PRIDE CHEKERAA particle of mass ‘m’, represents the earth moving under the
action of central gravitational attraction about the particle of
mass 푚 0 representing the sun as a focus. The above can also be
modeled in representation of the moon about the earth or a
satellite about the earth. The coordinate system used in the
above diagram is the polar coordinates in plane of motion.
According to the second law, during time dt the radius vector r
sweeps out area of: dA =^12 푟^2 dθ. This implies that the rate at
which the area is swept by the radius vector is 퐴̇ =^12 푟^2 휃̇, which
is constant. The first law is expressed by the following equation:
(^1) 푟 =^1 푎(+ 1 푒푐표푠휃− 푒 (^2) ) ...................(1.1)
From the above equation defining an ellipse trajectory, it follows
that: 푟푚푖푛 = a(1 – e) is an expression of the furthest distance of
the earth from the sun, or any other similar particle from its
focus. This distance is called apogee (aphelion); and
푟푚푎푥 = a(1 – e) is an expression of the nearest distance of the
earth from the sun, or any other similar particle from its focus.
This distance is called perigee (perihelion).
NOTE: The above equation 1.1 defines an ellipse only, and if
only, eccentricity ‘e’ is less than one, e> 1. For e> 1 it defines a
hyperbolic orbit and when e= 1 it represents a parabolic orbit.
The third law is defined by the following equation: