The gravitational attraction which holds us to the Earth's surface has a
value of 10^3 cm sec^-2 = 1 g. A deceleration of a = 10^-2 g = 10 cm
sec^-2 is almost unnoticible. How much time, t, would Earth take to stop
its rotation if the resulting deceleration were unnoticible? Earth's
equatorial angular velocity is W = 2pi/P = 7.3 x 10^-5 radians/sec;
the equatorial linear velocity is RW = 0.46 km/sec. Thus t = RW/a = 4600
secs, or a little over an hour.
The specific energy of the Earth's rotation is:
E = 1/2 IW^2/M = (approx) 1/5(RW)^2 = (approx) 10^8 erg gm^1,
where I is the Earth's principle moment of inertia. Thes is less than the
latent heat of fusion of silicates, L = (approx) 4 x 10^9 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 = (approx) 8 x 10^6 erg
gm^-1 deg^-1, the stopping and restarting of Earth in one day would have
imparted an *average* temperature increment of dT = 2E/c = (approx) 100
deg 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 = (approx) RW, dT = (approx)v^2/c = (approx) 240 deg K.
It is doubtful that the inhabitants would have failed to notive so
dramatic a climatic change. The deceleration might be tolerable if
gradual enough, but not the heat (_Broca's Brain_, Appendix 2).
I have found this most amusing. Sagan seems to grant that God *could*
have slowed down the earth gradually enough so things didn't fly off into
space, but darned if he could do anything about the increased temperature!