The earth-sun L5 Lagrange point is a point of stable equilibrium that trails the earth in its heliocentric orbit by \(60^{\circ}\) as the earth (and spacecraft) orbit the sun. Some gravity wave experimenters want to set up a gravity wave experiment at this point. The simplest trajectory from earth puts the spacecraft on an elliptical orbit with a period slightly longer than one year, so that, when the spacecraft returns to perihelion, the L5 point will be there.

(a) Show that the period of this orbit is 14 months.

(b) What is the semi-major axis of this elliptical orbit?

(c) What is the perihelion speed of the spacecraft in this orbit?

(d) When the spacecraft finally reaches the L5 point, how much velocity will it have to lose (using its engines) to settle into a circular heliocentric orbit at the L5 point?