Summary Session, 19 February 1957
Participants and Their Topics
Paul Herget (Panel Leader), Director, Cincinnati Observatory
Oberth, Ordnance Missile Laboratory, Redstone Arsenal
"A Satellite Attitude Control System"
Chief of Simulation, Glenn L. Martin Co., Baltimore, Md.
"Orbit Studies Using High Speed Digital Computers"
Fred L. Whipple,
Director, Smithsonian Astrophysical Observatory
"Orbital Accuracy and Ranges from Ground-Based Optical racking"
Samuel Herrick, Professor of Astronomy, University of California, Los
"Accurate Navigation of Intercontinental and Satellite Vehicles in the Earth's Gravitational Field"
Chief, Pre-Design and Systems Analysis, Convair-Astronautics
"Free and Powered Orbits in Cislunar Space"
Hans A. Lieske,
Head, Flight Mechanics Group, Rand Corporation, Santa Monica, California
"On the Accuracy Requirements for Trajectories in the Field of the Earth and the Moon"
Unlike some of the other panels, there wasn't what one might call unanimity of opinion amongst those who were invited to participate and who chose their own subjects. There was a rather wide variety of subjects, each of which is more or less independent of every other one.
The first paper was presented by Krafft Ehricke of Convair on "Free and Powered Orbits in Cislunar Space." He started out by defining cislunar space as this region of space between the earth and moon where neither the Earth nor Moon dominate the vehicle's orbit exclusively. In cislunar space there is a region where the perturbations by the earth (which are most severe when the vehicle is close to the earth and they become less severe as you move away) have diminished considerably, but the lunar perturbations have not yet begun to increase severely as you begin to approach the moon. This region is particularly important for both satellite orbits and also terminals of interplanetary paths. One of the applications of operations in cislunar space concerns the return from an interplanetary flight and of course the idea here is that you would like to use the minimum amount of capture energy. It turns out from his computations that you do this by arriving roughly at 50,000 nautical miles from the earth and this region, where the earth's oblateness perturbation has begun to peter out quite a bit before the lunar third-body effect begins to become very serious, has a rather broad flat minimum, somewhere between 10 to 25 earth's radii away from the earth; and of course, in this region, with the perturbations a minimum, orbits have the greatest stability. By the time you get out to 30 or 40 earth's radii toward the moon, the perturbations of the moon become pretty large. Ehricke has studied a great many orbits. There was not nearly enough time to present more than a few examples of all the work that he has done under a number of different assumptions and possibilities. He showed in particular a case in which the motion of the perigee and apogee was illustrated very clearly and showed the extreme ranges that came up in this case. The main effect so far, of these studies, is to give one a good feel for the kind of operations that will be most effective in cislunar space. The problems which remain have to do with exploring this whole field further.
Hans Lieske of Rand spoke next. He changed the printed title a little to make it a bit more accurate, a little more descriptive; "On the Accuracy Requirements for Trajectories in the Field of the Earth and the Moon." He also has made a great many computations of various types of orbits under various assumptions and different conditions. He, too, was able to give only a few cases. He emphasized the high accuracy requirements of the velocity vector of an object which is leaving the earth on a ballistic trajectory, depending upon the objectives. If one wants just to hit the moon at all, an accuracy of the velocity vector of 100 feet per second in magnitude, and one degree in pointing angle is required. The accuracy requirements are much higher if one wants to actually land on the moon without collision or to make a close pass at the moon and return to the atmosphere of the earth, say an altitude of 50,000 feet. The values are certainly one foot per second or less in the magnitude of the velocity vector and roughly from a hundredth to a thousandth of a degree in the pointing angle. On the other hand, the accuracy requirements open up quite a bit for a single trip around the moon with as much leeway as twenty days in the total travel time. Such leeway means a range of about 80,000 miles in the minimum approach to the moon. The values would be about 150 feet per second or so in the magnitude of the vector, and about 10 degrees in the pointing angle. You would have been there, but it is up to you where you would be after you had been there.
In the next paper Professor Oberth presented an Attitude Control System. He described a device in which a pendulum would be mounted off-center in a vehicle; this pendulum would be used as an attitude indicator. He gave the equations for the stresses and the tidal forces which would be acting on some point on the rotating vehicle. The equations are so general that they would apply irrespective of the rotation of the vehicle, that is, as to whether it is a rotation on its own axis or whether you are thinking of the change of attitude as it goes around in its orbit. The error signal of the pendulum is then used, presumably, for attitude control. This will appear as a report from the Army Ballistic Missile Agency at Redstone and, of course, this is only in the preliminary stages. If this is to be used, there is much yet to be done there.
In the next presentation, Professor Samuel Herrick, of UCLA and Systems Laboratories, spoke on "Accurate Navigation of Intercontinental and Satellite Vehicles in the Earth's Gravitational Field." He emphasized particularly the need for accurate values of a primary gravitational constant, k2, and of the coefficients J and K of the second and fourth harmonics in the earth's potential.
Herrick pointed out first that Gauss' value of k2, for heliocentric orbits with the astronomical unit as unit of distance, was accurate to nine significant figures, whereas neither the laboratory value of G nor a laboratory unit of distance such as the meter would permit an accuracy of more than three or four significant figures.
The corresponding value for geocentric orbits, ke2, is best determined from values of the earth's equatorial radius and acceleration of gravity, taking into account J, K, and the effects of the earth's rotation and atmosphere. The last three are determined from theory with sufficient accuracy. J is best determined at present from astronomical sources, but a value consistent with the international value of the earth's flattening, f = 1/297, is in sufficiently close agreement to be adopted. The Army Map Service has recently determined a highly accurate value of the earth's equatorial radius. With these values and an independent study of sources of information on the acceleration of gravity, the speaker and his associates have recently determined an improved value of ke2. The difference between the improved value and that probably being used in ICBM trajectory calculations would amount to 3000 or 4000 feet at the end point. Herrick expressed the opinion that whereas studies of the Vanguard Satellite would almost certainly improve J, the outlook for ke was decidedly less hopeful. He also stated his belief that proposed methods in either special perturbations or general perturbations, though they might be sufficient for ephemeris calculations, would be inadequate to handle the highly accurate orbit calculations necessary for improving the geophysical constants and similar problems.
The next presentation was by Dr. Whipple on "Orbital Accuracy and Ranges from Ground Based Optical Tracking" and the main burden of Dr. Whipple's remarks in this connection was that the situation is much farther on the poor side than we would like. One can get an accuracy in the case of the Vanguard program of presumably a few seconds or so of arc. Therefore it is not unreasonable to talk in terms of an accuracy of one second of arc, which might be obtained in other cases where the angular velocities are not so severe. However, this kind of observation comes with a time lag of about three hours or more for the reduction of photographic images, etc. If one assumes that these observations have been made somewhere along the earth, then one can imagine a base line of roughly 4,000 miles from one observation to the next. Then the absolute position in space has an accuracy which is proportional to the base line and inversely to the square of the distance. Thus, for the distant objects this accuracy, when one tries to get an absolute position in space, goes down rather severely. The time lag which is inevitable in the reduction of photographic observations appears to be much too great for guidance in vehicles of the Vanguard type or other dose satellites.
If one considers objects at the distance of the moon, then the accuracy of a second of arc is comparable to two kilometers. However, by the time the possible errors in base line and so on are taken into consideration, the absolute position in space at the distance of the moon becomes more nearly 200 kilometers. At this distance, to get an accuracy of about one degree in the angular direction of the velocity vector would take about four horns. This time is required to get an accuracy of one degree in position observations and to determine the vector from these observations. During this time the object has gone 15,000 kilometers and you are an additional four hours behind for data reduction. This method is bad insofar as using such information for guidance is concerned.
Another point which Dr. Whipple brought out has to do with the visibility of objects which are beyond the distance of the moon. He suggested that if there were about a ten-meter diameter reflector, it would provide enough illumination to make it photographically observable. Of course, the reflector must be oriented properly to be observed at all. In planetary cases, (forty million miles to Mars or of the order of magnitude of hundreds of millions of miles around the solar system) making contact with a planet imposes severe requirements, of course, but the distances now become tremendous. The accuracy goes down a lot on the basis of the previous discussion. With baselines no larger than what can be obtained from the surface of the earth errors of the order of millions of miles result at the distances of the planets. On the other hand, if the distance from the earth to the moon is the base line, the error is reduced to the order of magnitude of a hundred thousand kilometers. Such reduction doesn't help too much, really, so that Dr. Whipple is forced to conclude that observations must be made aboard the vehicle in order to get accuracies of the order of a thousand kilometers in absolute positions in the regions of the planetary system. This means that space vehicles will themselves need to have precision guidance systems and to make their own observations in order to get any kind of precision that would permit navigation to the planets. He concluded by saying that this was a Herculean task. I don't know if this precisely defines the problem, but it gives the order of magnitude.
The next paper was to be presented by Dr. John DeNike, of the Glenn L. Martin Company, concerning "Orbit Studies Using High Speed Digital Computers." Unfortunately for personal reasons he was unable to come at the last minute and we are really grateful that he sent an able replacement, Wilhelm Elfers, Chief of Simulation. He presented the material on the orbit studies which had been made at Glenn Martin, particularly in connection with their responsibility under the Vanguard project. In their computation laboratory they have set up systems which enable them to simulate powered flight. Taken into account are: The take-off trajectory as well as the trajectory above the atmosphere, the aerodynamic forces using the wind in a three dimensional model. In their studies they are also able to include the characteristics of the hardware, gyro reference system, etc. This kind of simulation permits them to study the response of various components in the system to see if they are able to meet the tolerances. This also permits some leeway to experiment with different designs in order to see from the performance capabilities what the optimum design would be. At the same time they have anticipated on all of this work that it should be done on a level which would be adequate for the analysis of their flight test data when the test vehicle program of the Vanguard gets under way. All of these computations of course include not only drag but also oblateness. One of the problems of the future which he mentioned in his conclusion has to do with space navigation and the extent to which the present hardware is applicable. This can be studied in terms of the computing system which they have set up. They are also in a position to study the effect of cut-off errors and, of course, this is complimentary to Mr. Lieske's remarks about the accuracy requirements that are needed and the requirements for monitoring devices in mid-course guidance. He didn't dwell too much on this, but it was part of the potential of this computing system which they have set up. Finally, what is the best kind of computing system to use? For the one which they have designed and are using, they have tried to be as general as possible without getting so general that results are inconclusive. He feels that their present facility is adequate for the kind of studies they are interested in making in connection with all the problems that preceded here.
Finally, the Chairman put his neck in the noose, as he had put all the other speakers before him, and described some of the work which has to do with the oblateness perturbations of the earth when they are treated in terms of Fourier series or general perturbations. For this purpose the gravitational potential of the earth has been represented by two spherical harmonics and the equations which we have been playing around with, and sort of decided upon, as those we like the best, are all rigorous equations. There are no Taylor's series expansions involved in these processes to make approximations. The intention is to use these processes by means of an iterative procedure. This means that these processes can be repeated as many times as is needed to gain the full accuracy because the equations themselves are rigorous. From the amount of work which we have done so far it appears that for prediction purposes the first order might very well be entirely adequate but the methods which we are pursuing, I am confident, will enable us to represent the effects of the earth's gravitational field with all the accuracy that will be demanded when one comes to analyze the observations that are collected. It was pointed out that it is just a fact, whether one likes it or not, that since we have had high speed electronic computers nearly everyone has solved his problems by means of numerical integration and step-by-step processes. Everyone, including astronomers, has not been operating very much in the methods of using Fourier series. There is room here for the possibility of improving techniques simply by working along these lines rather than present lines. When you get a feel for the problem you might get a bright idea to go along with it. Other problems in this connection, as I see them, are that once these methods are set up and these equations are decided upon, whatever seems to be the best form, then one would test various cases which might arise. Not only the Vanguard Satellite but any other kind of a satellite that anybody wants to put up for whatever kind of looking or riding can be used to test the adequacy of these methods. Also there is the possibility that if one has seen everything that can be done with the method which we are presently following, we could find some other method which would be an improvement for the kind of cases with which he would like to deal. However, at the present time my impression is that we will be able to handle any satellite case insofar as the earth's oblateness perturbation is concerned by these methods; but that it is not an open and shut case. There is probably room for improvement, but it is not so much a problem anymore, as it is just a matter of doing what is indicated to be done. We have not yet dealt with the drag perturbation, but this subject came up in the question period. We hope to try to deal with the drag perturbation in the form of these general perturbation equations. However, we are not being fooled, there comes a time when the drag is such a severe part of the perturbation that you really don't have a perturbation problem anymore and these methods will completely collapse. In the end there will come a time when we will have to resort to numerical integration. I think, Mr. Chairman, this concludes what I have to say.
A. R. Hibbs, Jet Propulsion Laboratory:
I have a question in regard to the perturbation scheme which you discussed. It seemed that they were most applicable when you knew the perturbations in which to compute the orbit. I wondered whether or not these same perturbation schemes could enable you with equal ease or equal difficulty to compute the perturbations knowing the orbit?
I don't quite understand what you mean?
A. R. Hibbs:
Well, if you know the perturbations you can, with the schemes you outlined, I believe, compute the orbit from them, but if you know the orbit characteristics can you go the other way around with equal ease and compute the perturbations which lead to the perturbed orbit? If you have the observations on the trajectory can you now compute the coefficients of the oblateness, for instance, from the observations on the trajectory as easily as you can go the other way around knowing the oblateness of the earth?
Anything is easy when you know it. The point is: what we will have to do in the case of the Vanguard, is to take the earliest observations we can get and make the closest approximation we can on the elliptic character of the trajectory. We have to assume this elliptic character to develop all the coefficients in the general perturbations. Then we use this as if it were correct (except that it really isn't, because it is based on such shaky grounds). Then whatever-observations we get, say, after six or a dozen revolutions, we use to make an adjustment of the constants of integration or the basic ellipse in order to agree more precisely with the observations. This is also an iterative process; we recompute the perturbations, then you use them to represent the observations again, and presumably except for second order effects, the residuals aren't very big. As time goes on, the object will run off the latest orbit. So we make another differential correction of the basic starting value.
A. R. Hibbs:
And you feel that any drag corrections can be handled in a similar way?
Fred L. Whipple:
May I add to this conversation? I think your question really concerns the final analysis of all the data; at least that is the point of view that I would take. After all the observations are in, perhaps a thousand accurate measurements of either right ascension or declination, one takes the most complete theory available and solves as unknowns for these constants that deal with the distribution of mass in the earth, the positions of the observatories relative to each other, and for the orbital characteristics as a function of time, out of which one then will get the drag determinations, too. So there are about a hundred unknowns to solve for eventually out of perhaps ten times that many observations. The addition of more satellites keeps on adding to this basic information so that, if you have several satellites, you increase your total knowledge of the constants you asked about, the station locations, and the atmospheric drag.
A. R. Hibbs:
My particular question was directed as to whether or not the perturbation scheme as it is now being developed is adequate to do this from the point of view of having quite adequate trajectory data and wishing to treat as unknowns, the unknowns of the gravitational potential?
This remains to be seen. If there are enough observations and you make a least-squares solution which tells you what the probable errors of these unknowns are, if they are good you believe them and if they are not, you are sorry and you just wait for more observations.
A. R. Hibbs:
However the computing scheme is adequate.
I wonder if I could make a few comments to both of these points here. Certain it is, that there are well nigh a hundred things you would like to measure. Of course, there are some of them that produce rather bigger effects than others, so you expect it would rather be easier to boil down on those and get an accurate determination. Certainly it is also true that the largest effect that we expect is that of the oblateness of the earth. To Hibbs' question here: there are some people at Ramo-Wooldridge that made a small unclassified study of this point. They found that by using very modest down-graded kind of radar accuracies and by using only two passes and reasonable kinds of smoothing times within the observation, one could obtain the oblateness coefficient, the "J," to something like a factor of three better than the present geophysical measurements. I wonder if you people agree or disagree with this sort of a statement?
Intuitively, I take a completely dim view of that. I might echo that sentiment too.
Hinteregger, Air Force Cambridge Research Center:
I would like to throw in at this point a remark which is of an organizational character. Mentioning that we had three different panels on orbits, communications, and measurements, all of which have a common interest in one topic which I would suggest that in the next Symposium would be raised to the level of a separate panel. I think this should be the attitude control or aspect control because for any practically planned experiments this is of extreme importance. Anyone who wants to plan ahead to do some experiments will be particularly concerned with this question and as of this Symposium we have heard only Professor Oberth's proposal about the pendulum. I want to question in connection with this if there are similar proposals in consideration.
Dr. von Karman:
You are correct, Panels do overlap. This is very hard to avoid, because there is no such clear classification. Either you have gaps or overlapping. I completely agree with you that this is correct.
I didn't mean this as a criticism to the present Symposium, just as a suggestion for a future one.
Dr. von Karman:
The remark on the intuition which was just made reminds me of a story, a remark by Professor Milne to Dr. Chandrasekhar. Dr. Chandrasekhar was then working on his theory of white dwarfs and he got a critical radius, a critical mass for the white dwarf, and Professor Milne remarked, "Somehow I feel it in my bones that the theory is not right." Dr. Chandrasekhar's remark was characteristic, he said, "I will be happy if Professor Milne treats it in some more reasonable part of his anatomy."
I can be glad that I didn't say that I felt it in my bones.
Dale Romig, Goodyear Aircraft:
I think that of all the problems that I have heard discussed so far this afternoon that if we were forced to say whether or not within the next ten or twenty years we could start now to produce an operational vehicle to get man into a satellite, the one that I would ponder longest would be the problem of re-entry. In that connection, still along the lines the panel suggested, I think it could probably be handled by designing in accordance with the data that is to be accumulated or that has been accumulated. But I still believe that this question of waves (atmospheric bumps) might make the problem at least five or ten times as bad if they are there. So I got to wondering in connection with this discussion at just the previous panel, whether or not this analysis of the orbit might possibly yield revelations with regard to such drag variations. To be specific, I am talking about wave gradients that might be from total amplitudes of equal contour and altitude of two to four miles in, say, a thousand to two thousand miles longitudinal pitch. Or the condition, to put it simpler, which would double the drag in a matter of a minute or two or three of satellite travel: could that be told?
Fred will want to answer this too. My feeling is that just unfortunately we can't get enough observations because the Minitrack, for example, gives you only one per revolution and there aren't enough photographic observing stations mounted around the world so that these kinds of things, I am afraid, won't show up very much.
Could I add two points to that question. Do you think the rocket data that we have at present or will get (sounding rockets) would be that sensitive? If not one of these, would there be any other way of doing it?
I have considered this problem rather carefully and I would like to put the answer this way. If a wave is predictable on any theory (lunar-tide, solar-tide, diurnal) or in terms of a limited time effect such as solar activity, then every time something happens on the sun, for example, you might expect a wave at a certain part of the atmosphere. Any of these that are periodic or predictable we can at least look for. In terms of present observations, no indications of this type of effect, (the measurements are fairly sensitive) has been observed up to a little over a hundred kilometers. Now we do know that there are tidal waves in the "P" layer of the ionosphere, but it has not revealed itself to a hundred kilometers and what will happen at two hundred, four hundred and above is problematical, but I do think it is true that there will be no way either by sounding rockets or by satellites to find a random, unpredictable, uncorrelatible wave at high altitudes.