Plantary Society: Of inclinations and azimuths

On Tuesday, April 3, a National Reconnaissance Office satellite roared into orbit atop a Delta IV rocket from Vandenberg Air Force base in California. Despite the classified nature of the the innocuously dubbed NROL-25 mission, one detail about the launch is publicly known: the satellite’s unusual orbital inclination of 123 degrees. What makes this trajectory so unique? Pondering the answer affords the opportunity to learn some deceptively tricky concepts about the nature of all spacecraft orbits, not just the military ones.
NROL-25 lifts off from Vandenberg Air Force Base on April 3, 2012. The payload, a classified satellite, was bound for an unusual, 123 degree retrograde orbit. It was also the inaugural launch for a Delta IV Medium rocket in its 5-meter payload fairing, two solid rocket booster configuration. Credit: Rodney Jones / USAF
Orbital inclination is the angle of the satellite’s orbital plane with respect to the Earth’s equatorial plane. Measure starting from due East on the equator, and trace an angle to the orbital plane on the side of the equator in which the satellite is travelling after it crosses. Inclinations always measure between 0 and 180 degrees. An orbit with an inclination between 0 and ...