The orbit of an artificial satellite about the Earth, or any other body, can be treated mathematically in exactly the same way as the motion of binary stars, or the planets. The orbit is an ellipse obeying Kepler’s laws. The period of a satellite grazing the Earth’s surface (if it were possible) is 84.3 minutes, and that of a satellite in a 500-km circular orbit is 94.6 minutes. The energy required to put an object from the ground into such an orbit is at least 30 million joules per kilogram; far more is actually expended by the rocket motors on atmospheric drag and so forth. At 500-km altitude, the orbital velocity is 7.73kms”1, about 0.4kmg”1 of which can be obtained from the rotational velocity of the Earth if the satellite is launched in an easterly direction from a site in the tropics. The orbit is then DIRECT or PROGRADE.
The orbit would remain fixed in space with the Earth rotating uniformly under it if there were no perturbing forces acting on the satellite. If the orbit is inclined to the equator however, the bulge of the Earth causes the nodes (points where the orbit crosses the equatorial plane) to regress, in a westerly direction for a direct orbit. Under certain conditions, such as an inclination of 80° and altitude of about 1100km, the period taken for one complete regression cycle is one year. Consequently, it is possible to place a satellite into a near-Earth orbit where it would remain continuously in sunlight. If the orbit is eccentric then the LINE OF APSIDES (joining perigee and apogee: the points on the orbit nearest and furthest from the Earth, respectively) will rotate completely in several hundreds of orbits. Other perturbing forces are due to drag from the residual atmosphere (which is largely responsible for the finite lifetime of the orbits of near-Earth satellites), solar radiation pressure, magnetic torques from the Earth’s magnetic field and the gravitational influences of the Sun and Moon.
At least two impulses must be delivered to a satellite to place it into a suitable orbit that does not intersect with the ground.The first impulse, usually applied in a vertical direction, places the object into a repetitive elliptical orbit with the Earth’s centre at one focus. The second impulse, perhaps in a horizontal direction at apogee, is of such a magnitude as to match the requirements of the desired final orbit. In general, the impulses are delivered over periods of several minutes by rocket engines, but the principle is much the same.
Rocket engines operate on the reaction produced when gas escapes through a hole from an otherwise closed container. An untied balloon which is released flies about because of this effect. The force on the motor itself is due to the rate of change of momentum of the gas. This THRUST is just the mass-loss rate of gas multiplied by the gas velocity. The product of a force and the time for which it acts is known as its IMPULSE, and clearly the larger the impulse, the larger- will be its effect on the final velocity oi the rocket. A useful concept for rocket propellants is that of the SPECIFIC IMPULSE, which is the total impulse on the rocket produced per unit mass of propellant consumed. It is equal to e exhaust velocity of the gases from the rocket engine when operated in a vacuum. Typical specific impulses from chemical propellants lie in the range of 1-5 km gr1. In order that the rocket may leave the ground, the thrust exerted by its motors must exceed the weight of the rocket and all its fuel. From our definition of thrust, and the above range of exhaust velocities, we see that the launch of a 1000-tonne weight rocket requires a fuel consumption of at least several tonnes per second. If the thrust only just overcomes the weight, as is usually the case, then the rocket acceleration is initially small. This prevents damage to pay load components as well as minimizing air drag, which is proportional to the square of the velocity and to the air density.
The final rocket velocity depends upon the MASS RATIO of initial to final rocket mass. This mass ratio exceeds unity because of the amount of propellent consumed and redundant fuel tanks ejected. Owing to the more continuous thrust operating in a rocket, as compared with the firing of a gun, the actual value of the final | velocity is given by the product of the exhaust velocity and the natural logarithm of mass ratio. The mass ratio must thus exceed 2.718 if the final velocity is to exceed the exhaust velocity, which as we have outlined, is between 1 and 5 kms-1 . Final velocities of 7kms-1 and above are required for Earth launch of satellites and probes; hence a large mass ratio and enormous rockets are necessary. Lift-off from the Moon into lunar orbit requires a final velocity of 2-3 km s”1; this is achievable with a high specific impulse and low mass ratio such as used in the Apollo lunar excursion module.
The specific impulse of a propellant is roughly equal to the speed of sound in the gas produced. This depends upon the square root of the ratio of gas temperature to mean molecular weight: high temperatures and low molecular weights are therefore necessary. Chemical rockets derive heat from combustion of the propellant, which may be hydrogen or kerosene as a fuel and oxidizer. Liquid propellants (hydrogen and oxygen would be stored as liquids) the most useful for large rockets, but solid fuel rockets are still common use. Usually, both a fuel and oxidizer are carried separately and mixed before combining, but some substances such as HYDRAZINE (N2H4) decompose in the presence of a catalyst to produce hot gases without combustion. The type of propellant chosen depends upon the conditions applying; solid-fuel motors are often used as boosters, liquid propellants for main engines, and hydrazine for mid-course manoeuvres owing to its ease of storage. Higher specific impulse values are obtained by increasing the exhaust velocity. Monatomic hydrogen recombining to form molecular hydrogen could yield specific impulses of 15000kms-1, but means have yet to be devised for storing such material. Nuclear reactors could, for example, be used to heat hydrogen to very high temperatures, or charged particles can be electrostatically accelerated in so-called ION MOTORS. The ultimate is the PHOTON ROCKET, the exhaust velocity of which is the speed of light. The energy requirements for such a device are prohibitive at the present. Solar radiation pressure may eventually be used to sail between the planets but in the following discussion we restrict ourselves to simple ballistic trajectories produced by relatively brief impulses. It is unlikely that any¬thing other than ehemieal rockets will be used for Earth launches in the near future.
The general technique for sending space probes out to the Moon and planets relies on injection of the probe into a suitable trajectory from an Earth orbit. The magnitude and direction of the impulse are chosen such that the probe follows an elliptical orbit that intersects with that of the desired planet. The timing (LAUNCH WINDOW) is chosen so that the planet and probe arrive simultaneously at the intersection of their orbits. Least energy is required if the probe’s orbit is an ellipse of perihelion and aphelion distances equal to the radii of the Earth and planet’s orbits. This is the HOHMANN TRANSFER ELLIPSE which takes approximately 145 days from Earth to Venus, and 260 days to Mars. Shortening these times by any significant extent enormously increases the energy requirements, and hence size of launch vehicle. Time is not usually the critical quantity in interplanetary missions, and they are usually optimized for maximum payload weight.
A further impulse must be applied to a space probe if it is required to orbit the planet. Such an impulse is usually produced by rocket motors, but a gravitational interaction with a planetary moon (if it has any) may suffice. This may be a very useful technique for orbiters of Jupiter or the other giant planets with relatively massive moons. The spacecraft orbit can be changed by a gravitational encounter with a massive body, even though it need not actually contact the surface – which would produce a dramatic change! Gravitational encounters with the giant planets them¬selves, or Venus, have been used to fling spacecraft on out to Saturn and beyond, and in to Mercury. Similar perturbations do, of course, change the orbits of comets. The extra energy is taken from the orbital angular momentum of the planet, which is changed by an infinitesimal amount. This technique of GRAVITY ASSIST is the key to extended exploration of the Solar System from quite modest launch vehicles. It is, for example, possible to use an encounter with Jupiter to fling a spacecraft into the Sun or perhaps more usefully into a near approach of a few solar radii. This is not yet possible by directly launching a spacecraft at the Sun, for it would have to lose the 30kms-1 orbital velocity of the Earth about the Sun. Present launchers for planetary missions can take probes directly only to Venus, Mars and Jupiter. Such celestial billiards can be used to send spacecraft from one planet to another. As might be expected, the launch windows are short, and the chance to visit most of the outer planets (including Pluto) in one mission starting about 1979 is going to be missed. The occasion will not recur for more than one hundred years, although several separate missions can perform this task at later dates. The end of the century may see spacecraft making repeated and never-ending close approaches within the Jovian satellite system, and Jupiter-flung probes exploring fast-moving comets as they swing near the Sun.
Spacecraft have to be most carefully constructed to withstand the rigours of space. The effects of high vacuum are considerable, although now well known. Any gases absorbed into surfaces leak out, causing movable, joints to stick and problems with electronic components. The continual bombardment by cosmic radiation, in number over 10 times more intense (and far more so in irradiation belt*) than at the Earth’s surface, gradually destroys electronic system8, and provides a steady unwelcome background to photon counting devices. Micrometeoroid dust adheres to surfaces. Temperature control is not trivial and is combat/ted by the gold-plated foil and painted chequer patterns common on spacecraft. Power may be generated by solar cells, or by radio-isotope generators for missions to the outer planets. Astronomical experiments require some form of stabilization and altitude sensing. The, launch itself imposes considerable constraints on spacecraft, volume, as well as mass, and vibration and stress forces may destroy delicate component”, designed for a future, weightless environment. Data usually ban to be returned to Earth, and this necessitates some form of communication system with aerials which may require Earth pointing. The: design in usually the result of trade-offs be¬tween scientific payload and necessary spacecraft structure, weight, volume and power requirements.