**Science
in Christian Perspective**

**
The Astrophysics of
Worlds in Collision
**
ROBERT C. NEWMAN

Biblical School of Theology

Hatfield, Pennsylvania 19440

From: *JASA ***25 **(December 1973): 146-151.

Robert C. Newman has a Ph.D. from Cornell University in theoretical
astrophysics
(1967), as well as five years of graduate training in theology.

**
Introduction**

**T**he solar system has been the scene of repeated catastrophes in the millennia
preceding the time of Christ, according to Immanuel Velikovsky.^{1 }In
his book Worlds
in Collision, first published in 1950, the author concentrates on the two most
recent alleged upheavals: our near collision with Venus about 1500 BC, and the
close approach of Mars in the period 800-600 BC. In addition, Velikovsky gives
a few hints that the deluge of Noah involved a similar phenomenon.^{2}
Jupiter also
is thought to have figured prominently in some previous eatastroplse.^{3} Although
Velikovsky apparently intended to devote another hook to these earlier events,
he seems to have been side-tracked by adverse reaction to Worlds its Collision.^{4}

In any case, Velikovsky believes that Venus was formed by being thrown out of
Jupiter during a near collision among the outer planets.^{5} At first Venus became
a comet with an elongated orbit extending from near Jupiter inward past the earth's
orbit.^{6 }On several occasions in the midst
of the second millennium BC, the comet Venus approached the earth, producing a
variety of physical calamities, including destructive meteor shnwers,^{7} extensive
volcanic flows,^{8} huge tidal waves,^{9} the tilting of the earth's axis and changes
in its speed of rotation,"' as well as years of semi-darkness during which
the sun was obscured.^{11
}

Velikovsky cleverly ties these phenomena to the events of the Exodus
of the Israelites
from Egypt and the conquest of Canaan: the ten plagues,^{12} the crossing of the
Red Sea^{13} and the Jordan River,^{14} the manna in the
wilderness,^{15} the
smoke, fire
and sounds at Mount Sinai,^{16} the cloudy and fiery pillar,^{17} the
fall of Jericho,^{18 }the "hailstones"^{19} and Joshua's long day^{20} at Gibeon. Velikovsky
also seeks to synchronize these calamities with the fall of Egypt's
Middle Kingdom,^{21}
the migrations of several ancient peoples,^{22} and the origin of a
substantial amount
of mythology in all parts of the world.^{23}

Having disrupted the earth's motion, destroyed a number of
civilizations, created
several new religions, and dumped enormous amounts of manna (=nectar
= ambrosia) ^{
24} and petroleum^{25} on the earth, the comet

Venus continued to threaten the earth for centuries, although no
further catastrophes
occurred, Finally, about 800 B.C., Venus nearly collided with the planet Mars.
As a result, the Martian surface was devastated and its orbit was
disrupted, while
Venus settled into a new orbit where it became a planet and no longer menaced
the earth.^{26}

Unfortunately, however, the new orbit of Mars now made it a threat to earth in
place of Venus. Although the Martian upheavals were not so violent as
the earlier
Venerian calamities,^{27} the red planet still succeeded in turning hack
the shadow
on the dial of Ahaz,^{28} wiping out the Assyrian hosts of Sennacherib besieging
Jerusalem,^{29} providing phenomena for the striking catastrophes
mentioned by several
of the Old Testament prophets,^{30} changing the length of the month
and the year,^{31}
influencing the outcome of the Trojan War,^{32} and adding a new war god
to the pantheon
of many pagan religions.^{33
}

**
Velikovsky and Christianity
**

It should be clear from this sketch of Velikovsky's reconstruction of ancient history that his work is a matter of concern for Christians. Although he gives a certain amount of historical credit to the Old Testament narratives, Velikovsky is no believer in supernatural revelation.

Some Christians, however, have been impressed by the fact that Velikovsky repudiates the uniformitarian outlook of science and that he admits the historicity of certain biblical catastrophes. Among several Christian writers who seem to have been influenced by him, one in particular-Donald W. Patten-seems to have attempted a "Christianization" of Velikovsky's general outlook in his work

In an article of this nature, there are severe limitations of space. Therefore we confine this discussion to two major areas of Velikovsky's astrophysics: orbital mechanics and rotational mechanics.

Velikovsky spends several pages discussing the old nebular and tidal theories for the origin of the solar system, finding them both inadequate.

Patten's alternative model is to suggest that the planets were randomly captured by our sun from interstellar space.

But there are two very serious problems of orbital mechanics which must he faced by such random capture or collision views. (1) The planetary orbits all lie very nearly in the same plane, and (2) these orbits are all very nearly circular.

Relative to the orbital plane of the earth, the orbital planes of the other planets are tilted by the amounts indicated in Table I. If the planets were randomly captured or involved in numerous collisions, we would expect their orbital planes to he randomly oriented, but they are not. To indicate just how unrandom the orientation is, let us calculate the probability that the planets would have as little tilt as they do if they had been captured randomly. The total probability is just the product of the probabilities for each planet separately.

The probability for a single planet can be calculated with the help of Figure
1. Drawing a sphere whose equator is the earth's orbit and whose
vertical is perpendicular
to that orbit, then a planet with orbital plane tilted by an angle
& has its
perpendicular fall somewhere on the cone shown in Figure 1. Any
planet with less
tilt has a perpendicular lying within the shaded area. Therefore the
probability
that a randomly captured planet has a tilt less than or equal to 0 is just the
ratio of the shaded area to the area of the whole sphere. Without going through
the derivation, this ratio and probability is

P = 1'2' (1 - cos theta)

The result for each planet is given in Table I. The total
probability is

P _{ tot} = (P _{Merc} ) (P _{ Ven} ) (P _{Mars}) ... (P _{Pluto})
which is __ P__ _{ tot} =6.9 x 10^{-26}.

Since this probability is roughly equal to the chance of finding one
marked penny
among a collection in which every inhabitant of half a million
planets with population
equal to ours each has a billion dollars in pennies, it is clear that Patten's
proposal lacks merit! Even assuming that only Venus and Mars have had
their orbits
disrupted (and Velikovsky certainly assumes more than this), the
combined probability
that Venus and Mars would have orbital planes as closely aligned with earth's
as they do is 2.7 x 10 , about one chance in four million. If you
knew that someone
in Virginia had stolen your wallet, a "random capture" of one of its
inhabitants would be about as likely to net the culprit!

In fact, these figures show that any theory for the origin of the solar system
must contain a mechanism for producing the planets in nearly
co-planar orbits.

A similar problem involves the shape of the planetary orbits. Two objects hound
by their gravitational attraction move in ellipses around their common center
of mass. For the solar system, this means that each planet moves very nearly in
an ellipse about the sun, since the effect of the planets on each other is very
small (at least at the present time). The shape of an ellipse is indicated by
a quantity called eccentricity, usually represented by the letter e.
If e is zero,
the ellipse is actually a circle. As e increases from zero toward
one, the ellipse
becomes more elongated, going to a straight line or parabola as e goes to one.
If a planet has been captured randomly or its motion around the sun
has been randomly
determined by close approaches to other planets, then all values of
eccentricity
between zero and one should be equally likely.

In fact, the eccentricities of the planets are unusually small, as
seen in ** Table II**. The orbits are much more circular than would be expected for random capture
or close approaches. This may be seen by calculating the individual
and collective
probabilities for such small values of e. Assuming that each value of a between
zero and one is equally likely, then the probability that e has a
value less than
or equal to some value x (between zero and one) is just the value x itself.

Thus, for instance, Mercury has an eccentricity of 0.206. The probability that a planet captured randomly would have an eccentricity less than or equal to 0.206 is just 0.206. The probability for the whole set of nine planets having as circular orbits as they do is again the product of the individual probabilities. i.e., 6.5 x 10-13, which again is very small. The probability that just Venus, Earth and Mars would be as circular as they are is only 1.1 x 10, again suggesting that the planets have not been randomly captured or greatly disrupted in their orbits.

**
Although he gives a certain amount of historical credit to the Old
Testament narratives,
Velikovsky is no believer in supernatural revelation.**

In contrast, the comets, which may well have been captured randomly
from interstellar
space, have much higher eccentricities. The twenty-five short-period
comets listed
by Motz and Duveeu range in eccentricity from 0.132 to 0.967 with an
average just
over 0.6^{44} This is not a representative sample of the comets either, because
must of the comets known have very long periods and eccentricities very close
to one.

For the theories of either Velikovsky or Patten to stand up, they need to find
some mechanism which circularizes the orbits of (at least) Venus and Mars. No
known physical laws will do the job, and the fact that Halley's comet has been
observed to return regularly since 240 B. C.^{45}, indicates that it has suffered
little change in eccentricity its the past 2000 years.

Problems of Rotational Mechanics

Now we consider the physical problems involved in stopping the rotation of the
earth or drastically tilting its axis of rotation. The physical laws governing
the rotation of a rigid object are not as familiar to most people as
those controlling
the movement of an object from place to place. However, the formulas
for rotational
motion are really rather similar to those for translational motion except that
a number of new quantities are defined. Thus the mass is is replaced
by the moment
of inertia I, the force F by the torque T, the linear momentum p by the angular
momentum L, and the linear velocity v by the angular velocity w. See Table Ill
for a comparison of three basic formulas.

We now calculate what torque would be necessary to stop the earth's rotation in
a relatively short time. Assuming a constant torque, we can integrate the last
equation in Table III to get T=(L/t). The Smithsonian Physical Tables give the
mass of the earth as 5.975 X 10^{27}g., its equatorial radius as 6,378
km,^{46} and its moment of
intertia as* I*= 0.333 mr^{2},^{47} from which we calculate
* I* = 8.12 x 10^{44}g cm2. The angular
velocity of the
earth is 7.3 x 10^{-5} radians/sec,^{48} so that we may calculate its angular momentum
from the first rotation formula in Table III as L = 5.93 x 10^{40 } g em2,'see.

If the reversal of the shadow of the dial of Ahaz (2 Kings 20) is understood as
a reversal of the earth's rotation, then the earth must be brought to a stop in
just a few minutes. Joshua's long day requires a stop in a fraction
of a day (and
a drastic tilt involves about the same change in momentum, and
therefore the same
torque). Using one full day for the time taken to stop the earth, we
find a torque
of 6.86 x 10^{35} dyne cm is necessary.

**
TABLE III **

Name Translation Formula Rotation Formula

Momentum p=mv L=IwKinetic Energy

E=1/2mv^{2 }E=i/2Iw2Change in Momentum F=dp/dt T=dL/dt

So far, none of these figures make much of an impression unless one
is thoroughly
familiar with the quantities involved. But now we consider how this
torque might
he obtained.

Could the torque have been exerted by the gravitational pull of Venus passing
very close to the earth? If we took Venus and the earth as rigid
spherical objects,
the answer is "no," for gravity would have nothing to
"grab"
to produce a torque. But the close approach of Venus would raise a tidal bulge
on the earth, which we can represent by thinking of the earth as
composed of two
masses, each equal to urn, separated by a small distance 2a. In this ease, the
planet Venus, with mass M, at a distance R from the earth (where R is
much larger
than a) would exert a torque on the earth given by

T= (C M m a^{2}_{/} 'RI) sin 2 0,

where C is the universal constant of gravitation and
0 is the angle between Venus and the earth's bulge. See ** Figure 2** for
the geometry
of this situation.

Let us choose the optimum value of 45 deg for 0.. For we use the necessary torque
calculated above. For simplicity, we use the earth's mass for both in
and M. For
a, let us choose the value 100 kilometers (about 60 miles), which
would represent
about as large a bulge as possible without producing large rips in the earth's
crust (the moon only produces a tidal bulge in the solid earth of a
few inches).
Putting all these quantities in the last formula, we solve for R to
see how close
Venus must come to produce enough gravitational torque to stop the
earth's rotation
in one day. The result is R = 7000 km, less than 5000 miles! But this is inside
the Roche Limit,^{49} which marks the point at which gravity will pull
apart a body
approaching the earth. Consequently, it appears that the earth and Venus would
disintegrate before they could get close enough together to stop the
earth's rotation
in one day!

Any theory for the origin of the solar
system must contain a mechanism for
producing the planets in nearly coplanar orbits.
Since magnetism is a stronger force than gravity, Velikovsky seems to
he inclined
to look in that direction for the necessary torque.^{50 }The earth already has
a magnetic field of its own, so if Venus could somehow apply a strong magnetic
field to the earth, it might he able to tilt it or stop its rotation.
The torque T which can be exerted by a magnetic field B oil an object having a
magnetic moment u (sinder optimum conditions) is T =uB.^{51} Using the required
torque 6.86 x 10^{35} dyne cm, and the earth's

**
Figure 2.** Schematic diagram of the quantities involved and the geometry for the
calculation of how close Venus must approach the earth to stop its rotation in
one day. The size of e is greatly exaggerated to clarify the picture.

magnetic moment u = 8.06 x 10^{25} egs units,^{52} the magnetic field required is B
= 8.53 x 10^{9} gauss!

For the sake of comparison, the earth's own magnetic field at the
surface is about
0.5 gauss; the strong magnetic fields in sunspots are a few thousand gauss; and
the largest sustained magnetic fields produced by man are a few
hundred thousand
gauss. Thus a field of over 8 billion gauss sustained for a day
thousands of miles
from its source (Venus) is preposterous. Velikovsky seems to sense the force
of this problem, and he tentatively suggests an earth-sized mass of
iron filings
(!) to do the job.53 Just how these all get together to form the planet Venus
after the job is done is not specified. In any ease, one shudders to think what
sort of remanent magnetism would have been left in our iron deposits if
the earth
had ever been subjected to such a strong field!

This does not end Velikovsky's difficulties with rotational mechanics, however.
It is easy to show that there is only a miniseule probability that Venus would
even pass as close to the earth as 6000 miles (in order to influence
its rotation)
under the conditions Velikovsky specifies. For according to Velikovsky, Venus
had an elliptical orbit from about 1500 B.C. to about 650B.C.,
during which time
its orbit presumably extended from about Jupiter's orbit inward to about Venus'
present orbit. In such a case, Venus would have an orbital period of at least
five years, and therefore it would cross the earth's orbit no more
than 340 times.

Assuming that Venus' orbit at that time had a tilt of only 1 deg (smaller than the
present tilt of Venus or its "parent" Jupiter), Venus could
be as much
as 1.7 million miles above or below the earth's orbit when it passed
by, of which
only the central 12 thousand miles would be close enough to the
earth. But Venus
must not only come this close to the earth's orbit, the earth must be
nearby when
it does. Since Venus is moving at least as fast as the earth when it
crosses its
orbit, the earth moves no more than 12,000 miles while

**
For the theories of either Velikovsky or Patten to stand up, they need to find
some mechanism which circularizes the orbits of Venus and Mars. No
known physical
laws will do the job.**

Venus is within 6,000 miles radially of its orbit. All this means
that when Venus
crosses earth's orbit, it must pass through a "window" 24,000 miles
long and 12,000 miles high to score a "hit"! If this sounds
easy, remember
that the target area is 3.4 million miles high and 600 million miles long (the
circumference of the earth's orbit)!

With 340 shots, the probability of only one hit is just 340 times the ratio of
the window or bullseye area to the target area as a whole. The result
is P = 4.8
x 10, about one chance in twenty thousand. Yet Velikovsky postulates at least
one close approach of earth and Venus, another of Venus and Mars, and a third
of earth and Mars!

As in the case of orbital mechanics, there are also some historical evidences
against any past permanent changes in the axis or rate of the earth's rotation.
The Palermo Stone from Egypt's Old Kingdom (thus before the Venus catastrophe
which supposedly destroyed the Middle Kingdom) seems to indicate a
365-day year.^{54} Unless this evidence can be discounted, Velikovsky would have to postulate
compensating changes in the length of both the day and the year to
preserve this
ratio.

In addition, the pyramids of Cheops and Chephren (also dating from
the Old Kingdom)
are aligned to present true north within five minutes of arc (1/12 of a degree).
^{55} On Velikovsky's assumption that the earth has been tilted, there would be no
physical way for the earth to "remember" and return to its previous
alignment. Of course, it might he claimed that the earth was previously aligned
90° or 180° away from its present orientation, but even so
the probability
of such an accurate realignment is
P= (1/12°)/90° =9.26x 10-4, about one chance in a thousand!

**
Conclusions**

Considerations of space have precluded a more thorough examination of orbital
and rotational problems associated with Velikovsky's (or Patteo's) scheme. It
is regretted that most derivations have been left out, but a
college-level physics
major should be able to reproduce them for himself, and anyone with
less training
has probably found this paper tedious enough already.

I had intended to devote another section to Venus as a comet, as Velikovsky's
thesis has several weak points in this area, but again space forbids.
I just observe
that Venus' total mass is probably a million times larger than that
of any known
comet, as is its density,56 and that a comet tail, being extended by the force
of the solar wind, could not possibly transport enough material to supply the
earth's petroleum even if it could penetrate the earth's
magnetosphere and atmosphere
(which is unlikely).

In conclusion it appears that Velikovsky must at least postulate the existence
of a number of rather specific unknown physical laws if he is to carry out his thesis. While it is very likely that there are still many
physical laws unknown
to man, it is extremely unlikely that we have missed any forces lurking in the
solar system with the strenth and range necessary to produce the
effects Velikovsky
must have.

My advice to fellow Bible-believers seeking to understand Joshua's
long day, the
flood, and other spectacular physical phenomena which have occurred
during human
history is not to quit looking, for very few discoveries are made by people who
are not searching for something. But I do suggest that this particular line of
investigation-the near collision of planets within the span of human history-is
a dead end.

**
REFERENCES
**

**
I suggest that the near-collision of planets within the span of human history
is a dead end as a mechanism for catastrophism.**

^{57}1 would like to thank my brother James I. Newman for his help in
preparing the
diagrams for this paper.