You and your team are engineers that have been contracted by Elliot Carver of the Carver Media Group Network (CMGN) to plan the launch of their new “communications” satellite. The satellite is meant to perform a geosynchronous pole-to-pole orbit.

The sattelite consists of a transmitter of mass ($m_t$ = 4500kg) connected to two perpendicularly directed ejectable spring loaded probes (each having mass $m_p$ = 400kg). Each probe is connected to a single, very stiff spring ($k_p$ = $5.3\times10^9$ N/m). The probes can be ejected by remote control from the CMGN headquarters in Freer, Texas; springs can be compressed as needed. A mockup from CMGN's lead designer, Wai Lin, appears below.

CMGN is going green with their satellite launches. Their new design uses no fossil fuels. The satellite itself is launched from CMGN's launch facility in the South Pole with yet another spring system, oriented vertically with respect to the flat launching platform. This very stiff spring ($k_L$ = $8.3\times10^8$ N/m) can be compressed as needed.

The satellite contains a gyroscope that self-orients the satellite with respect to the gravitational force due to the Earth, such that the satellite remains in its original orientation throughout the entirety of its trip.

Carver needs you to plan the launch and any subsequent course corrections needed to get the satellite into a geosynchronous pole-to-pole orbit.

Carver has a lot of money wrapped up in this satellite, so he wants your team to simulate the orbit of the satellite. His lead computer scientist, Henry Gupta, has gone missing, but left a piece of code that demonstrates the orbit of the satellite (or so he claims, Carver isn't really much of a scientist).

He wants you to make sure that Gupta's simulation does accurately represent the motion of the system. Using graphs of the movement of energy in the system and adding an arrow that represents the net force vector and its parallel and perpendicular components would really convince him.