Your mission: chase down the International Space Station in less than two days, even though it has nearly a 20,000 mi lead on you and is traveling at over 17,000 mph. Daunting? Sure seems like it! Yet armed with some insights into orbital rendezvous, what may seem impossible becomes not only possible, but quite doable.
The first fundamental of orbital rendezvous is the following law: to go fast, stay low. Want a proof in point? Compare the orbital speed of the ISS with that of the moon. The ISS is traveling at about 17,500 mph. How about the moon? Well, the moon is 238,000 mi away and requires one month to complete an orbit. Therefore, some simple math says that the moon is traveling at 2,200 mph – a lot slower in comparison. Therefore, we’ll use that to our advantage by launching the shuttle into a lower orbit than the ISS and stay there for a period of time to allow the shuttle to “catch up” to the ISS.
In the case of space shuttle Discovery for the STS-119 mission, it was launched into an initial orbit about 125 miles high on one side of its orbit and 85 miles on the other. If needed, Discovery could remain in that orbit to provide the fastest possible catch-up rate. In our case, the fastest rate is not needed. The Flight Dynamics Officer in Mission Control performs a calculation to determine the best catch-up rate, which in this particular case called for shaping the orbit into approximately a 145-by-125 mile orbit on Flight Day 1. The shuttle remains in that orbit through Flight Day 2 and into the morning of Flight Day 3.
Then the fun begins. It is “day of rendezvous,” a term of art that means the sequence of maneuvers nearly identical on all shuttle rendezvous missions designed to bring the shuttle to its rendezvous target, in our case the International Space Station.
The first maneuver of Flight Day 3 raises one side of the orbit to the same height as ISS and to arrive at a point 40 miles behind it. The next maneuver raises the other side to the point just below ISS such that the shuttle arrives at a point 8 miles behind the station 90 minutes later. At this point, the shuttle executes a burn that will have it arrive directly underneath the ISS 90 minutes later. There is a series of midcourse corrections burns that are performed following this last burn to refine the orbit based on onboard navigation data. The shuttle arrives just below ISS, performs a belly-flip to allow photography of its underside by the ISS crew, then approaches and docks, all while traveling at – you guessed it – 17,500 mph.
And that is how you accomplish an orbital rendezvous!