Using the last of Eqs. (5.131), along with Eq. (5.132), solve for the eccentricity e as a...

Using the last of Eqs. (5.131), along with Eq. (5.132), solve for the eccentricity e as a function of E, κ, and GmB.

(a) Using that result, along with fact that e ≥ 0, show that E < 0 corresponds to an elliptical orbit, E = 0 corresponds to a parabolic trajectory, and E > 0 corresponds to a hyperbolic trajectory.

(b) Show that for e = 0, the expression you found for e leads to Eq. (5.111).

Figure P5.97