The motion of Earth

Geodesy, GE 202
Kutubuddin ANSARI
kutubuddin.ansari@ikc.edu.tr
Lecture 4, Oct 25, 2016
Earth Motion

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

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 Precession
Precession 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 pole
CIO 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 Meridian
Perpendicular axis
X3
X1
X2

CELESTIAL REFERENCE
FRAME (CRF)
Angular Momentum Axis
Vernal Equinox
Perpendicular axix
X3
X1
X2

Need to:
1.Transform CRF to TRF or
2.TRF to CRF ?

M S N P
TRF 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)

The motion of Earth

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