One might think that a viable means of returning an Earth-orbiting spacecraft to our planet's surface could be effectively done by simply firing the rockets in reverse. But if you consult the Rocket Equation in Chapter 3, you will see that such an approach simply could not work.
In the example given in Chapter 3, the exhaust velocity of a near-optimum chemical rocket is 4.55 kilometers per second, and the velocity increment required to achieve minimal Earth orbit is about 7.45 kilometers per second. Substitution in the Rocket Equation reveals that a mass ratio of 5.14 is required to achieve a minimal Earth orbit. About 80% of the spacecraft's liftoff mass is fuel and oxidizer.
Now let's assume that enough fuel is required so that the rocket can exactly cancel its orbital velocity relative to Earth's surface. The velocity increment is now 14.90 kilometers per second. Solution of the Rocket Equation reveals that the minimum required mass ratio is now about 26.4. In this case, more than 95% of the rocket's lift-off mass consists of oxidizer and fuel.
If such large mass ratios were the only way to achieve earth-return, it is very doubtful if large, people-carrying spacecraft would ever have orbited the Earth, let alone ventured to the Moon. But our planet's atmosphere provides another solution.
Astronomers had actually been aware of the velocity-braking properties of Earth's atmosphere for centuries. Every time Earth intersects a comet's solar orbit, it encounters tiny grains of dust and ice from the comet's tail. As these grains approach our planet, they decelerate as they collide with air molecules in Earth's upper atmosphere. During these encounters, the comet grains' energy of motion is converted to heat. The grains begin to glow visibly as they streak across the sky and most of them evaporate at altitudes of 50 kilometers or so above Earth's surface.
The first terrestrial to enter orbit was the dog Laika, on board Sputnik 2 in November 1957. Because the problems of reentry had not been addressed at this early date, Laika became the first space casualty. She died in orbit after about one week in space.
The safe return of astronauts and cosmonauts from orbital missions was not the only driver to reentry research. Early in the Space Age, both American and Soviet mission planners realized the utility of returning high-resolution film to Earth in capsules released from spy satellites. Robotic reentry has also been used in a wide variety of scientific missions.
Both space powers arrived at the same general approach for returning astronauts or cosmonauts from orbit. At the conclusion of the flight, a space capsule is oriented to enable a small retrorocket to be fired in a direction opposite to the spacecraft's velocity. The capsule then descends until it encounters the outer fringes of Earth's atmosphere. As the craft descends into denser air, more and more of its energy of motion is converted into heat through friction between it and the molecules of air.
Spacecraft reentry is demanding in terms of trajectory. If a vehicle enters the atmosphere too steeply, it may burn up. If the reentry angle is too shallow the spacecraft may "surf' along atmospheric layers and skip back into space.
The aft end of the space capsule is coated with a special ablative shield. As friction with atmospheric molecules raises the temperature of the reentry shield to thousands of degrees Celsius, bits of the shield flake off or ablate. Much of the heat generated during reentry is carried away by the evaporated shield material, much to the relief of the crew!
At an altitude of perhaps 30 kilometers, the ship's velocity is low enough and the atmospheric is thick enough to enable aerodynamic surfaces and parachutes to be used for further deceleration.
Some contemporary spacecraft, notably the American space shuttle, are coated with temperature-resistant tiles rather than a solid shield, but as many of the shuttle's tiles must be replaced after each mission, this is a time-consuming process that contributes to the high cost of space-shuttle missions.
Although some Russian and American crews have died during reentry, shields or tiles have an otherwise perfect safety record during peopled space flights. The April 1967 the reentry death of Vladimir Komarov on board Soyuz 1 was due to failures in the attitude control system that caused the spacecraft to spin so violently that the parachutes could not deploy. A few years later, the crew of Soyuz 11 performed a flawless reentry—but the crew was found to be dead in the capsule because of a faulty air seal. The more recent loss of space shuttle Columbia was due to structural damage occurring when ice and foam flaked off the external tank during the ascent to orbit.
Astronauts and cosmonauts do not easily relax during their wild return to Earth. It's a bumpy ride and the realization that only a thin ablative shield or tile layer separates them from ionized gases at temperatures of thousands of degrees cannot be good for digestion. The meteor-like trajectories of returning spacecraft are impressive displays, attracting the attention of hordes of amateur astronomers.
A different form of "green" space technology saw its first utilization during the 1970s when NASA launched the first probes toward the outer planets and stars. These were Pioneers 10 and 11 and Voyagers 1 and 2. These craft flew past all of the giant planets of the solar system—-Jupiter, Saturn, Uranus, and Neptune—and have continued to radio back data from the edge of interstellar space. And they could not have succeeded without application of a space-propulsion technique that takes advantage of the environments of these giant worlds—planetary gravity assists.
As mission planners began to consider sending probes to the outer solar system, it was soon realized that conventional thinking simply would not do. Let's say we wish to launch a rocket to Jupiter along an energy-efficient trajectory. One approach is to fly along a so-called Hohmann transfer. In such a trajectory, the part of the elliptical transfer orbit closest to the Sun (the perihelion) is tangent to Earth's solar orbit. The part of the transfer orbit closest to the destination planet (the aphelion) is tangent to the solar orbit of the destination world. A spacecraft traveling along a Hohmann transfer to Jupiter must depart the Earth with an excess velocity of 8.57 kilometers per second relative to the Earth (this is called the "hyperbolic excess velocity''). The duration of the voyage is about 2.74 years. If we wish to use the same approach to visit Saturn, the spacecraft must depart Earth with a hyperbolic excess velocity of about 10 kilometers per second and the flight duration is about 6 years. To perform a Hohmann-transfer flyby ofNeptune, the mission planners must be patient indeed—the voyage duration would be approximately 46 years.
Fortunately for humanity's deep-space aspirations, there is another approach. If a spacecraft flies by a giant planet along just the right path, it can "borrow" some of the giant world's orbital energy. The spacecraft departs its encounter with the giant world at a higher velocity relative to the Sun. Thanks to the mass difference between the two objects (the small spacecraft and the massive planet), the planet's heliocentric velocity is reduced by an inconsequential amount.
This sounds like magic, but it is actually a consequence of a basic principle of Newtonian physics, the Conservation of Angular Momentum.
Everybody who has played a game ofbilliards or pool has experienced a related physical principle, the Conservation of Linear Momentum.
The linear momentum of an object is defined as the product of the object's mass (M) and its velocity (V). If you consider an isolated system, say a cue ball (c) and a billiard ball (b), the total linear momentum of the system is Mc Vc + Mb Vb. In any interaction between the two balls, you can rearrange their individual linear momentum. But the total linear momentum of the two-ball system remains constant.
Let's say that you are taking careful aim on a billiard ball to strike it head-on with the cue ball in order to sink the billiard ball in a pocket. You first impart linear momentum to the cue pool with the pool stick. Upon impact, the linear momentum of the cue ball is transferred to the billiard ball. The cue ball becomes stationary after the collision and the billiard ball moves off until it enters the pocket.
The angular momentum of a planet of mass M in a circular orbit a distance R from the center of the Sun is expressed as MVR, where V is the planet's solar-orbital velocity. The total angular momentum of a system is also conserved. If you watch a figure-skater or ballerina in a fast spin, she can slow down by stretching out her arms. Since the distance R of her hands from the center of curvature increases in this manner, her velocity slows.
In a three-body system composed of a spacecraft and planet both orbiting the Sun, the individual angular momentum of the spacecraft and the planet can be rearranged, but the total angular momentum of the system is constant. During an unpowered gravity-assist maneuver, the spacecraft departs the planet's gravitational influence at the same speed relative to the planet that it had during its approach to that world. The spacecraft's trajectory direction, however, is altered by the gravity-assist maneuver, as is its velocity relative to the Sun.
A gravity-assisted mission to an outer-solar-system or extrasolar destination might proceed as follows. The spacecraft is inserted into a Jupiter-bound trajectory after leaving the Earth. If it flies by the giant planet in just the right manner (as illustrated in Figure 4.1), some of Jupiter's angular momentum can be transferred to the spacecraft. If the spacecraft's Sun-centered trajectory is deflected during the encounter by 90 degrees, the spacecraft's velocity relative to the Sun is increased by Jupiter's Sun-orbital velocity, about 13 kilometers per second. Jupiter's angular momentum decreases by an immeasurably small amount during the encounter.
Many spacecraft, including the Pioneers, Voyagers, Ulysees, and Cassini/Huygens have used flybys of Jupiter to alter their trajectories. Pioneer 11 and the Voyagers have also performed close flybys of Saturn. One famous probe—Voyager 2—performed close flybys of all of the solar system's giant planets—Jupiter, Saturn, Uranus, and Neptune.
To optimize a gravity-assist maneuver, a spacecraft should pass as close to its target planet as possible, with a low velocity relative to that target
planet. Voyager 2, the probe that flew past all the solar system's giant worlds, was on a trajectory that was designed to optimize the studies of these giant worlds, not one attempting to achieve a maximum solarsystem exit velocity. As a result, its sister ship Voyager 1 is slightly faster, cruising through the fringes of our solar system at about 17 kilometers per second. This is a blistering velocity from a human's point of view— Voyager 1 could traverse the length of Manhattan Island in about one second, but in the cosmic scheme of things, the Voyagers crawl along at a snail's pace. If they were directed toward our Sun's nearest stellar neighbor (which, however, is not the case), the Voyagers would require more than 70,000 years to complete the interstellar transit.
Certain missions have utilized gravity assists from planets smaller than the giants. The Galileo mission to Jupiter was launched using a booster that was too small to reach the giant world directly. As a consequence, this probe spent several years in the inner solar system altering its trajectory with multiple flybys of Venus and the Earth.
Gravity-assist maneuvers to date have been basically unpowered, carefully tailored, flybys of solar-system worlds. But there is another, theoretical, approach that can improve the efficiency of flyby maneuvers.
The gravity field of a planet or star can act as a force multiplier if an impulsive maneuver is performed while a spacecraft is near its closest approach to that celestial object. In other words, a greater velocity increment is possible if the spacecraft is equipped with a rocket that can be fired during the gravity-assist maneuver. Also, firing this rocket deep within a planet's or a star's gravity well produces a greater change in velocity than if the rocket is fired in gravity-free deep space.
Consider, for example, a probe that approaches the Sun within 1.5 million kilometers along a parabolic solar orbit. If a rocket is fired when the spacecraft is closest to the Sun to produce a velocity increase of 2 kilometers per second, the probe will depart the solar system at 41 kilometers per second—about three times the velocity of the Voyager probes!
Spacecraft dynamics using planetary gravitational fields is an evolving discipline that is far from exhausted. Advanced computational techniques have been utilized by mathematicians—notably Edward Belbruno at Princeton University—to analyze a family of low-energy trajectories in the Earth-Moon system. These "weak-stability boundary'' trajectories trade increased travel time for reduced thrust requirements. These techniques were first applied in 1991 to transfer the japanese Hiten probe from Earth orbit to the vicinity of the Moon.
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