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The general Kepler orbit is given in polar coordinates by

Chapter 8, Problem 8.30

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QUESTION:

The general Kepler orbit is given in polar coordinates by (8.49). Rewrite this in Cartesian coordinates for the cases that E = 1 and E > 1. Show that if E = 1, you get the parabola (8.60), and if E > 1, the hyperbola (8.61). For the latter, identify the constants a, ,8, and 6 in terms of c and E.

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QUESTION:

The general Kepler orbit is given in polar coordinates by (8.49). Rewrite this in Cartesian coordinates for the cases that E = 1 and E > 1. Show that if E = 1, you get the parabola (8.60), and if E > 1, the hyperbola (8.61). For the latter, identify the constants a, ,8, and 6 in terms of c and E.

ANSWER:

Step 1 of 4

The Kepler orbit in polar coordinates is given as,

                

Here,  is the eccentricity and  is the length.

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