The Origin and Evolution of the Solar System

Planetary orbits and solar spin 5Figure 1.1. The characteristics of an elliptical orbit.The second and third Kepler laws can be stated in these terms asÖ ¾ È ¾ ¿ where È ¾Ò is the orbital period and Ô Ô is the intrinsic angularmomentum or angular momentum per unit mass.For a full specification of the orbit in space it is necessary to add to the twoelliptical elements ( ), which define the shape of the orbit, three orientationangles and a time fix. To define angles requires a coordinate system and, conventionally,the ecliptic, the plane of the Earth’s orbit, is taken as the – plane for arectangular Cartesian system. The positive -axis is towards the north so all thatis required to define the coordinate system completely is to define an directionin the ecliptic. Relative to the Earth, during the year the Sun moves round in theecliptic and twice a year, in spring and autumn, it crosses the Earth’s equatorialplane. These are the times of the equinoxes, when all points on the Earth haveday and night of equal duration. The equinox when the Sun passes from southof the equator to north is the vernal (spring) equinox. The direction of the vernalequinox, called the First Point of Aires, is taken as the positive direction.The first orientation angle for defining the orbit is the inclination, , whichis the angle made by the plane of the orbit with the ecliptic. However, this doesnot define the orbit completely since if the orbit is rotated about the normal to itsplane , and remain the same but the orientation changes. What does remainunchanged is the line of intersection of the orbital plane with the ecliptic. Thisline is called the line of nodes; the point on the line where the orbit crosses theecliptic going from south to north is the ascending node and the descending nodewhere it goes from north to south.