[LEAPSECS] Reliability

[Magnus Danielson]

Dear Brian,

blb8 at po.cwru.edu skrev:

>> From: Rob Seaman <seaman at noao.edu>

>> ...

>> 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.

> 

> Nice, now we have extra days!

> 

> A "leap year" is every four years except every one hundred years except every four hundred years.  Put another way, if Y is the number of the year then Y is a leap year if:  (Y%4==0)&&((Y%100!=0)||(Y%400==0)) where that's the modulus operator, of course.  In a four-hundred year cycle, that's 24 leap years per century except the start of the century (minus one), and then one leap year at the start of the millenium (minus one).

> 

> That's 303*365+97*366=146097 days for an average of 365.2425 days per year.  Woo!

> 

> I guess being on break for two weeks means I haven't gotten my fill of teaching arithmetic.


I think you have mixed up your solar days with sidereal days. The 
sidereal day is the time it takes the earth to turn 360 degrees, and to 
measure that one often uses a fix-star as reference. A sidereal day is 
is about 23 hours and 56 minutes long. A solar day is the time it takes 
for the earth to turn until the sun is at the same place in the sky 
(i.e. using the sun as the fix-star). These are not the same thing since 
we have a significant movement around the sun where as a more distant 
fix-star has a much less angular distorsion.

Your arthmetic describes solar days, but fails to describe the sidereal 
days.

The side-real day is important. The GPS satellite orbits is 11 hour and 
58 minutes long, so that their orbit around the world causes a near 
perfect re-tracing over the world.

So yes, we have an extra day, but since the earth turns in the direction 
is does the solar day count is one less.

Cheers,
Magnus