[LEAPSECS] Straw men

[Rob Seaman]

Warner Losh wrote:


> I'm asking for either of the plots, rescaled with a second based on the average second of 1900 rather than on the average second of 1820ish that newcomb's second (which is what the SI second wound up being based on) wound up being based on…


The y-axis is length-of-day (that is, the synodic day) minus a constant.  Changing the constant just relabels the axis.  Or print it out and draw a horizontal line as a new x-axis with a ruler passing through the point corresponding to the epoch you want.


> Another way of asking the question is 'what would the rate of leap seconds (or slope of TAI - UT or TT-UT)' if the definition of a second gave is an average LOD - 86400s of more like 1ms or 100us.


Integrate (over the period in question) between the line drawn above and the curve.  Area above the line is positive leap seconds (Earth slow), below the line negative (Earth fast).  TAI, TT, etc. don't enter here.

Cheap estimate of the area is to draw the rectangle corresponding to some decade that looks like it has the same area as the irregular curve.  The boundary should pass somewhere in the middle of the seasonal variations.  So just eyeballing the 1990's on http://ucolick.org/~sla/leapsecs/amsci.pdf it looks like the height of the rectangle relative to that x-axis is 1.8 ms per day.  (Tough since the decade starts out slowing but then speeds up.)

Take the reciprocal of 0.0018 and there should be a leap second every 555 days or about 6.5 over the decade.  Steve has helpfully marked the leap seconds with dotted lines.  There were seven in the 90's (not counting the one at the start).  By relabeling the graph the height of the rectangle is simply changed.*  The height actually is the rate:

	number per decade = height (ms) X 3.65

(Canceling the thousands top and bottom.)


Rob

* Could improve the integration by using triangles, but no need to reinvent Numerical Recipes.