Question

Calculate the path that the Icarus 2 would have to take to rendezvous with the Icarus. Assume that both the Icarus and the Icarus 2 are in orbits around Mercury, similar to the elliptical orbits of NASA's Mercury mission. You must rotate the orbits into a configuration that would satisfy the distance that the movie says that the spacecrafts are separated by (the movie says its 10,000 to 15,000 miles, but it makes more sense for this distance to be 15,000 km, so assume 15,000 km). To make your calculations easier, assume that the Icarus 2 leaves it's orbit at its apoapsis, and rendezvous with the Icarus 1 at its apoapsis.

Answer 1

The Icarus 2 must undertake a carefully timed Hohmann transfer maneuver at its apoapsis to rendezvous with the Icarus, which could involve calculating the required delta-v and ensuring alignment and timing with the orbits around Mercury.

Step-by-step explanation:

To calculate the path the Icarus 2 would have to take to rendezvous with the Icarus, both spacecraft need to be on orbits that allow for such a maneuver. Given that the Icarus 2 leaves its orbit at its apoapsis and intends to rendezvous with Icarus at its apoapsis, the process involves orbital mechanics and timing, utilizing Kepler's laws of planetary motion.

Since the distance for the rendezvous is assumed to be 15,000 km, one can calculate the change in the velocity needed for Icarus 2 to reach Icarus by applying the Hohmann transfer orbit principles, as well as considering the specific orbital mechanics around Mercury. The initial and final orbits need to be aligned such that the transfer orbit's apoapsis coincides with the target spacecraft's orbit at the time of rendezvous.

The transfer orbit will be an elliptical one, with the periapsis located at the orbit of Icarus 2 and the apoapsis at the 15,000 km separation point from the Icarus. The semi-major axis of the transfer ellipse will be the average of the periapsis and apoapsis distances, and we can use this to calculate the necessary delta-v (change in velocity) at Icarus 2's apoapsis to achieve the transfer.

Timing is crucial, as maneuvers must be executed such that the spacecraft reaches the rendezvous point when Icarus is also at its apoapsis. This kind of maneuver is contingent upon launching at the right time which is determined by the synodic period of the two orbits.