# Astronautics

Astronautics is the science and technology of space flight. With the rapid expansion of technology, this relatively new term was required to cover the broad range of scientific and engineering activities related to the exploration of space.

There are two major landmarks in the history of this group of disciplines. The first was Isaac Newton's formulation of the laws of celestial mechanics. In fact, Newton noted the possibility of creating an artificial satellite. The second was the development of large rockets for space travel. The Russian mathematician Konstantin Tsiolkov-sky pointed out the possibilities of rocket flight in the 1890's. Robert Goddard, the American physicist, pioneered the development of the rocket for exploration of the upper atmosphere of the earth in the 1920's and 1930's, and a German group under Hermann Oberth undertook studies on interplanetary travel during the 1920's.

Photo by Stacy Braswell

## Principles of Astronautics

Astrodynamics, with which this article is primarily concerned, is the foundation of astronautics. It is the mathematics and physics of the motions of bodies (in this case, spacecraft) in space flight. Astrodynamics concerns itself with the motion of the center of mass of a spacecraft, as well as with the motions of the craft about that center of mass.

Mass should not be confused with weight. In the Newtonian sense, mass is a property possessed by all matter and is defined for any particle in the universe by its ability to attract another particle. Weight is a force resulting from the attraction of the earth (or other body) on the particle and is best defined as being proportional to the mass of the particle times the acceleration produced by the earth. A satellite in orbit has mass but no weight, whereas if the spacecraft were on the earth, it would have weight as well as mass.

The physicist, in calculating the motions of bodies in space, thinks of each body as a point in which all the body's mass has been concentrated. This point is called the center of mass, or center of gravity, of the body. It is a particularly useful concept when the bodies under discussion are separated by distances that are large in comparison to their sizes.

## Laws of Gravity and Motion

Underlying these astrodynamical studies are the physical laws governing the motions of particles through space. These laws apply to the motions of all bodies, and an understanding of them is essential to an understanding of the problems of space flight. The laws were formulated by Isaac Newton in the 1680's and form the basis of modern physics, although in some aspects the laws are only good approximations.

Newton's law of gravitation states that any particle of matter in the universe is attracted to any other particle with a force equal to the product of the two masses divided by the square of the distance between them. Thus, suppose that the gravitational force between two particles a certain distance apart is calculated. If these particles were twice as far apart, the force between them would be only one fourth as great as that force first calculated.

The laws of motion state that: (1) a particle moving through space tends to move in a straight line unless acted upon by some force; (2) the strength of such a force can be calculated as the acceleration it produces times the mass of the particle; and (3) for every force there is an equal and opposite reacting force. The concept of equal and opposite reaction is necessary to the understanding of the operation of a rocket. A rocket is propelled forward in reaction to its ejection rearward of small but rapidly moving particles of hot gas.

These laws of gravity and motion apply to all particles or bodies in space: the stars, the planets, the moon, and artificial satellites and spacecraft. However, generalized mathematical solutions to the equations of motion are possible only when no more than two bodies are involved—the so-called "two-body" problem. If three or more bodies are involved—the earth, the moon, and a spacecraft, for example—only approximate, computer-produced solutions can be obtained.

## Kepler's Laws

Other laws governing the motions of bodies in space can be derived from the basic law of gravitation. Thus, Newton generalized Johann Kepler's laws concerning or-its about 70 years after Kepler had deduced them from observations made by Tycho Brahe. Kepler's laws state that: (1) the orbit of any planet (body) about the sun (another body) is an ellipse, with the sun as one focus of the ellipse; (2) an imaginary line joining a planet and the sun would sweep over equal areas of space in equal intervals of time; and (3) the squares of the periods of any two planets, each multiplied by the sum of that planet's mass and the sun's mass, are in the same proportion as the cubes of their average distances from the sun.

The first two laws are of particular importance to space flight. The third law is of more interest in theoretical astronomy.

## Applications of Astronautic Principles

Space flight can be categorized and discussed usefully as being either earth orbital or planetary  flight. The laws of motion and gravitation apply to each category, but the conditions and results involved are different.

## Earth Orbital Flight

In earth orbital flight the gravitational field of the earth dominates the motion of the spacecraft. For this discussion the effect of the earth's atmosphere (which creates drag on the spacecraft, causing it to slow down and eventually fall back to earth) can be neglected. So can the effects of such phenomena as the shape of the earth, the lunar and solar gravitational attractions, and other small but nonetheless real perturbations of the motion of the spacecraft.

A spacecraft flight begins with the ignition of the engine or engines of the booster rocket. As thrust builds up to an amount where it is greater than the weight of the space vehicle (booster rocket plus spacecraft), the vehicle rises. It climbs faster and faster as its weight is decreased by the burning propellants. The trajectory is determined by the guidance equipment in the space vehicle, usually augmented by a radio guidance system. Each stage of the booster rocket adds to the velocity required to orbit the spacecraft. Injection of the spacecraft into orbit occurs when it is at the desired altitude and is given the proper amount of thrust parallel to the surface of the earth.

The Newtonian laws explain why the spacecraft stays in orbit and account for the other properties of its motion around the earth. Thus, the spacecraft would tend to travel in a straight line unless acted upon by some force. The force causing it to follow a curved path around the earth is the earth's gravitational attraction. If the velocity of the craft is too low, it falls back to earth; if too high, the craft may escape the earth's attraction.

At intermediate velocities there is a balance of forces acting on the craft, which moves around the earth in an elliptical path. The ellipse has the center of gravity of the earth as one of its foci. The speed of the spacecraft is greatest at perigee (the point of closest approach to the earth) and lowest at apogee (the point of maximum distance from the earth). An imaginary line connecting the spacecraft and the earth's center of gravity would sweep out equal areas of space in equal intervals of time.

## Earth Orbital Flight

In planetary flight the objective is to have the spacecraft approach (either to land on or to fly by) the moon or one of the planets. The launch trajectory may be the same as for earth orbital flight except that the injection velocity is higher. (See Table.) The trajectory is influenced by the gravitational attraction of the earth for the first few days of flight. Then it is influenced for a long period by the attraction of the sun. For the last few days of approach to the moon or planet the spacecraft's trajectory is influenced by the gravitational attraction of that planet.

The solar system lies in a flat disk with the planets orbiting the sun in nearly circular paths of different periods. The motions of the planets limit the times of day and the years during which spacecraft can be sent to the planets. The trajectory and duration of such a flight are determined by the velocity with which the spacecraft starts out. A spacecraft moves under the gravitational influence of the sun for most of its flight, so that it follows Newtonian laws and travels along an ellipse with the sun at one focus. If the spacecraft misses the target planet, it ultimately falls back toward the sun along the other half of the ellipse and becomes a tiny "planet" orbiting the sun.

An important aspect of flight trajectories (whether planetary or earth-orbiting) is that they are essentially ballistic. That is, the spacecraft is given a push much as a rifle ejects a bullet, although more gently and slowly. The craft then coasts along the largest part of its trajectory, responding to the gravitational pull of the nearby astronomical bodies. Successful space flight therefore requires precise aiming, because the target is small and far away. It requires precise timing of the launch as well, because the target is moving and because the launch site is itself a moving platform—a certain latitude on the earth—with a velocity determined by the rate of the earth's rotation and the latitude.

Aiming and timing cannot be absolutely accurate, however, and the concept of midcourse correction becomes very important. For example, on a flight to Mars a small rocket engine is carried on the spacecraft to provide midcourse velocity correction. For a few days after launch the craft is tracked by radio, and its speed and direction are precisely determined. The change in velocity required to make the spacecraft hit the target area (which may be simply a "hole" in space if the mission objective is to fly by the planet) is computed, and the spacecraft rocket is fired at the right time and for the right duration to provide the required velocity correction.

Since there are a great many variables to consider in planning a flight to a planet, graphs are the best way of showing the required data.

## Planetary Flight

The flight to the moon is of special interest because it is the first target for manned space exploration beyond the immediate environs of the earth. The trajectory to the moon is complex because the spaceship must first move in the gravitational field of the earth, then in that of the moon, and in both cases the sun is also acting on the ship.

There are a number of different flight plans possible for the flight to the moon and back. Thus, a space vehicle can be launched from the surface of the earth at the right time and in the right direction to fly directly to the moon, using rockets in the spacecraft to slow it to a gentle landing on the surface. (This is the way the U.S. Surveyor unmanned landings were made.) An alternative is to orbit the earth first, then fire a rocket engine and transfer to the moon, using the engine again to slow down and land directly on the lunar surface. Another alternative is to orbit the earth, then transfer to the moon and enter a lunar orbit, finally descending and landing in a lunar module.

Each alternative has its advantages. The first requires the least number of maneuvers. In the second a larger rocket can be assembled during the earth-orbital phase by using several launches and having the parts rendezvous in space. The third method requires the least amount of propellants. It was the one that was chosen for the U.S. Apollo missions.

## Interplanetary Flights

Space flights to the planets are of great interest for scientific and technological reasons. So far, successful flights have been made to Mercury, Venus, Mars, and Jupiter. Jupiter is the largest planet in the solar system. It is the key to the exploration of the entire solar system because it is possible to play a kind of "celestial billiards" with the giant planet.

A mission to Jupiter would have the same characteristics as those to other planets. The initial velocity would have to be about 50,000 feet (15,000 meters) per second in order to reach Jupiter within 600 days. The spacecraft would move under the gravitational attraction of the sun for most of the journey.

By passing close to Jupiter, however, it becomes possible to go beyond Jupiter to the limits of the solar system, to fly out of the orbital plane of the planets, or to turn back and pass very close to the sun. The reason for this is that the powerful gravitational field of Jupiter can be used to change both the speed and the direction of the spacecraft—in a sense,- to toss it farther out into space or back toward the sun. The advantages of this use of the gravity of Jupiter are particularly apparent in the fact that the time of flight to Saturn is shortened from five years to three years by this method.

## Manned Flight

The principles of space flight that have been discussed apply equally well to a manned spacecraft or an unmanned spacecraft. Whether a space flight is manned or unmanned is determined by the mission objectives. The reasons for manned flight are many. Space is a new frontier that man as a pioneer wants to explore, for the same reasons that he has explored the limits of the earth on which he lives. Space exploration is a means of increasing his knowledge and understanding of the universe. It is a means of applying new tools, such as those the fields of meteorology and communications, for the benefit of all mankind.

Although most of the objectives of space exploration could be accomplished by unmanned automatic spacecraft, man will go into space because it is in his nature to do so.

Man in space, whether as a pilot, explorer, or scientist, brings new dimensions and new difficulties to space flight. He is small, adaptable, and an extraordinarily efficient computer. But he must be carefully protected from the hostile environment of space, where there is no atmosphere to breathe, to keep him warm, to protect him from the radiations of the sun, and to shield him from the cosmic rays or the micro-meteorites and other bits of matter moving through space at high velocities.

Thus, a vehicle carrying man into space must be designed to get him there safely, protect him while there, and bring him back without injury. It is a shelter that must provide man with the oxygen, water, and food he requires and that must remove the toxic wastes that would in time bring about death. For all these reasons the structures, the machinery, and the supplies required to maintain man in space add up to a considerable amount of weight. The Apollo command module needed to house and support three men on a 14-day lunar mission weighs 11,000 pounds (4,950 kg).

## Present and Future Developments

The astrodynamic aspect of astronautics is highly developed today, largely because of the availability to the mathematician-physicist of powerful computers. In determining the motions of bodies in space, exact analytical solutions to problems are possible only when no more than two bodies are involved. Thus the multibody problems that arise in space exploration, where trajectories involve the gravitational effects of many bodies, cannot be solved analytically but only through the use of computers. With computers a series of approximate numerical solutions are made to a problem, the approximations becoming quite exact after many repetitions and many hours of computation.

Although there have already been many remarkable achievements in space exploration through the use of such methods, more difficult problems remain. Thus, there is still no adequate mathematical procedure, either numerical or analytical, to handle the problem of a spacecraft moving through interplanetary space under continuous thrust or propulsion. This problem, quite important for long-distance space flight using nuclear propulsion, remains unsolved as yet.

As a discipline, astronautics has developed rapidly by drawing on a wide range of scientific and technological fields: mathematics, physics, engineering, biology and biosciences, management, and so forth. In large part the initial pioneering is over and the early objectives of astronautics have been realized. The basic techniques and skills required for extensive manned and unmanned space flight have been developed and demonstrated. The facilities—research and development laboratories, launch complexes, and manufacturing plants—have been built. Man is about ready to undertake the systematic and definitive exploration of space.

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