Planetary Orbits Use the polar equation in completing the
Chapter 8, Problem 8.1.1.398(choose chapter or problem)
Planetary Orbits Use the polar equation \(r=a\left(1-e^{2}\right) /(1+e \cos \theta)\) in completing the following activities.
(a) Use the fact that \(-1 \leq \cos \theta \leq 1\) to prove that the perihelion distance of any planet is a(1 - e) and the aphelion distance is a(1 + e).
(b) Use e = c/a to confirm that a(1 - e) = a - c and a(1 + e) = a + c.
(c) Use the formulas a(1 - e) and a(1 + e) to compute the perihelion and aphelion distances of each planet listed in Table 8.4.
(d) For which of these planets is the difference between the perihelion and aphelion distance the greatest?
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