[LEAPSECS] Reliability

[Rob Seaman]

M. Warner Losh wrote:


> Rob Seaman writes:

>

>> Apparent solar time is derived from mean solar time, not the other  

>> way around.

>>

>

> Can you explain this, since I thought it was the other way around...


We live in an empirical world.  When investigating the behavior of a  
class of objects (or processes, in astronomy the difference isn't  
always clear), measurements are often combined in weird and wonderful  
ways through population studies.  In that case, a measure of central  
tendency like the mean is taken as an estimator of a typical value for  
the class.

For instance, the cosmological distance ladder is built from large  
numbers of measurements of classes of objects like supernovae and  
cepheid variables.  One might also perform solar system studies on the  
population dynamics of different classes of asteroids or Kuiper belt  
objects.

Studying the orbital/rotational dynamics of a single object - for  
instance, the Earth - is different in that a measure of central  
tendency would be used to refine an estimate of a characteristic  
intrinsic to a single object, not of a class.

So the point of that preface is that the meaning of the word "mean"  
depends on the purpose of the exercise.

In particular, ignoring relativistic issues and perturbation theory  
and other stuff out of my depth, the orbital dynamics of the solar  
system have been a solved issue since Kepler and Newton and a lot of  
clever French mathematicians.

Like I keep saying, the mean solar day is trivial to compute from the  
sidereal day.  Look at it this way, there are "really" 366.25 days per  
year.  That extra day just gets sliced and diced among all the others.

Rather than mean solar time being some mysterious created artifact  
that is assembled out of vast numbers of independent "real"  
measurements of a time series of apparent solar positions in the sky,  
the apparent position of the sun is calculable from (and dependent on)  
the Earth's orbital parameters (e.g., semi-major axis and  
eccentricity), the tilt of its axis, the corresponding rates, and  
latitude and longitude.

To some extent it is just a point of view which are the independent  
and which are the dependent variables, but few are likely to choose  
the bizarre curlicues made by the Sun and planets on the celestial  
sphere as their fundamental coordinate system.

Instead, a handful of parameters describe the elliptical orbit of each  
of the planets.  The spinning planets (just angular velocity vectors)  
are layered on the orbits.  And the apparent position of each of the  
other solar system objects in the Earth's sky is a function of  
latitude and longitude layered on top of the Earth's spin and the two  
orbits in question.

It's the usual familiar layered architecture and the apparent position  
of the Sun is from a higher layer then the - so-called - mean  
position.  Astronomers confuse the issue by using phrases like  
"fictitious Sun", but then astronomical terminology is always upside- 
down and backwards.

Rob