Orbital Shapes and Paths

In planning the flight of a satellite about a body in space, there are many factors which we must take into consideration. But none is of greater importance than the shape and path of the orbit. We have to decide whether we want the shape of the orbit to be circular or elliptical. We have to decide how large we want it to be. We have to decide what path on the body we want the satellite to fly over and how often. Naturally, the decision will be based primarily on what we want our satellite to do in space. We must understand how the physical principles that govern the flight of all satellites can be used to give the orbital shape and path we want. [Music] [Music] Reviewing those principles briefly, we recall that a satellite remains in orbit because of the combined effects of inertia and gravitation and that orbital planes of all satellites pass through the center of gravity of the bay. We recall that a satellite possesses a constant sum of two kinds of energy, kinetic and potential. In a circular orbit, a satellite's kinetic energy or speed and its potential energy or altitude each remain fixed. When rockets are fired to go into an elliptical orbit, the satellite's two kinds of energy interchange, although the total sum of energy remains constant. As the satellite climbs toward its high point or apogee, it loses speed or kinetic energy as it gains altitude or potential energy. And as the satellite falls toward its low point or perigee, it gains speed or kinetic energy as it loses altitude or potential energy. The speed change that occurs between perigee and apogee is exactly reversed between apogee and parige. If no outside forces are applied, the satellite will continue to orbit through those points forever. Now let's look at some of the ways we can use the principles which govern the flight of satellites. Suppose that we have a satellite. Let's say the spaceship of one Andy astronaut in a circular orbit around a body in space. How can we change the shape of Andy's orbit? Simply by using rocket motors to change the kinetic energy or speed of his spaceship. An increase in speed will provide too much speed for gravity to hold it in that orbit. The result is of course an elliptical orbit. At the high point or apogee, the spaceship is at too low a speed to remain at this altitude and falls back toward Earth to return precisely through the point where the rocket motor was fired. Now the low point or perigee. We could also alter this orbit, should we use the rocket motors again to change the speed of the spaceship. If at the high point, for instance, we increase the speed, Andy's spaceship will begin to fly out away from the ellipse. If the increase in speed is exactly right, the new orbit will be a circle. If the increase is greater than required for a circular orbit, the spaceship will fly out away, not only from the ellipse, but away from the circle as well into a new, larger elliptical orbit. We can also change the shape and size of an orbit by reducing the speed of the spaceship. We do this by turning the spaceship around and using the rocket motors to apply thrust opposite to the direction of flight. Should we apply these space brakes just at the low point of our elliptical orbit, for example, the spaceship loses speed and gravitation pulls it inward toward the body. Depending on how much the speed is reduced, the new orbit will either be a circle or an ellipse. If the speed was reduced enough, the new orbit would have carried Andy's spaceship down to the surface. This is how actual spacecraft are brought out of orbit. Now, let's put Andy in an orbit around his own mother earth. What is his path of travel over the surface first traveling in a circular orbit above his equatorial path? and he could look down and see the Atlantic Ocean, the heartland of Africa, the Indian Ocean, the islands of the East Indies, the Great Pacific Ocean, the northern part of South America. Then his journey would begin to look familiar. Again and again, he would see the same oceans, the same lands. In order to give Andy some new views of the Earth, let's tilt the orbit of his spaceship. If the Earth were somehow stuck on its axis, not rotating, Andy would again find himself flying repeatedly over the same path. [Music] Even if we tilted the orbit until Andy passed over the North and South poles, he would again soon find himself over the same familiar path. In reality, of course, the Earth is rotating. It rotates on its axis once every 24 hours. Notice, however, that the plane of Andy's orbit does not rotate, but remains fixed in space. Now, the surface of the revolving Earth sweeps through the orbital plane, giving Andy a new path over the Earth's surface on each orbit. The fact that the orbits remain fixed in space like train tracks while the Earth turns beneath enables him to fly over many specific points such as this one. We can see that as soon as his spaceship passes over a point on the revolving Earth's surface, the point moves out from beneath the orbital plane. Had we marked a number of these points on the Earth's surface, we can visualize the spaceship's path of travel. When the spaceship returns, it will pass over new points. This is the orbit that Andy would use if he wanted to observe the entire Earth's surface in a single day, as our weather satellites do. At least once a day, he could observe and report weather as it developed any place in the world. Now, let's explore the orbital paths of a satellite at an inclination to the equator, similar to that used in Mercury or Geminy. Let's launch Andy and his spaceship from Cape Kennedy out over the Atlantic Ocean down across the equator into an imaginary orbit which we will speed up for purposes of illustration. Further, let's trace Andy's path as he passes over the surface of the Earth. When Andy has completed his first orbit, he discovers, as he would expect, that the revolving Earth has moved Kate Kennedy and his original ground path out from beneath his orbital plane. completing his second orbit. Andy sees that Cape Kennedy has moved even further away from beneath his orbital plane. After several more orbits, Cape Kennedy has moved entirely out of view. It is not until Andy completes a full day's orbit that he finds he is at last again above Cape Kennedy, the Earth having turned a complete revolution, and he begins to retrace his orbital path. On a flat map of the world, Andy's orbital path for a day would look like this. [Music] Still another variable affecting Andy's flight is the orbital period or time required to complete one orbit. At an altitude of 100 m or so, Andy must travel at 17,500 mph in order to stay in orbit. His orbital period is 90 minutes. If we send him higher, the gravitational force on the spaceship is smaller and less speed is needed to keep him in orbit. As a result, his orbital period increases. Using this fact, we can, if we wish, send Andy to an altitude above the Earth's equator requiring an orbital period of exactly 1 day, the same time required for the Earth to make one revolution. At this altitude, approximately 22,000 mi, his equatorial orbit would be synchronized with the rotation of the Earth. Andy's spaceship now acts like one of our synchronous satellites, which appear to remain fixed over one point on Earth and can thus continuously relay signals from one portion of the Earth to another. Since television signals travel only in a straight line of sight, synchronized satellites in effect bounce signals around the Earth. This is how television is relayed by satellite from one continent to another. If we wanted to increase the period of Andy's orbit still more, we could send him to the altitude of the moon, approximately a quarter of a million miles from Earth, where he would orbit the Earth once every 28 days, just as the moon does. [Music] Thus, by combining our ability to control orbital shapes with our ability to determine orbital paths and periods, we can fly missions to do almost whatever we choose in space. Our primary tools are the physical principles which govern the flight of all satellites. It is the use of these tools that challenges our imagination. [Music] My [Applause] [Music]