sunlight which is more spread out (winter).
Earth Revolution
Earth Revolution
The hemisphere tilted toward the Sun receives sunlight at higher angles than the hemisphere tilted away from the Sun.Higher insolation angle means greater intensity of radiant energy (the sun shines more directly on a smaller area).
Earth Revolution
Earth Revolution
Earth PrecessionPrecession is a change in the orientation of the rotational
axis of a rotating body. Earth goes through one such complete precessional cycle in a period of approximately 26,000 years or 1° every 72 years.
Gravitational forces of the Sun and the Moon pulling on the Earth as it rotates causes the Earth to undergo a top-like motion create precession
Nutation
Nutation is nodding motion in the axis of rotation of a largely axially symmetric object.
Chandler Period: 430 days
Chandler Period: 430 days
Polar motion of the earth’s rotation axis
Forced motion
Polar motion
CEP Celestial ephemeris poleCIO Conventional international origin
Sidereal time is the hour angle of the vernal equinox, the ascending node of the ecliptic on the celestial equator.
Sidereal time
Reference Frame
Celestial Reference Frame (CRF) Terrestrial Reference Frame (TRF)
TERRESTRIAL REFERENCE FRAME (TRF)
Earth Rotation Axis
Greenwich MeridianPerpendicular axis
X3
X1
X2
CELESTIAL REFERENCE FRAME (CRF)
Angular Momentum Axis
Vernal EquinoxPerpendicular axix
X3
X1
X2
Need to:
1. Transform CRF to TRF or
2. TRF to CRF ?
M S N PTRF CRFx R R R R x
CRF TO TRF
Laws of Planetary Motion• Law 1 - Law of Ellipses• Law 2 - Law of Equal Areas• Law 3 - Harmonic Law (P2=ka3)
Kepler’s laws provide a concise and simple description of the motions of the planets
Kepler’s Law
Kepler's Laws:
Kepler's Second Law: Line joining planet and the Sun sweeps out equal areas in equal times
Kepler's First Law:Each planet’s orbit around the Sun is an ellipse, with the Sun at one focus.
Kepler's Third Law: The squares of the periods of the planets are proportional to the cubes of their semi-major axes:
Extending Kepler’s Law
Newton found that ellipses were not the only orbital paths.
possible orbital paths• ellipse (bound)• parabola (unbound)• hyperbola (unbound)
