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copy rights w.h.g. lewin November 3, 1999. Some Netes on Kepler Orbits, The figure shows an ellipse; Q and § are the foci. The semi-major axis a = OA (= OP), the semi-minor axis ’ = OB. QO (= OS} = ae (is called the eccentricity). For the special case that the eccentricity is zero, Q, § and O coincide and we have a circle with radius & = a = b. If two of the three parameters a, b, and € are known, the third can be calculated. Convince yourself of this. Keep in mind that OC + CS = QB + BS =QA + AS = 2a; that is a property of an ellipse. A satellite (planet) with mass m goes around the earth (sun) in an elliptical orbit. The earth (sun) has a mass Mf and is at one of the foci, Q, of the ellipse. The orbital period T is only a function of M and of the semi-major axis a (see Example 6, page 222 in Ohanian): T2=472a3/MG a For a circular orbit, the semi-major axis is replaced by the radius (8) of the circle (see eq. 15 on page 217 of Ohanian). The total energy of the mass m anywhere in orbit is: Eto = -MmG/2a (2) For a circular orbit, a is replaced by R (see eq. 27 on page 226 of Ohanian). AtD: Exot = mv¥g2/2 - MmG/tg = -MmG/2a GB) The angular momentum (about Q where Af is located) of m is conserved; there is no 
