Rendezvous Part 2 – What’s an Orbit?

In my book Shuttle, Houston: My Life in the Center Seat of Mission Control, I bring readers deep into the middle of how Mission Control worked during the Space Shuttle era. I give readers a glimpse of both the technology and the humanity required to put humans in space on a routine basis. There are many parts to this thirty-year story, and only a small portion of the tales fit into the book – so here is an excerpt from an unused chapter on the process of rendezvousing the shuttle with other objects in orbit.

Rendezvousing in space is a matter of first matching orbital planes. All orbits include the center of mass of the planet in their plane – that is a given. But the plane of the orbit can then be inclined relative to the equator by whatever amount is required for the mission. If you launch from the equator going due east, you will have an inclination of zero degrees. If you launch pointed straight over the pole, the inclination will be 90o. The inclination determines how far north or south you will go, and how much of the earth’s surface you will cross. If you launch due east from the equator, you can put the maximum mass into orbit, or get as high as possible with the fuel available to you. Inclining the plane to something other than zero will let you see more of the earth, but because some of your launch energy is going into making you go north and south, and less is directed to the east, you will not get as high of altitude – and you can’t carry as much mass to orbit.

The equator looks pretty good for launching spacecraft, because not only can you launch due east to put all your energy into altitude or mass carrying, any spot on the equator is already going about 1,000 feet per second “eastward”, so you are getting a head start on the velocity you need to get to orbit. Move your launch site north or south, and because you are closer to the axis of rotation, your actual tangential velocity on the ground decreases as you move towards the pole – until you would get no help at all if you launched from 90o north (or south). So, for a spacefaring nation, having some launch real estate on the equator looks rather good! It’s never simple though – and engineering doesn’t trump political boundaries or logistical considerations of operating far from home. The Europeans have maintained their launch site in South America for the Arianne series of rockets because it makes good engineering sense – but operating there is logistically difficult, for a variety of reasons.
Russia has always launched from within the borders of the old Soviet Union, and their launch site of choice is Baikonur in the central Asian steppe. The United States, of course, has created its primary launch center in Florida, getting as close to the equator as we could while staying within our borders – and having the opportunity to drop spent rocket stages into the ocean by launching off the east coast. But launching north or south of the equator means that unless you spend a lot of launch energy steering your orbital lane back down to zero, you can only have an inclination as low as the latitude from where you launch. For Kennedy Space Center, that is about 28.5o.
Now orbits are fixed in what we call Inertial Space. For everything, there is a reference, and in order to make navigation easier, we choose inertial space as our reference, rather than using the earth’s rotating coordinate system. The inertial coordinate system is fixed relative to the stars – which doesn’t really mean it is fixed, but it is close enough for space missions of the durations we usually fly. At any rate – once you lift off from the surface of the planet, and accelerate yourself to orbital velocity, your orbital path is fixed relative to the stars and the earth rotates underneath you. This is why, when you look at the big tracking map in the front of Mission Control, you see sine waves that represent the current and future orbits of the space vehicle. Imagine holding a halo around a globe, with the plane of the halo tilted relative to the equator, say at 45o. That halo is your orbit, and it is fixed relative to the walls of the room in which you’re doing this experiment. Now spin the globe – you’ll see that if you had a spaceship flying along the halo, every time it came back around to cross the equator in a south to north direction, it will cross the equator at a different point over the earth because the earth is rotating underneath it.
Now let’s add some complication – let’s put two spacecrafts out there, in similar orbits, with one trying to catch the other. The first thing we must do is to get the in the same orbital plane. If the points at which the two planes cross the equator are different, they will only come together once in a great while and will cross paths at an extremely high relative velocity. If the crossing point at the equator is the same, but the planes are at different inclinations, a similar thing will occur – they two spacecraft might occasionally meet, but they will zoom past one another.

So we need to get the two spacecrafts in the same plane, and the only reasonable way to do this on a short mission is to time the launch of the second spacecraft so that we actually insert it into the same plane as that occupied by the first – within a reasonable margin of error. If launches were instantaneous, going from the pad to full orbital speed with not time delay, you would launch when you are exactly in the plane with the target vehicle. But, alas, it takes the shuttle about eight and a half minutes to go from zero to orbital velocity, so some complicated math was required to launch it BEFORE you got in plane, and then during the acceleration phase, you slowly converged on the plane you wanted. It’s conceptually like leading the target with a shotgun when you’re hunting – but it takes a lot of smart folks to write the computer code to do the predictions and consider all the variables.

We’ll bring you the next portion of “Rendezvous” next week right here! If you enjoyed this look inside the Shuttle program, you can find many more details and stories in the book – look for it wherever you buy your paper books, or add it to your favorite E-reader or audio book account.

Great news! We have partnered with our pals Emily and Mike at Speleobooks to provide autographed/specially inscribed copies of Ironflight’s book at a great price. Please go to their site to check out the details and order:
Christmas is coming!

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