Certain kinds of space missions are particularly interesting because they can, with reasonable certainty, be accomplished with equipments and techniques available now or in the next few years. These are briefly described in the following sections.
The projection velocity required to propel a ballistic missile to various ranges is shown in figure 1. It is to be noted that there is no limit to achievable missile range except the finite circumference of the Earth.
The first scientific use of rockets was for vertical ascents, or "soundings" of the atmosphere. The projection velocity required to reach various altitudes, as well as total time of flights is shown in figure 2. This figure also shows the net velocity capability required to establish satellites in circular orbits at various altitudes.
To establish a vehicle in a satellite orbit around the Earth, it is generally necessary to have two powered phases, separated by an interval of coasting flight.. The first powered phase is like that of a ballistic
missile. After the vehicle coasts to the maximum altitude of its elliptical ascent path (the apogee), another powered phase must give the vehicle enough speed to keep it in orbit (fig. 3). The number of powered stages required in each of these two phases is determined by the design of the vehicle. For example, the Army's Explorer satellites were established by a single booster-the Jupiter C-firing during the first phase followed by three stages fired in succession at orbital altitude. The Vanguard satellite, on the other hand, is programmed to use 2 stages during the initial boost phase, and only 1 stage to provide the velocity increment at orbital altitude.
If the designer so chooses, a satellite could also be established using a continuously powered ascent trajectory-that is, one in which the coasting phase vanishes.
The main orbit features of Earth satellites are the period of revolution and the orbital velocity. These vary according to the satellite's mean distance from the center of the Earth (fig. 4).
At an altitude of about 22,000 miles the period of the satellite is exactly 1 day and the orbital velocity is about 10,000 feet per second. If a vehicle were established in an equatorial orbit at this altitude, rotating eastward, it would remain fixed over a point on the surface of the earth.
The equatorial bulge of the earth and other irregularities cause disturbances of satellite orbits over long periods of time; in particular, detailed changes in the orientation of the orbit in space. 1 These disturbances can be exploited in some applications. For example, if a satellite is established in an orbit inclined about 83° from the Equator and moving in a westerly direction, the Earth's bulge will cause the orbit plane to move in such a way that it remains fixed relative to the Sun as the Earth moves in its orbit.
An interesting extension of the basic method of launching a satellite is to provide the vehicle with an additional powered stage for use in so-called "kick-in-the-apogee" type of maneuver (fig. 5). Assume for example, that a given booster vehicle is capable of carrying a satellite to an altitude of 200 miles and that the satellite's final burnout velocity can be made greater than the circular orbital velocity corresponding to that altitude. The resulting satellite orbit will, therefore, have an apogee altitude greater than the initial 200-mile altitude-say, 500 miles as an example. If the additional powered stage, correctly oriented, is fired at the 500-mile apogee point the perigee (minimum) altitude of the new satellite orbit will be raised so that a final orbit can be achieved that is not limited by the projection altitude limit of the basic booster rocket.
An extra rocket stage can also be used to make corrections or modifications to the altitude or eccentricity of a satellite orbit to tailor it for a specific application. Additional rockets can also be used to change the inclination of the orbital plane relative to the Earth's Equator.
1 Kalensher, B. E., Equations of Motion of a Missile and a Satellite for an Oblate- Spheroidal Rotating Earth. Jet Propulsion Laboratory, California Institute of Technology memorandum No. 20-142, April 12, 1957.
Satellites can fairly easily be made to survive the heating encountered in returning to the Earth after natural orbit decay due to air drag. All that a satellite like Vanguard would need would be a shell of a high-temperature alloy such as is used in jet-engine turbine. 2
Using reentry techniques derived from ballistic missile developments, it should be possible to bring satellite payloads back to the Earth for study. In fact, controlled recovery of biomedical and other experiments from satellite orbits is planned to start early in 1959 as part of Project Discoverer. 3
To eject an object from a satellite orbit onto a trajectory that intersects the Earth's surface, a rocket is needed to provide thrust at the proper time and in the proper direction. The minimum velocity that
2 Gazley, C, Jr., and D. J. Masson, A Recoverable Scientific Satellite, The RAND Corp., Paper P-958, October 6,1956.
3 Department of Defense, minutes of press conference held by Mr. Roy W. Johnson, Director. ARPA, December 3, 1958, 11 a.m.
will accomplish recovery is shown in figure 6 for a range of satellite altitudes. The required ejection velocity is in no case as much as
5,000 feet per second. Vehicle reentry velocities are also shown in figure 6.
If the satellite payload is to be returned to a specific recovery area, the satellite must descend fairly steeply. Such descents require greater ejection velocity than the minimum amounts shown in figure 6.
The ejection velocity required to bring down a payload from a 300-mile orbit is plotted in figure 7 as a function of the descent range - the distance over the ground covered by the payload from the ejection to impact. The ejection velocity grows rapidly as descent range becomes less.
The sensitivity of impact location to an error in control of ejection velocity is also plotted in figure 7. Accuracy of recovery improves as the descent range becomes less. For example, at a descent range of 5,500 nautical miles an impact miss of about 4 nautical miles will be produced by an error of 1 foot per second in ejection velocity. Other sources of error, of course, also enter into the situation, particularly control of direction of ejection velocity.
The minimum velocity that will cause a vehicle to reach the Moon is only slightly less than the local escape velocity from the Earth, which at an altitude of 350 statute miles is 34,800 feet per second. An altitude of about 350 statute miles is a reasonably representative altitude at which to start free flight, and it will be assumed to apply throughout as a standard reference case. The powered-flight trajectory up to this altitude is not of particular interest in this discussion.
The free-flight portion of a sample trajectory which terminates on the Moon is shown in figure 8. The trajectory is plotted in such a way that it appears about as it would to an observer at the North Pole. The elliptical nature of the trajectory over about the first 2 days of flight is evident. The effect of the Moon's gravitational attraction becomes large only during the last half day of the flight, as it causes curvature of the terminal portion of the path, leading to an impact on the surface of the Moon.
The same, trajectory is shown in figure 9 as it would appear to an observer on the moon. 4
The variation of the impact point on the Moon caused by errors in the initial,velocity is shown in figure 10. The central curve, defined by an initial velocity of 35,000 feet per second, corresponds to the trajectory shown previously in figure 8. For a velocity that is 35 feet per second too low the impact point moves to the western limb of the Moon; for 50 feet per second too much velocity it moves to a point beyond the eastern limb. Some of the possible impact points would not be visible from the Earth. It can be seen that errors of -35 to +50 feet per second are allowable around this design Point for simple lunar impact trajectories. This tolerance is critically dependent upon the nominal initial velocity selected.
4 Lieske, H. A., Lunar Instrument Carrier-Trajectory Studies, The RAND Corp., Research Memorandum RM-1728, June 4, 1956.
Figure 11 presents the "hit band" showing the allowable variation of combinations of initial velocity and path angle for trajectories which end somewhere on the Moon. This "hit band" corresponds to a specific initial trajectory position angle relative to the Moon and altitude above the surface of the Earth.
Initial velocity-Earth angle combinations lying along the left edge of the shaded band define trajectories which are tangent to the Moon near the eastern limb, while combinations along the right-hand edge of the band define trajectories which are tangent near the west limb of the Moon.
A curve defining the locus of trajectories which are normal to the lunar surface lies approximately midway between the solid lines.
The terminal trajectory variation shown previously in figure 10 corresponds to a vertical slice through the lower portion of the hit band.
Since the slope of the hit band varies from nearly horizontal (variation in path angle) to nearly vertical (variation in velocity), the relative values of the tolerances in velocity and path angle will vary as a function of the magnitude of the initial velocity.
We can define the total tolerances in either velocity or path angles as the allowable increment in the parameter which causes the impact point to shift from one limb of the Moon to the other. Plotting the tolerances as a function of the initial velocity which corresponds to an impact normal to the surface of the Moon gives the curves shown in figure 12. At near-minimum initial velocities the allowable path angle tolerance is about 41/2°, but decreases rapidly to a value of approximately one-half degree for higher velocities.
The velocity tolerance rises gradually to a value of about 300 feet per second as the initial velocity is increased to a value of about 35,100 feet per second. The notation (W-E) indicates that the impact points shift from the west limb of the Moon to the east limb. Above an initial velocity of about 35,500 feet per-second the velocity tolerance decreases gradually. In this portion of the curve the impacts move from the east limb to the west limb. The portion of the curve labeled (W-E-W) corresponds to the nearly vertical portion of the hit band of figure 11. In this region of the curve, the lunar impact point shifts from the west limb to a point near the east limb and then back to the west limb. The tolerance of 600 feet per second occurs for trajectories which are defined by a path angle corresponding to the left-hand edge of the "hit band." Therefore, nominal trajectories which allow these extremely large initial velocity tolerances are extremely sensitive to the exact value of the initial path angle.
The variation of initial velocity and path angle tolerances shown in figure 12 is representative of transit trajectories which are defined by relatively low initial path angles. As the initial path angle of the free-flight trajectory approaches 90° (fired from an initial position which "leads" the Moon), the reflex portion of the "hit band" in figure 11 moves to extremely high initial velocities so that the velocity of tolerance curve rises more gradually than shown in figure 12. 5
5 Lieske, H. A., Lunar Trajectory Studies, The RAND Corp., Paper P-1293, February 26, 1958.
In general, therefore, it is possible to "tailor" the nominal transit trajectory design point (and the corresponding initial tolerances) to accommodate particular accuracy capabilities of the ascent guidance System.
The transit time for free-flight trajectories from the Earth to the Moon is also strongly dependent upon the magnitude of the initial velocity, as shown in figure 13. The longest flight time, 5.5 days, corresponds to the minimum-velocity trajectory. If the initial velocity is increased by only 1 percent, the transit time is decreased to a value of 2 days. The flight time planned for the Air Force Pioneer Moon shots was about 2.6 days, while that planned for the Army Juno II Moon shots was only 1.4 days. From figure 13 it can be seen that this sharp difference in flight time involves a velocity difference of only about 2.5 percent.
Impact on the Moon might be signaled to Earth observers by detonating about 10 pounds of standard illuminant powder. 6
A vehicle can be fired on a circumlunar trajectory which returns to the vicinity of the Earth with no further propulsion stage if the initial velocity at the Earth is less than the local escape velocity. 7 The vehicle must be launched so that it will intersect the Moon's orbit at a point ahead of the Moon, in order to be swung around by the Moon's field for return.
The distance of closest approach to the Moon will vary widely for trajectories based on different initial conditions, and this distance may vary from a grazing passage to as much as 80,000 miles.
The time of closest approach to the Moon is primarily a function of the initial velocity at the Earth, as shown in figure 13, but is also affected slightly by the distance of closest approach to the Moon. The position, on the lunar surface, below the point of closest passage is also variable. 8
6 Dole, S. H., Visual Detection of Light Sources on or Near the Moon, The RAND Corp. Research Memorandum RM-1900, May 24,1957.
7 Lieske, H. A., Circumlunar Trajectory Studies, The RAND Corp., Paper P-1441, June 25, 1958.
8 See footnote 7.
Typical examples of the two major classes of free-flight circumlunar trajectories are shown in figures 14 and 15. A typical low-velocity trajectory is given in figure 14-an example of the "figure eight" orbit often referred to in the popular literature. The velocity of the vehicle in the vicinity of the Moon is relatively low (but greater than lunar escape velocity), so that the Moon's motion and gravitational attraction causes the trajectory to be strongly perturbed. In this sketch, the vehicle passes above the Earth on its return. Figure 15 shows a typical trajectory defined by a somewhat higher initial velocity. In this example, the vehicle's velocity in the vicinity of the Moon is somewhat higher, so that the Moon's perturbing influence is less pronounced. The vehicle continues to some distance beyond the Moon's orbit before returning to the vicinity of the Earth. It passes below the Earth on return. Free-flight trajectories defined by velocities between those of figures 14 and 15 will return to impact somewhere on the Earth. The distance of closest approach to the Moon in both these cases is about 3,000 miles.
The total flight time from start to return to the Earth can vary from a minimum of about 6 days to as much as a month, depending upon the initial velocity. A small change in initial velocity can produce a very great change in total flight time. This is a matter of considerable practical importance, since points on the Earth are moving rapidly due to the rotation of the Earth. Thus, for example, a vehicle returning from a 10-day circumlunar trip intended for recovery at, say Edwards Air Force Base, will find the base 800 miles away if it is just 1 hour off schedule.
This extreme trajectory sensitivity for a completely unpowered vehicle can, of course, be reduced by providing it with the ability to make one or more corrective velocity changes during transit.
A circumlunar flight with physical recovery on Earth would be suitable for such applications as acquiring high-quality photographs of the Moon's hidden side. 9 Reentry design techniques for such a return are within the capabilities of current technology. 10 11
9 Davies, M. E., A Photographic System for Close-Up Lunar Exploration, The RAND Corp., RM-2183, May 23, 1958.
10 Gazley, C., Jr., and D. J. Masson, Recovery of Circum-Lunar Instrument Carrier, American Rocket Society, preprint No. 488-57, October 1957.
11 Gazley, C., Jr., Deceleration and Heating of a Body Entering a Planetary Atmosphere From Space, Vistas In Astronautics, Pergamon Press, 1958.
Moon to escape
The Moon's orbital motion and gravitational field can be used to accelerate a vehicle out of the Earth-Moon system and into an independent orbit around the Sun.
A typical trajectory which is changed from an elliptical to a hyperbolic orbit as a result of the Moon's action is shown in figure 16. The lunar-miss distance for this particular trajectory is about 600 miles, and the resulting effective initial-velocity increase is approximately 400 feet per second. The maximum possible effective increase by the Moon is about 500 feet per second.
Landing a vehicle on the Moon requires an additional rocket stage to decelerate it to a safe landing speed. The approach velocity at the Moon is a function of the initial velocity at the Earth, but is never less than about 8,000 feet per second. Control of the direction of braking rocket thrust for landing introduces a need for control of vehicle orientation. The signal for firing the retrorocket must either be sent from the Earth or generated in the vehicle itself (for example, by measurement of the lunar altitude) .
The transit trajectory for a lunar landing will be generally similar to that for a lunar impact discussed above and shown in figure 8.
Satellites of the Moon can be established if provision is made for a velocity reduction in the vicinity of the Moon. 12
12 Buchheim, R. W., Artificial Satellites of the Moon, The RAND Corp., Research Memorandum RM-1941, June 14, 1956.
A transit trajectory for a lunar satellite is shown in figure 17. At a predetermined distance from the moon-near the point of closest approach-the vehicle's velocity must be reduced to a value which will allow the Moon to capture the vehicle as a satellite. A representative value for this velocity change would be of the order of 4,000 feet per second-about half the value required for a lunar landing. If the velocity increment is added at the point of closest approach of the transit trajectory shown in figure 17, the initial portion of the lunar satellite will be as shown in figure 18.
A lunar satellite was the flight objective of the pioneer shots.
Launching of a vehicle from the Moon to return to the Earth will be of considerable interest in the future. 13 The initial velocity at the Moon would typically be around 10,000-15,000 feet per second. As in the case of Earth-to-Moon trajectories, the transit time is a function of the initial velocity. The variation is more gradual, however. An initial velocity difference of about 3,000 feet per second at the Moon corresponds to a change in transit time from a value of about 1.5 to about 2.5 days.
Merely hitting the Earth from the Moon is considerably easier than hitting the Moon from the Earth, since the Earth is larger and its gravitational field is much stronger. Typical values of the initial tolerances at the Moon might be plus or minus 1,500 feet per second in velocity and plus or minus 5° in path angle. The requirements for hitting a given area on the Earth however, are considerably more severe-mainly because the Earth's rotation on its axis causes the "target" to move. Thus, very accurate control of initial velocity at the Moon is required mainly to closely fix the flight time.
One of the special solutions to the equations of motion in the classical "Problem of Three Bodies" predicts the existence of 5 singular points in the vicinity of the 2 massive bodies at which a vehicle can be held stationary without application of thrust." The locations of
13 Buchhelm R. W., and H. A. Lieske. Lunar Flight Dynamics The RAND Corp. paper P-1453, August 6, 1958.
these points, known as "centers of Libration," are indicated in figure 19. Three lie on the line joining the Earth and the Moon, while the other two form equilateral triangles with the Earth and Moon.
Motion in the vicinity of the straight-line points is unstable; that is any small displacement from the exact point will result in the particle moving indefinitely far away.
Motion of a particle in the vicinity of the equilateral triangle points, however, is stable-at least to disturbances arising from within the system-so a vehicle near one of these points could be made to "float" in space as a "space buoy." 14 The "Trojan" asteroids, which oscillate in the vicinity of such points relative to the Sun-Jupiter system, tend to check this theory. 15
If vehicles containing the appropriate equipment could be established at, or near, each of these equilateral triangle points relative to the Earth-Moon system, they could provide a baseline which is about
14 Buchhelm, R. W., Motion of a Small Body In Earth-Moon Space, The RAND Corp., Research Memorandum RM-1726, June 4,1956.
15 Baker, R. H., Astronomy, D. Van Nostrand Co., New York, 1950.
400,000 miles long for such uses as tracking vehicles on interplanetary flights. The displacement of these "space buoys" by the Sun's net gravitational attraction would have to be investigated. Also, if the bodies were low-density structures, the acceleration due to solar radiation pressure would cause displacements.
A small manmade body in orbit around the Sun would be properly termed an artificial asteroid. Such vehicles, carrying instruments, can be established by simply launching them at any speed greater than escape velocity, regardless of direction. This fact has been recognized in laying out the plan for the Army lunar probes, which will be launched with enough speed to take up an artificial asteroid orbit if they miss the Moon.
Instrumented asteroids could probe the space environment around the Sun. Also, if made optically observable-by carrying large reflecting balloons-or fitted with transponders for radar range measurements, such vehicles could be used just as natural asteroids now are in obtaining a fundamental measurement of the length of the astronomical unit (distance from Earth to Sun).
A vehicle brought near one of the planets could be placed in orbit around the planet in much the same manner as was discussed in connection with satellites of the Moon. Some form of terminal guidance would be required with propulsion to make it effective.
Manmade satellites for Mars and Venus should be achievable in a relatively few years. Mercury and Jupiter could be given satellites at a later date.
Landings on Venus and Mars
It should be possible, with provision of midcourse and/or terminal guidance, to land some hundreds of pounds of instruments on the surfaces of Venus and Mars with basic rockets now in development.
Any flights in interplanetary space will require use of flight equipments with very long reliable life-a year or more in most cases. The actual achievement of interplanetary flight is critically dependent upon fulfilling this requirement.
No firm assessment can be made at this time of the extent to which manned vehicles can undertake many of these various kinds of flights (except, of course, to cull out obviously unusable types like unchecked impact on the Moon). Performance calculations alone would indicate feasibility of rather extensive flights, like circumlunar flights and flights to even greater distances from the Earth. However, firm judgment on these kinds of possibilities must await results of further experimentation to determine detailed requirements of manned flight, as is planned in the X-15 program, the NASA manned capsule satellite program, 16 and the Dyna-Soar program.
16 Industry Invited To Submit Space Capsule Design Proposal, National Aeronautics and Space Administration release, November 7, 1958.
Nature of the problem
The payload that can be carried to any target region with a given launching rocket depends to a large extent upon the nature of the trajectory followed. Some relative positions of the Earth and a target body allow transit between them on favorable trajectories, while other positions impose trajectories that seriously tax rocket performance. Since the positions of bodies in the solar system are continuously changing with time, the passage of time continuously changes the trajectory requirements and, hence, the payload capability realizable with a given kind of equipment. Therefore, there are literally "good days" and "bad days" for every kind of space launching-in fact, with limited rocket performance, there are some days that are simply "no-go days." Since the position of the launch point on Earth is moving with Earth's daily rotation, there are also "good" times of day and 'bad" times of day. A launching arranged for a given time on a given day must take place on schedule or not at all, unless a large sacrifice in payload is made.
Generally speaking, a rocket system displays its best payload capability when fired over a rather closely circumscribed powered-flight trajectory; and any substantial departure from this trajectory will greatly reduce its payload. For large liquid rockets on lunar flights, the powered-flight trajectory terminates with the rocket moving nearly horizontally with respect to the Earth. The trajectory has a certain total length determined by the duration of the propulsion phase. Given these fairly inflexible powered-flight conditions, there is a corresponding limited range of positions of the Moon that are reachable from a given launch site.
The shape of the powered trajectory determines the time of day of favorable launching-10 minutes is a fairly representative figure for the duration of this favorable period, which occurs at approximately daily intervals.
The plane of the free-flight trajectory from Earth to Moon is defined by three points: The center of the Earth, the center of the Moon, and the location of the launch point. The inclination of this plane to the Earth's Equator changes as the Moon moves around the Earth in its monthly journey. A rocket fired in this plane at the "best" time of the month will be aimed more nearly east than one fired at some other time. The more nearly east a rocket is fired, the more velocity it will pick up from the Earth's rotation, and the larger will be its payload.
Even at the most favorable time of month, a launching from a latitude greater than 28.5° will not be directed exactly east, since the Moon's orbit never tips any more than 28.5° from the Equator. However, this tip of the Moon's orbit varies over an 18.6-year period, and at the points of maximum inclination, a Moon launching can be made more nearly east than at other times. Thus, there are best times within this 18.6-year cycle.
The distance from Earth to Moon varies somewhat during the month, but this distance variation itself does not have a large influence on the choice of launching times.
In summary, then, there is a best time to shoot during a given day, a best day during a given month, and a best month once every 18.6 years. The influence of time of day on payload is very strong (strong enough to make the whole operation possible only at the best time); the influence of the time of month is less strong (not likely to be the difference between feasibility and infeasibility except with marginal systems); and the effect of the 18.6-year cycle is rather minor.
It is of interest to note that at present the Moon is near its least favorable inclination. It will reach its best inclination in 1969.
If visual reconnaissance of some portion of the Moon's surface is desired, then the phase of the Moon will dictate the time of month of launch, even though the unfavorable position of the Moon may cause a considerable reduction in payload weight. For example, if it is decided to photograph the far side of the Moon, then the lunar rocket should pass behind the moon during the time of new Moon, when the far side is illuminated.
Another consideration that may be important in the determination of launch time is any restrictions on the direction of launch available due to a need to pass over a guidance range or a need to avoid trajectories that could pass over population centers.
The free-flight trajectory of a vehicle fired from the Earth to another planet will generally be a section of an elliptical orbit around the Sun (fig. 20). Maximum payload will be carried if the vehicle traverses exactly half of this ellipse between perihelion (point closest to Sun) and aphelion (point farthest from Sun), so the start and end of the voyage lie directly across the Sun from one another. The payload
will be less if the vehicle must traverse either less than or more than half an ellipse.
The situation leading to maximum payload (or any payload at all in many cases) is only possible, of course, when the relative positions of Earth and the target planet are proper-a fairly rare occurrence except for the inner planets Venus and Mercury.
Figure 20 illustrates the situation for flights to Venus. The maximum-payload case, in which the vehicle travels over exactly half an ellipse (Venus in position 2), involves a flight time of about 4 months.The flight to Venus in position 1 takes less time, but requires greater initial velocity and therefore permits less payload for a given rocket. Flight to Venus in a position like position 3 takes more time and more initial velocity then a flight to position 2. Thus, flights to a position like position 3 are under the disadvantage of both long flight times and low payload, relative to the position 2 case. Flights to positions like 1 must also be conducted with lower net payload; however, the advantage of lower flight time may be more than enough to offset this
disability. For example, in manned flight the weight of stores necessary to sustain the crew will be less if flight time is less, so a short flight at lesser total payload at takeoff may actually arrive at the target planet with more usable payload.
|Earth to Mars
Earth to Venus
NOTE. - The increase in launch velocity required at times
beyond most favorable launch dates are indicated in figure 21.