Use the work-energy principle applied between periapsis P and r = ∞, along with the potent...

Use the work-energy principle applied between periapsis P and r = ∞, along with the potential energy of the force of gravity given in Eq. (4.35).

(a) Show that a satellite on a hyperbolic trajectory arrives at r = ∞ with speed

(b) In addition, using Eqs. (5.106) and (5.109), show that for a hyperbolic trajectory, , which means that the square root in the above equation must always yield a real value.

Figure P5.112