Orbital Dynamics

As a follow up to some of my previous posts about space flight, I have decided to discuss orbital dynamics.  The general public is grossly misinformed about real space flight thanks to so much misinformation in movies and on TV.  The Jet Propulsion Laboratory has an excellent tutorial here for those who want to get into even more detail about space flight.

Why discuss orbital dynamics?  Because every body in the universe is in orbit around something. Furthermore, orbital dynamics are interesting because they are so non-intuitive when it comes to maneuvering a space ship. Understanding orbital dynamics is essential to real space flight.

Johannes Kepler discovered by observation that planets follow elliptical orbits around the sun.  Isaac Newton showed that elliptical orbits are a consequence of the inverse square law of gravity.  More generally, orbits are conic sections.  When you throw a baseball, its path is a parabola.  A comet that only approaches the sun once, and then heads for interstellar space is following a hyperbolic curve.

If two space craft are orbiting the earth in the same orbit, but separated by some distance, how can they rendezvous or send items back and forth.  MIT Professor Walter Lewin discusses this problem in his ham sandwich lecture, which is posted online here.  As Lewin states it, how do you throw a ham sandwich to the hungry astronaut in the space ship that is in orbit ahead of you?  You might want to just throw it toward him, but that would put the ham sandwich into a higher orbit, thus ultimately slowing it down and sending it further away from the hungry astronaut.  The right way to send him the ham sandwich is to throw it backwards, away from his space ship.  This would initially slow down the ham sandwich, but then it would pick up speed as it fell into a lower orbit.  If done just right, the elliptical orbit of the ham sandwich would intersect the more circular orbit of the hungry astronaut's space ship at just the right time on the next orbit.

The astronauts in the Gemini program in the 60s, the first to execute a rendezvous in earth orbit, had to learn to go contrary to their intuition.  The first required maneuver was to match the plane of the target.  Next, it was necessary for the perusing ship to be in a lower orbit so it could gain on the target.  Once the target was in sight, the astronauts had to fight their natural tendency to fire thrusters to move their space ship toward the target.  Instead, they needed to maintain their lower orbit, only pulling up into the same orbit as the target at exactly the right moment.  Of course, this is all old hat now for real astronauts, but the complex and intricate details are not always fully appreciated by a general public fed with a steady diet of Star Trek and Star Wars.

Orbital dynamics also come into play in planning trajectories for interplanetary travel, but that is a subject for another post.  If you can't wait until then, check out the JPL Space Flight Tutorial I mentioned previously.