MOTIONS OF THE EARTH

WOBBLE OF INSTANTANEOUS SPIN AXIS

• The 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° ´ 2) for precession
• The period of nutation was originally calculated using Euler's differential equations as

• 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 http://hpiers.obspm.fr/ to read about the sources of external torque that cause this phenomenon

The Vernal Equinox and Other Matters

• One point on the Earth's orbit of primary importance to surveying is the vernal equinox, ^. (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 (orbital plane.)
  • 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, ^.
  • The spin axis of the earth is inclined by 66.5° with respect to the ecliptic
  • 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. (~January 3 and July 3, respectively)
  • Since precession is approximately 26,000 years, the yearly movement of the vernal point moves approximately 360°/26,000 yrs 0.014°/yr
  • 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" = 25,765 years.
  
  
  

OBSERVATION OF POLAR MOTIONS

1. 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/
1. Go to the Earth Orientation Parameters link to more about these parameters.
2. The problem of the motion of the spin axis of the earth was noted by the 19^th 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 previous years.
3. This data can be used astronomically measured latitude (F), longitude (L), or azimuth (A). The correction for astronomically observed azimuths is

A = Az_obs - (x_p sin l + y_p cos l) sec f
L = L_obs - (x_p sin l + y_p cos l) tan f  + y_p tan f_G
F = F_obs - x_p cos l + y_p sin l

where A is the corrected astronomic azimuth, Az_obs is the observed azimuth, and f and l are the geodetic coordinates of the observing station. The term f_G (latitude of Greenwich) is usually omitted in the formula for L, so that the mean meridian of Greenwich remains fixed, rather than the astronomical longitude of Greenwich.

Last updated August 26, 2009
Prepared by Charles D. Ghilani, Ph.D.
Penn State Surveying Program, Copyright © 2000-2007