Replacing Newtons Cannon

In Chapter 2, we discussed the nature of orbital motion using Newton's cannon as a means of achieving orbit. Clearly we do not have a handy 200-km-high (124-mile-high) mountain upon which to build such a structure, so instead we resort to rocket-powered launch vehicles to place our satellites into orbit. It is fairly easy to see how the substitution is made. As we saw earlier, to enter a low orbit around Earth, a cannonball needs to be traveling horizontally out of the cannon's barrel at around 8 km/sec (5 miles/sec) at an altitude of 200 km. Thereafter, we saw that the curvature of the cannonball's trajectory matched that of Earth's surface, thus avoiding ground impact and ensuring the cannonball's orbital state. If we wish to launch a satellite installed on top of a launch vehicle into the same orbit, then we have to ensure that the same initial conditions are met; if the launcher can lift the satellite to an altitude of 200 km and boost its speed to the required 8 km/sec in a horizontal direction, then the same orbital motion will result.

The launch vehicle is more versatile than the cannon, as the latter is somewhat constrained in its performance by being fixed to its supporting platform—the mountain—at a 200-km altitude. If the launcher is powerful enough, it can lift the satellite to higher altitudes, and vary the satellite's initial speed and direction to enter a variety of orbits as discussed in Chapter 2. For example, if the launch vehicle were to release its payload at a height of 700 km (435 miles) in a horizontal direction with a speed of 7.5 km/sec (4.7 miles/sec), the satellite will enter a circular orbit at that altitude. Furthermore, if the satellite was to be released in the same way at this height with a speed of 10.6 km/sec (6.6 miles/sec), then it would eventually escape Earth on a parabolic trajectory (see Chapters 1 and 2).

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