the entire elliptical orbit, and ε (the angle between the equatorial plane and the ecliptic plane) is the maximum value of δ for the Sun and the average maximum value for the Moon over an entire 18.6 year cycle. Precession is: where ω is Earth's angular velocity and Cω is Earth's angular momentum. Thus the first order component of precession due to the Sun is: whereas that due to the Moon is: where i is the angle between the plane of the Moon's orbit and the ecliptic plane. In these two equations, the Sun's parameters are within square brackets labeled S, the Moon's parameters are within square brackets labeled L, and the Earth's parameters are within square brackets labeled E. The term accounts for the inclination of the Moon's orbit relative to the ecliptic. The term is Earth's dynamical ellipticity or flattening, which is adjusted to the observed precession because Earth's internal structure is not known with sufficient detail. If Earth were homogeneous the term would equal its third eccentricity squared, where a is the equatorial radius () and c is the polar radius (), so . Applicable parameters for J2000.0 rounded to seven significant digits (excluding leading 1) are: which yield dψS/dt = 2.450183 /s dψL/dt = 5.334529 /s both of which must be converted to ″/a (arcseconds/annum) by the number of arcseconds in 2π radians (1.296″/2π) and the number of seconds in one annum (a Julian year) (3.15576s/a): dψS/dt = 15.948788″/a vs 15.948870″/a from Williams dψL/dt = 34.723638″/a vs 34.457698″/a from Williams. The solar equation is a good representation of precession due to the Sun because Earth's orbit is close to an ellipse, being only slightly perturbed by the other planets. The lunar equation is not as good a representation of precession due to the Moon because the Moon's orbit is greatly distorted by the Sun and neither the radius nor the eccentricity is constant over the year. Values Simon Newcomb's calculation at the end of the 19th century for general precession (p) in longitude gave a value of 5,025.64 arcseconds per tropical century, and was the generally accepted value until artificial satellites delivered more accurate observations and electronic computers allowed more elaborate models to be calculated. Jay Henry Lieske developed an updated theory in 1976, where p equals 5,029.0966 arcseconds (or 1.3969713 degrees) per Julian century. Modern techniques such as VLBI and LLR allowed further refinements, and