were new, their existence not having been previously
suspected.
In their science paper, Hays et al. (1976) used a spectral
analysis technique which they applied to geological
records and to the numerical values of the astronomical
parameters calculated by Brouwer and Van Woerkom
(1950) and Vernekar (1972) and found also 125,000 and
96,000 years for e, 41,000 years for e, and 23,000 and
19,000 years for precession.
Orbit of the Earth around the Sun and
its axis of rotation
The plane of the Earth’s elliptical orbit around the Sun is
called the ecliptic. The Sun is not located at the center of
the ellipse but rather at one of the foci, a fact that was demonstrated in the seventeenth century by the German
astronomer Johannes Kepler (1571–1630) whose three
laws are:
• Kepler’s first law. Each planet moves in an ellipse with
the Sun at one focus.
• Kepler’s second law. The radius vector from the Sun to
any one planet describes equal areas in equal times.
• Kepler’s third law. For any two planets, the squares of
the periods are proportional to the cubes of the
semimajor axes of their orbits.
As the Earth travels counterclockwise around its orbit
each year, it is sometimes nearer to and sometimes farther
away from the Sun. Today, the Earth reaches the point in
its orbital path known as perihelion, the point at which it
is the closest to the Sun, on or about 3 January. On or about
4 July, it reaches aphelion, the point farthest from the Sun.
At aphelion the distance between the Earth and the Sun,
which is in average roughly 150 million kilometers, is
about 5 million kilometers greater than it is at perihelion.
Figure 1 displays the various elements of the Earth’s
orbit. The ellipse drawn through the perihelion, P, the
Earth, E, and the aphelion, A, represents the orbit of the
Earth around the Sun.
The Earth’s eccentricity, e, which is a measure of its
elliptical shape, is given by
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
a 2 À b
2
p
=a, where a is the
semimajor axis and b the semiminor axis. The vernal
point, g, also called the First Point of Aries, is the position
of the Sun in the sky seen from the Earth at the time of the
spring equinox, SE, i.e., in Figure 1 when the Earth
crosses the celestial equator from the austral to the boreal
hemisphere. It is the origin from which the ecliptical longitudes are measured. The winter (ww) and summer
(ss) solstices and g are shown at their present-day positions. In such a heliocentric system, g is in the direction
of the fall equinox, FE. In practice, observations are made
from the Earth and the Sun is considered as if it were
revolving around the Earth. In such a case, the system of
Astronomical Frequencies in Paleoclimates, Figure 1 The Earth (E)’s orbit around the Sun (S). The astronomical elements are
defined in the manuscript. a is the semimajor axis of the elliptical orbit and b its semiminor axis, P is the perihelion, A is the aphelion,
SE is spring equinox, SS is summer solstice, FE is fall equinox, WW is winter solstice, SQ is the perpendicular to the plane of the
ecliptic, S NP is a parallel to the axis of rotation of the Earth describing the cone of precession, o is the longitude of the perigee, e
o is
the longitude of the perihelion relative to the moving vernal point g, l is the longitude of the Earth in its orbit, u is the true anomaly,
and e is the obliquity.
26
ASTRONOMICAL FREQUENCIES IN PALEOCLIMATES
suspected.
In their science paper, Hays et al. (1976) used a spectral
analysis technique which they applied to geological
records and to the numerical values of the astronomical
parameters calculated by Brouwer and Van Woerkom
(1950) and Vernekar (1972) and found also 125,000 and
96,000 years for e, 41,000 years for e, and 23,000 and
19,000 years for precession.
Orbit of the Earth around the Sun and
its axis of rotation
The plane of the Earth’s elliptical orbit around the Sun is
called the ecliptic. The Sun is not located at the center of
the ellipse but rather at one of the foci, a fact that was demonstrated in the seventeenth century by the German
astronomer Johannes Kepler (1571–1630) whose three
laws are:
• Kepler’s first law. Each planet moves in an ellipse with
the Sun at one focus.
• Kepler’s second law. The radius vector from the Sun to
any one planet describes equal areas in equal times.
• Kepler’s third law. For any two planets, the squares of
the periods are proportional to the cubes of the
semimajor axes of their orbits.
As the Earth travels counterclockwise around its orbit
each year, it is sometimes nearer to and sometimes farther
away from the Sun. Today, the Earth reaches the point in
its orbital path known as perihelion, the point at which it
is the closest to the Sun, on or about 3 January. On or about
4 July, it reaches aphelion, the point farthest from the Sun.
At aphelion the distance between the Earth and the Sun,
which is in average roughly 150 million kilometers, is
about 5 million kilometers greater than it is at perihelion.
Figure 1 displays the various elements of the Earth’s
orbit. The ellipse drawn through the perihelion, P, the
Earth, E, and the aphelion, A, represents the orbit of the
Earth around the Sun.
The Earth’s eccentricity, e, which is a measure of its
elliptical shape, is given by
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
a 2 À b
2
p
=a, where a is the
semimajor axis and b the semiminor axis. The vernal
point, g, also called the First Point of Aries, is the position
of the Sun in the sky seen from the Earth at the time of the
spring equinox, SE, i.e., in Figure 1 when the Earth
crosses the celestial equator from the austral to the boreal
hemisphere. It is the origin from which the ecliptical longitudes are measured. The winter (ww) and summer
(ss) solstices and g are shown at their present-day positions. In such a heliocentric system, g is in the direction
of the fall equinox, FE. In practice, observations are made
from the Earth and the Sun is considered as if it were
revolving around the Earth. In such a case, the system of
Astronomical Frequencies in Paleoclimates, Figure 1 The Earth (E)’s orbit around the Sun (S). The astronomical elements are
defined in the manuscript. a is the semimajor axis of the elliptical orbit and b its semiminor axis, P is the perihelion, A is the aphelion,
SE is spring equinox, SS is summer solstice, FE is fall equinox, WW is winter solstice, SQ is the perpendicular to the plane of the
ecliptic, S NP is a parallel to the axis of rotation of the Earth describing the cone of precession, o is the longitude of the perigee, e
o is
the longitude of the perihelion relative to the moving vernal point g, l is the longitude of the Earth in its orbit, u is the true anomaly,
and e is the obliquity.
26
ASTRONOMICAL FREQUENCIES IN PALEOCLIMATES