Broca's Brain - Carl Sagan [177]
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 cp = 8 × 106 erg gm−1 deg−1, the stopping and restarting of Earth in one day would have imparted an average temperature increment of ΔT 2E/cp 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 RΩ, ΔT v2/cp 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