(a) Express in terms of rmin and vmax the angular momentum per unit mass, h, and the total energy per unit mass, E/m, of a space vehicle moving under the gravitational attraction of a planet of mass M.

(b) Eliminating vmax between the equations obtained, derive the formula.

(c) Show that the eccentricity ε of the trajectory of the vehicle can be expressed as

(d) Further show that the trajectory of the vehicle is a hyperbola, an ellipse, or a parabola, depending on whether E is positive, negative, or zero.

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