## Minimize the Cost

Everyone wants to save a buck. In this chapter and the next, I diverge from the ordinary-life lesson and talk about how rocket scientists try to save time and money.

When a shuttle astronaut drinks a sixteen-ounce bottle of water it costs about \$10,000.

Why is it so expensive? There are two reasons. The first is the poor design of the shuttle itself, which has unfortunately made space travel more expensive (not to mention more dangerous) than it has to be. (More on this point later.)

The second reason has to do with the laws of orbital mechanics. To get that bottle of water into orbit (along with the astronauts, their life-support system, and everything else), it has to be accelerated to a speed of five miles per second. After the rocket engine burns out, the bottle will be in free fallâ€”it will fall toward Earth, but it is moving so fast that Earth's surface curves away from the bottle at the same rate that the bottle falls toward the ground. These two effects, the falling of the bottle and the curving of Earth's surface, cancel out at five miles per second. To be placed in a circular orbit, the bottle must be moving parallel to Earth's surface at this incredible speed.

So weightlessness is not the absence of gravity at allâ€”weightlessness is falling under the pull of gravity. If you want the sensation to last indefinitely (and who doesn't?), then you have to be traveling at the fantastically fast speed of five miles per second. (This is technically known as the "circular speed" for low-Earth orbit.) At this speed, a spacecraft will zip past the entire United States in under eight minutes; in ten minutes it will cross the Atlantic Ocean.

To get the spacecraft into orbit, it is placed in the payload bay of a launch vehicle such as a Delta, an Atlas, or the shuttle. The launch vehicle is ignited and launched straight up into the air. As it ascends vertically to greater and greater heights, it starts to tilt

Chapter 35 Minimize the Cost over to one side. This tipping is intentional. The rocket continues to tip while gaining altitude until it is no longer traveling vertically, but instead is traveling horizontally. When the rocket reaches a height of one hundred miles it achieves a speed of five miles per second and is traveling parallel to Earth's surface. The engine cuts off, and the astronauts experience falling without ever hitting the ground (i.e., weightlessness).

The tipping rate of the launch vehicle is determined by a control scheme called "the steering law." If the tipping occurs too fast, it will cost more pounds of propellant to get into orbit. If it occurs too slowly, it will also cost more.

Rocket scientists use a type of mathematics called "calculus of variations" to find the cheapest way to get into orbit. According to the theory, the steering law that takes the minimum time to reach orbit is best because the rocket burns the least amount of propellant.

When rocket scientists apply this technique to the shuttle, the result is that it costs \$10,000 to give an astronaut a drink of water!

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