MOTIONS OF THE EARTH
- Our solar system moves with the Milky Way galaxy with respect to other galaxies.
- The "big-bang" theory is based on a red-shift in the visible light spectrum from using basic elements
such as hydrogen. This indicates that all galaxies are moving away from Earth. That is, the one's
ahead of us are moving faster than Earth, and the one's behind us are moving slower. Thus, everything is expanding
- The Milky Way rotates about its center. Thus, our solar system circulates within the Milky way
Directions for Viewing 3d Animation of Solar System
- You will need a VRML 2.0 viewer to see the animation to the left.
Download and install the free Cortona vrml plug-in.
- Select the graphic in the left screen or the link below it.
- Please press the cube to expand your mind and see the entire solar
system to scale from the outside edge.
- Press the cube labeled "HOME" to return back to the inner planets.
- While viewing the animation, you can select the "study"
and "turn" buttons on the left panel to roll the entire
image so that the rotations can be viewed from any perspective. the
"restore" button in the lower panel will reset the image to
its original orientation.
- It revolves around the sun
- Sidereal year - One year with respect to the stars is 366.256362268 days
(365 d 6h 9m 9.7s solar days)
- Solar year - One year with respect to sun.
- Sun is at one foci of the elliptical orbit of the earth.
- One day in the sidereal year is "lost" due to orbit of earth around sun.
- Aphelion is point were Earth is farthest from Sun. Note helios
is the Greek word for sun, thus aphelion is a derivative of this word.
- This is approximately July 3rd each year
- Perihelion is point were Earth is closest to Sun
- This is approximately January 3rd each year
- The Earth rotates about its instantaneous spin axis
- If the earth was a rigid body, this would be similar to the motion a "top"
displays when an external force is applied to it.
- The earth's spin axis is inclined with respect to the ecliptic by about
23.5°. This is known as obliquity. Interesting fact: Obliquity causes
days to be longer in the summer and shorter in the winter.
- Since the Earth is tilted with respect to the orbital plane (ecliptic), there is a greater pull on the
nearer hemisphere as compared to the farther one. Since these pulls do not
lie in the C-H plane, there is a torque exerted on the spin axis of the
Earth. This results in a "wobble" of the Earth's axis, and thus an
instantaneous spin axis.
- Pole will be closest to Polaris in 2102 (about 30″)
- Geodesist concentrate on items 3 & 4 since they directly affect our observations.
Annual motions of earth follow Kepler's Laws:
- The orbit of any body is an ellipse with the sun stand at one foci.
You can view this motion at
by Jennifer Loomis.
- Note second foci lies within the sun's diameter, so orbit is nearly circular.
- A satellite moves at a constant "areal" velocity
- Areal velocity is the area swept by the radius vector for a particular period of time
- The ratio of the square of the orbital period (m) to the cube of the length of the semi-major axis (a) is a constant
- Ecliptic is the plane defined by the Earth's orbit
- The point on the ecliptic where the Sun appears to "rise" into the
northern hemisphere is know as the vernal point,
WOBBLE OF INSTANTANEOUS SPIN AXIS
The period of nutation was originally calculated using Euler's differential equations as
Earth's "wobble" is composed two primary motions called precession and nutation.
- The original investigation of this phenomenon used a "rigid" body for the earth.
- The sun and the moon are the primary sources of force that cause these motions.
- The Earth's instantaneous spin axis coincides with the Earth's principal axis of the
maximum moment of inertia that passes through the Earth's center of mass.
- Precession is the result of an external torque being applied to a rotating body
- 1 cycle of precession occurs approximately every 26,000 years, and is known as a
Platonic year. I am about 0.0019 platonic years old.
How old are you?
- The Moon's orbital plane is inclined to the ecliptic by about 5°11'
- The intersection of where the moon's orbital plane crosses the ecliptic is
known as the nodal line.
- The nodal line rotates about the ecliptic once every 18.6 years.
- Nutation is primarily caused by the moon
- Each nutation is approximately 18.42" as compared to 47° (23.5°
- However, the Earth does not behave like a rigid body, and thus observations have shown that the Euler period is ~40% too
short. The observed period varies, but is approximately 435 sidereal days. This period is known as the Chandler Period,
and can be observed in the figure at the end of this lesson.
- Other source of torque include the other celestial bodies, ice/snow build up, etc. These are all relatively small in
comparison to the sun and moon's effects. Go to
to read about
the sources of external torque that cause this phenomenon
Picture taken by Darren Hauser in summer of 2010 at 12:45 A.M.
The Vernal Equinox and Other Matters
The spin axis of the earth is inclined by 66.5° with respect to the ecliptic
- One point on the Earth's orbit of primary importance to surveying is the
^. (First day of Spring)
- An equinox is a day in the year when night and daytime are equal (12 hrs).
- The line of equinox is defined by the intersection of the equatorial plane with that of the ecliptic
- This can be observed by simply noting the time of sunrise and sunset.
- This occurs at two points on the Earth's orbit
- Autumnal equinox (first day of fall ~ Sept 21)
- Vernal equinox (first day of spring ~ March 21)
- The exact time for the equinox is determined by the exact time that the
sun crosses the equator.
- Point where sun crosses equator in March is called the vernal point, and is the basis for celestial coordinate
systems. It is designated by the astrological symbol of a ram's head,
Since precession is approximately 26,000 years, the yearly movement of the vernal point moves approximately
360°/26,000 yrs 0.014°/yr
- Thus a 23.5° angle between Earth's equator and ecliptic plane (Note this is ½ of 47°)
- The inclination of the earth's spin axis is known as obliquity
- Obliquity results in polar areas have "days" without nights and vice-versa.
- Latitudes of most northerly and southerly travel of sun are Tropic of Cancer and Tropic of Capricorn, respectively.
- Note in sketch, the southern hemisphere as the shortest period of daylight,
Thus, it is experiencing winter. This
occurs at perihelion for the southern hemisphere and aphelion for the northern hemisphere.
3 and July 3, respectively)
- However since movement of vernal equinox is measurable, we can compute yearly movement of the vernal
equinox. It has been measured as approximately 50.3" ±0.1" per year. So platonic year is (360°×3600"/°)/50.3"
OBSERVATION OF POLAR MOTIONS
), or azimuth (A). The correction for astronomically
observed azimuths is
- The International Earth Rotation Service (IERS) was created in 1988 by the International Union of Geodesy and Geophysics
(IUGG), and the International Astronomical Union (IAU). It replaced the Earth rotation section of the Bureau International de
l'Heure ( BIH ), and the International Polar Motion Service (IPMS). It is a member of the Federation of Astronomical and
Geophysical Data Analysis Services (FAGS). It monitors the position of the pole. Its web site is http://hpiers.obspm.fr/
- Go to the
Earth Orientation Parameters link to
more about these parameters.
The problem of the motion of the spin axis of the
earth was noted by the 19th century. In 1899, the
International Astronomical Union (IAU) established the
International Latitude Service (ILS) to monitor the
instantaneous spin axis. Initially, the ILS consisted of 5
observing stations at approximately the same latitude of
39°08' N. (To learn more about how the Earth's
Orientation Parameters (EOP) are measured visit
http://hpiers.obspm.fr/eop-pc/. This position was known as the Conventional
Terrestrial Pole (CTP) formerly known as the Conventional International
Origin (CIO). It was adopted as the mean position
of the Earth's pole between the years of 1900.0 and
1905.0. Today, network of observing stations as grown
to more than one-hundred observation sites, and is known as the Conventional
Terrestrial Pole (CTP). As shown in Figure 4, the position
of the instantaneous pole is referenced to the CTP by an
xy Cartesian coordinate system with the x-axis
coinciding with the Greenwich Meridian. Positions are
maintained in 0.05 sidereal year intervals (~18.3 days). A listing of the
positions of the CTP from 1900.0 is given at http://hpiers.obspm.fr/eoppc/eop/eopc01/mean-pole.tab by the IERS.
Bulletin B contains a listing of the positions during the current and
data can be used astronomically measured latitude (Φ), longitude (Λ
A = Azobs−
λ + yp cos
A = Aobs − (xp sin λ + yp cos λ) sec φ
Λ = Λobs -
λ + yp cos λ)
tan φ + yp
- xp cos
λ + yp
where A is the corrected astronomic azimuth, Azobs is the observed azimuth, and φ and λ are the geodetic coordinates of the
observing station. The term φG (latitude
of Greenwich) is usually omitted in the formula for
so that the mean meridian of Greenwich remains fixed, rather than the
astronomical longitude of Greenwich.
August 30, 2010
Prepared by Charles D. Ghilani, Ph.D.
Penn State Surveying Program, Copyright © 2000-2007