Broca's Brain: The Romance of Science

THE GRAVITATIONAL acceleration which holds us to the Earth’s surface has a value of 10³ cm sec^?2 = 1 g. A deceleration of a = 10^?2 g = 10 cm sec^?2 is almost unnoticeable. How much time, ?, would Earth take to stop its rotation if the resulting deceleration were unnoticeable? Earth’s equatorial angular velocity is ? = 2?/P = 7.3 ? 10^?5 radians/sec; the equatorial linear velocity is R? = 0.46 km/sec. Thus, ? = R?/a = 4600 secs, or a little over an hour.

The specific energy of the Earth’s rotation is

where I is the Earth’s principal moment of inertia. This is less than the latent heat of fusion for silicates, L 4 ? 10⁹ erg gm^?1. Thus, Clarence Darrow was wrong about the Earth melting. Nevertheless, he was on the right track: thermal considerations are in fact fatal to the Joshua story. With a typical specific heat capacity of c_p = 8 ? 10⁶ erg gm^?1 deg^?1, the stopping and restarting of Earth in one day would have imparted an average temperature increment of ?T 2E/c_p 100°K, enough to raise the temperature above the normal boiling point of water. It would have been even worse near the surface and at low latitudes; with v R?, ?T v²/c_p 240°K. It is doubtful that the inhabitants would have failed to notice so dramatic a climatic change. The deceleration might be tolerable if gradual enough, but not the heat.

APPENDIX 3

Present Temperature of Venus If Heated by a Close Passage to the Sun

THE HEATING of Venus by a presumed close passage by the Sun, and the planet’s subsequent cooling by radiation to space are central to the Velikovskian thesis. But nowhere does he calculate either the amount of heating or the rate of cooling. However, at least a crude calculation can readily be performed. An object which grazes the solar photosphere must travel at very high velocities if it originates in the outer solar system: 500 km/sec is a typical value at perihelion passage. But the radius of the Sun is 7 ? 10¹⁰ cm. Therefore a typical time scale for the heating of Velikovsky’s comet is (1.4 ? 10¹¹cm) / (5 ? 10⁷ cm/sec) 3000 secs, which is less than an hour. The highest temperature the comet could possibly reach because of its close approach to the Sun is 6,000° K, the temperature of the solar photosphere. Velikovsky does not discuss any further sun-grazing events by his comet; subsequently it becomes the planet Venus, and cools to space-events which occupy, say, 3,500 years up to the present. But both heating and cooling occur radiatively, and the physics of both events is controlled in the same way by the Stefan-Boltzmann law of thermodynamics, according to which the amount of heating and the rate of cooling both are proportional to the temperature to the fourth power. Therefore the ratio of the temperature increment experienced by the comet in 3,000 secs of solar heating to its temperature decrement in 3,500 yrs of radiative cooling is (3 ? 10³ secs/10¹¹ secs)1/4 = 0.013. The present temperature of Venus from this source would then be at most only 6000 ? 0.013 = 79° K, or about the temperature at which air freezes. Velikovsky’s mechanism cannot keep Venus hot, even with very generous definitions of the word “hot.”

The conclusion would not be altered materially were there to have been several close passes, rather than just one, through the solar photosphere. The source of the high temperature of Venus cannot be one or a few heating events, no matter how dramatic. The hot surface requires a continuous source of heat-which could be either endogenous (radioactive heating from the planetary interior) or exogenous (sunlight). It is now evident, as suggested many years ago (see Wildt, 1940; Sagan, 1960), that the latter is the case: it is the present radiation of the Sun, continuously falling on Venus, which is responsible for its high surface temperature.

APPENDIX 4

Magnetic Field Strengths Necessary to Circularize an Eccentric Cometary Orbit

ALTHOUGH VELIKOVSKY has not, we can calculate approximately the order of magnitude of the magnetic field strength necessary to make a significant perturbation on the motion of a comet. The perturbing field might be from a planet, such as Earth or Mars, to which the comet is about to make a close approach, or from the interplanetary magnetic field. For this field to play an important role, its energy density must be comparable to the kinetic energy density of the comet. (We do not even worry about whether the comet has a distribution of charges and fields which will permit it to respond to the imposed field.) Thus, the condition is

where B is the magnetic field strength in gauss, R is the radius of the comet, m its mass, v its velocity and ? its density. We note that the condition is independent of the mass of the comet. Taking a typical cometary velocity in the inner solar system of about 25 km/sec, and ? as the density of Venus, about 5 gm/cm³, we find that a magnetic field strength of over 10 million gauss is required. (A similar value in electrostatic units would apply if the circularization is electrical rather than magnetic.) Earth’s equatorial surface field is about 0.5 gauss. The fields of Mars and Venus are less than 0.01 gauss. The Sun’s field is several gauss, ranging up to several hundred gauss in sunspots. Jupiter’s field as measured by Pioneer 10 is less than 10 gauss. Typical interplanetary fields are 10^?5 gauss. There is no way to generate anything approaching a 10 megagauss field on a large scale in the solar system. And there is no sign that such a field was ever experienced in the vicinity of Earth. We recall that the magnetic domains of molten rock in the course of refreezing are oriented by the prevailing field. Had Earth experienced, even fairly briefly, a 10 Mg field 3,500 years ago, rock magnetization evidence would show it clearly. It does not.

Carl Sagan

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[1] Chlorine is a deadly poison gas employed on European battlefields in World War I. Sodium is a corrosive metal which burns upon contact with water. Together they make a placid and unpoisonous material, table salt. Why each of these substances has the properties it does is a subject called chemistry, which requires more than 10 bits of information to understand.