Broca's Brain: The Romance of Science

APPENDIX 2

Q. Now, Mr. Bryan, have you ever pondered what would have happened to the Earth if it had stood still?

A. No. The God I believe in could have taken care of that, Mr. Darrow.

Q. Don’t you know that it would have been converted into a molten mass of matter?

A. You testify to that when you get on the stand. I will give you a chance.

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, τ, would Earth take to stop its rotation if the resulting deceleration were unnoticeable? Earth’s equatorial angular velocity is Ω = 2π/P = 7.3 × 10⁻⁵ radians/sec; the equatorial linear velocity is RΩ = 0.46 km/sec. Thus, τ = RΩ/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 ΔT 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 RΩ, ΔT 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.