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The Orbits of Venus
Copyright 1972 by C. J. Ransom and L. H. Hoffee
Dr. Ransom is a plasma physicist at the Electro-optics and Reconnaissance Group of General Dynamics, Convair Aerospace Division, Fort Worth, Texas. Hoffee is an optical engineer.
In 1950, Immanuel Velikovsky suggested that several orbital changes had occurred among members of the solar system (1). These changes resulted in near-collisions between celestial bodies and a reordering of the solar system. In the following paragraphs, known changes in the orbits of comets, commonly considered not to be possible, will be discussed. In addition, calculations which provide approximate orbital parameters for the celestial bodies which Velikovsky contends were involved in these collisions are presented.
In Worlds in Collision, the term "comet" often arises with respect to Venus. This is a result of the ancient definition of a comet as a celestial object with an extended atmosphere, and in fact the word "comet" is derived from the Greek word for "hair". Therefore, such references to Venus as a comet are used in this context rather than according to the modern, although imprecise, definition of a comet. That the modern definition is little better than the ancient definition is seen from the following two statements: Roemer said that although Comet Arend-Rigaux had an orbit similar to a minor planet, it was designated as a comet because it, on occasion showed some diffuseness. When Bade discovered Hidalgo, he was undecided whether to call it a minor planet or a comet, so he called it a minor planet because they were more popular at the time (2).
Although an exact definition of a comet may be in question, observation of the motions of accepted comets can be used to illustrate that some types of changes in the orbits of celestial bodies required as a result of Velikovsky's contentions are physically possible. For example, Brooks' Comet (1889V) went 313 degrees around Jupiter and changed its orbital period from 29 years to 7 years. Furthermore, in 1875 Comet Wolf had a close encounter with Jupiter; and as a result, its perihelion was changed from 2.5 AU to 1.5 AU. In 1922, the same comet had a second encounter with Jupiter and reverted to almost its original orbit of before 1875. Its aphelion remained almost constant throughout these encounters (3). Fokin states that during a near approach to Jupiter the comet Oterma III, which before 1938 had an orbit entirely between the orbits of Jupiter and Saturn, changed its orbit so that it was entirely between Mars and Jupiter (4). After 1965, its orbit was again between Jupiter and Saturn (5).
A series of orbital configurations that is not inconsistent with either the events described by Velikovksy or the laws of physics is illustrated in Figure 1. Table 1 lists the orbital parameters for each of the four configurations.
A possible orbital configuration for the period after the ejection of Venus by Jupiter and prior to the encounter between Venus and Earth is illustrated in Figure la. The period of Venus in this configuration is 7.1 years and the period of Mars is 0.56 years. A year is defined as the orbital period of the earth at that time and is independent of the number of times the earth revolved on its axis in one of its years. The 7.1 year period of Venus is in agreement with such literary references as the seven-year cycle of sabbatical years as practiced by the Israelites (6).
A possible orbital configuration for the period between the time of the encounters between Venus and Earth and prior to the encounter between Venus and Mars is illustrated in Figure lb.
A possible orbital configuration for the period between the time of the encounter between Venus and Mars and prior to the encounter between Mars and Earth is illustrated in Figure 1c.
The present configuration of the orbits of Mars, Earth, and Venus is illustrated in Figure 1d. The present near-circular orbit of Venus is often discussed as an orbital oddity. Sherrerd of Bell Laboratories has shown that an orbit of this nature would be expected were Venus in a near plastic state while acquiring this orbit (7). Tidal friction would tend to keep the body hot and change the orbit, by the laws of Cassini, to one which would minimize energy lost by tidal friction.
PLANET a e
PERIOD1 PERIOD2 SYNODIC
Jupiter 5.2 0.048 4335 16.28 1.07 4.95 AU 5.45 AU
Venus 3.0 0.80 1898 7.13 1.16 0.6 5.4
Earth 0.8 0.07 266.3 1.0 —— 0.74 0.86
Mars 0.55 0.05 149 0.56 1.27 0.52 0.58
Jupiter 5.2 0.048 4335 10.29 1.11 4.95 5.45
Venus 1.0 0.5 365 1.15 6.51 0.5 1.5
Earth 1.1 0.17 421 1.0 —— 0.92 1.28
Mars 0.55 0.05 149 0.35 0.55 0.52 0.58
Jupiter 5.2 0.048 4335 10.29 1.11 4.95 5.45
Venus 0.7 0.007 224.5 0.53 1.14 0.7 0.7
Earth 1.1 0.17 421.4 1.0 —— 0.91 1.29
Mars 1.0 0.4 365 0.87 6.51 0.6 1.4
Jupiter 5.2 0.048 4335 11.87 1.09 4.95 5.45
Venus 0.7 0.007 224.5 0.62 1.6 0.69 0.71
Earth 1.0 0.017 365 1.0 —— 0.98 1.02
Mars 1.52 0.093 687 1.88 2.14 1.38 1.66
(1) Expressed in present earth days
(2) Expressed in earth years
In order to prove that the orbit of Venus as shown in Figure 1a has more than a minute possibility of occurrence, a computer program was written and executed on a Hewlett-Packard Model 9810A calculator (8). The program assumes that an object is 1) placed at a specified distance from the sun, and is 2) moving at a specified angle relative to a line drawn through the object and the sun at 3) a specified velocity. The program operates on these three quantities and calculates orbital eccentricity (e) and semi-major axis (a). In practice, the initial distance is taken to be 4.4 AU, the initial angle is zero degrees, and the initial velocity is zero kilometers per second: and a solution for a and e is then calculated. The distance is increased by 0.01 AU increments until maximum of 5.4 AU is reached, the angle is increased by 0.5 degree increments until 180 degrees is reached, and the velocity is increased by 0.001 km/sec. A solution for a and e is calculated for each combination of distance, angle, and velocity.
Figure 2 is a plot of the resulting calculations. Ejection angle is plotted as a function of velocity for an orbital eccentricity of 0.80 and distances of 4.4 AU and 5.4 AU. The limits for the ejection angle are 40 degrees and 140 degrees with the angles above 90 degrees being read from the right hand scale. Thus, all points lying between the lines labeled 4.4 AU and 5.4 AU result in orbits with an eccentricity of 0.80. Further, all points lying within the shaded area result in orbits with the added characteristic of possessing semi-major axes of between 2.95 AU and 3.05 AU. It can be seen from the figure that the probability of an object achieving the required orbit is not minute as is often assumed.
The equations used to arrive at the above conclusions can be found in references (9) through (11); the work of Rose and Vaughan was used to verify the results of independent calculations, and provided refined orbital parameters for Mars, including the suggestion of the possibility of Mars having an interior orbit.
In summary, it can be stated that some objections to the contentions stated by Velikovsky in regard to orbital changes have been answered by the method of counter example. It can also be stated that objections based on the contention that the probability of Venus acquiring the necessary orbital parameters is too small to even warrant consideration is shown to be unfounded. Granted, the probability is not unity; however, the point in question is not whether a celestial body will assume such an orbit either after being ejected by Jupiter or after its orbit is affected by Jupiter, but rather that the required orbit is theoretically possible.
In conclusion, the authors wish to express their hope that results of orbital calculations presented in this paper will be viewed as a starting point for further studies of the past orbital configurations of the planets. This work will be continued by the authors, and they express their interest in cooperating with other investigators in this endeavor.
 I. Velikovsky, Worlds in Collision (Doubleday, 1950).
 E. Roemer, Astronomical Journal, 66 (1961), 368.
 R. A. Lyttleton, The Comets and Their Origin (Cambridge university Press, 1953), p. 13.
 A. V. Fokin, Soviet Astro. AJ 2 (1958), 628.
 Middlehurst and G. Kuiper, Moon, Meteorites and Comets (University of Chicago Press, 1963), p. 559.
 I. Velikovsky, Worlds in Collision (Doubleday, 1950) p. 153-56.
 C. Sherrerd, Pensée, 2 (May 1972), 43.
 The authors would like to thank Hewlett-Packard, 201 East Arapaho Road, Richardson, Texas, for the use of the 9810A calculator and plotter.
 L. Rose and R. Vaughan, Pensée, 2 (May, 1972), 42.
 A. G. Webster, The Dynamics of Particles and of Rigid, Elastic, and Fluid Bodies (Hafner Publishing company, New York, 1949), p. 40.
 F. R. Moulton, An Introduction to Celestial Mechanics, Second Edition (Macmillan Company, 1914), p. 150.
PENSEE Journal III
[1.] a and e in this figure were given by Rose and Vaughan (9). For convenience, orbits are drawn with perihelion to the right.