PRECESSION OF THE EQUINOXES

 

In astronomy, the ecliptic is apparent great-circle annual path of the sun in the celestial sphere (the projection of objects in space into their apparent positions in the sky as viewed from the Earth) , as seem from the earth. The plane of the path, called the plane of the ecliptic, interesects the celestial equator (the projection of the earth's equator on the celestial sphere) at an angle of about 23.5. This angle is known as the obliquity of the ecliptic and is approximately constant over a period of millions of years.

   

The two points at which the ecliptic interesects the celestial equator are called nodes, or equinoxes. The sun is at the vernal equinox about March 21st and at the autumnal equinox about September 23rd.

   

The equinoxes do not occur at the same points of the ecliptic every year, for the plane of the ecliptic and the plane of the equator revolve in opposite directions, respectively. The two planes make a complete revolution with respect to each other once every 25,868 years. This movement of the equinoxes along the ecliptic is called the precession of the equinoxes.

   
     

NEWTON'S WORK ON THE PRECESSION OF THE EQUINOXES

Sir Isaac Newton was an English physicist and mathematician who was born into a poor farming family. Luckily for humanity, Newton was not a good farmer. . At Cambridge, Newton studied mathematics, being especially strongly influenced by Euclid, although he was also influenced by Baconian and Cartesian philosophies. Newton was forced to leave Cambridge when it was closed because of a plague, and it was during this period that he made some of his most significant discoveries. Newton did not, however, publish his results.

When Newton began devoting his efforts to theological speculation and put the calculations on elliptical motion aside, telling Edmund Halley (of which Halley's comet was named after) he had lost them. Halley, who had become interested in orbits, finally convinced Newton to expand and publish his calculations. Newton devoted the period from August 1684 to spring 1686 to this task, and the result became one of the most important and influential works on physics of all times, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), often shortened to Principia Mathematica or simply "the Principia."

In Book I of Principia, Newton opened with definitions and the three laws of motion now known as Newton's Laws (laws of inertia, action and reaction, and acceleration proportional to force). Book II presented Newton's new scientific philosophy which came to replace Cartesianism. Finally, Book III consisted of applications of his dynamics, including an explanation for tides, a theory of lunar motion, and how he found the precession of the equinoxes.

Newton knew that the Earth is not a perfect sphere; it bulges slightly around the equator. The gravitational attraction of both the Sun and the Moon tries to pull the Earth's equatorial bulge into the Moon's and the Sun's orbital planes. Acting like a spinning top, the rotating Earth resists this pull. The result of the Sun's and Moon's attraction and the Earth's resistance is that the Earth's axis of rotation moves slowly westward around the pole of the ecliptic. Because of this, the points of intersection between the celestial equator and the ecliptic shift westward along the ecliptic at a rate of about 50 minutes of arc per year or over 1 per century. Thus, the equinoxes precess completely around the ecliptic in 25,868 years.

   
     
     

ASTRONOMICAL COORDINATES

To designate the position of a star, the astronomer considers an imaginary great circle passing through the celestial poles and through the star in question. This is the star's hour circle, analogous to a meridian of longitude on earth. The astronomer then measures the angle between the vernal equinox and the point where the hour circle intersects the celestial equator. This angle is called the star's right ascension and is measured in hours, minutes, and seconds rather than in the more familiar degrees, minutes, and seconds. (There are 360 degrees or 24 hours in a full circle.) The right ascension is always measured eastward from the vernal equinox. Next the observer measures along the star's hour circle the angle between the celestial equator and the position of the star. This angle is called the declination of the star and is measured in degrees, minutes, and seconds north or south of the celestial equator, analogous to latitude on the earth. Right ascension and declination together determine the location of a star on the celestial sphere. The right ascensions and declinations of many stars are listed in various reference tables published for astronomers and navigators. However, because a star's position may change slightly due to the precession of the equinoxes, such tables must be revised at regular intervals. By definition, the vernal equinox is located at right ascension 0h and declination 0.

   
     

 

ILLUSTRATED SEQUENCE OF PRECESSION OF THE EQUINOXES

figure 1: Let this illustration denote the current position of the Earth's celestial pole.
Note that the north celestial pole would be pointing towards Polaris (the current north star).

figure 2: After about 3233 years, the north celestial pole and the equinoxes have made
a 45 CCW rotation around the precessional axis (a vertical passing through the Earth's
center). Notice also that the north celestial pole would no longer be pointing at Polaris.

figure 3: After a total of 6467 years have past, the north celestial pole and the
equinoxes has a net rotation of 90.

figure 4: at around 9700 years, the north celestial pole and the equinoxes has rotated
135 around the axis of precession.

figure 5: Now after 12,934 years, the north celestial pole and the equinoxes has made a
180 rotation.

 

figure 6: So after a total of 25,878 years, the north celestial pole and the equinoxes has
made one complete revolution around the precessional axis. Also, the north celestial
pole is once again, pointing towards polaris.