Re: slowing down the earth's spin

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

> Barger and Olsson page 295 claim that the earth's rotation is slowing
> down at 44 ns per day due to tidal friction. ... they then say this
> amounts to 28 s/century. Unless I'm being really dumb (always
> possible, if not probable), this is about 4 orders of magnitude too
> large.

What Barger and Olson mean is the following:

The angular speed of the Earth is

   w = 2*pi/T

where T = 1 day.  It is changing at a rate

   alpha = dw/dt = -2*pi/T^2*(dT/dt)

where dT/dt = 44 ns/day

Thus, in a time t the earth spins through a total angle

   theta = w_o*t+(1/2)alpha*t^2

The last term represents the correction due to the acceleration.
Evaluating the correction we find that the Earth's cumulative
rotation differs from what it would have been by

  delta_theta = 1/2(-2*pi/(1 day)^2)*(44 ns/day)*(1 century)^2 = -2.13 mrad

This corresponds to a cumulative time difference of

  delta t = (0.213 mrad)*(1 day/2*pi rad) = 29 s.

--
   A. John Mallinckrodt        http://www.csupomona.edu/~ajm
   Professor of Physics      mailto:ajm@csupomona.edu
   Physics Department         voice:909-869-4054
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This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.