Trajectories and Orbits
The key contribution of physics is celestial mechanics, the laws that govern the motions of bodies moving under the influence of gravitation. By combining Newton's law of universal gravitation and his laws of motion, the path of a rocket in the earth's vicinity can be calculated. This path, known as the trajectory, is strictly determined by the initial thrust imparted to the rocket, the gravitational field of the earth, and the atmospheric drag encountered. Although the manner in which these factors interact is highly complex, it is possible to determine accurately in advance the trajectory of any rocket and even to alter its course by remote control. If a satellite or unpowered spacecraft is close to the earth, the effects of other heavenly bodies can be ignored and its orbit will be a conic section: circular or elliptical for a satellite that remains in a closed orbit around the earth, and parabolic or hyperbolic for a spacecraft or space probe that escapes the earth's gravitational field into an open orbit.
The criterion that separates the closed and open orbits is the escape velocity, which for the earth is 7 mi (11.3 km) per sec. If the initial thrust provided by a rocket gives the object a speed greater than the escape velocity, it will move away from the earth in an open orbit; if the final velocity is smaller than the escape velocity, it will remain at finite distance from the earth in a closed orbit; if the final velocity is less than 5 mi (8 km) per sec, the flight will be suborbital and the object will follow an arc that returns it to earth.
A satellite in orbit around the earth typically travels at a height of several hundred miles with a velocity of about 5 mi (8 km) per sec and a period of revolution of 90 min. For certain satellites, however—such as communications satellites—synchronous orbits are desirable; at a distance of 22,300 mi (35,900 km), a satellite's period is exactly 24 hours, so it appears to hover over the same point on the earth's surface. Circular orbits are usually the most desirable but are the hardest to achieve. If a satellite is launched eastward near the equator, it receives a boost from the earth's rotation, but the resulting orbit necessarily lies in the earth's equatorial plane. For some applications, polar orbits, which pass near both of the earth's poles, are preferred. In a polar orbit, a satellite will periodically pass directly over every point on the earth's surface. Translunar and interplanetary trajectories are highly complex, because no simplifying assumptions can be made; the gravitational influences of the sun, moon, and other planets must be considered. Such gravitational forces can be exploited advantageously; for example, in the slingshot effect, a space probe is accelerated as it swings past a planet on the correct trajectory.
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