And to think, I just used a CD4046 phase locked loop to multiply a precise
60 Hz by 1465 and then divide the resultant 87,900 Hz by 1461 to get 60 Hz
times 1.00273785 or 60.164271 Hz to drive a digital clock. The error
between using 1.00273785 and 1.00273790934, as determined by Reid and
Honeycut, was only -0.005 seconds per day or -1.85 seconds per year.
John WA4WDL
--------------------------------------------------
From: "Magnus Danielson" <mag...@rubidium.dyndns.org>
Sent: Friday, January 15, 2010 9:47 PM
To: <j...@quik.com>; "Discussion of precise time and frequency measurement"
<time-nuts@febo.com>
Subject: Re: [time-nuts] Sidereal time
J. Forster wrote:
That's the point I was making earlier.
Most telescopes have a FOV of at least 15 arc-minutes. You only need to
get the guide stars into the field and go from there.
Also, a telescope's pointing can be off in BOTH RA and Dec. Dec has
nothing to do with siderial time.
While displaying Hour Minutes and Seconds of apparent local sidereal time
may be fun, the actual need is to calculate an angle in degrees and
minutes for which the object of interest position can be converted into
suitable pointing angle.
The simplest approximation can make use of the fact that on 365,25 normal
days, there is 366,25 sidreal days. The error of that approximation is
366,25/366,2425/365,25*365,2425 - 1 = -5,6E-8 days/day or -1,211 arcmin
per day or -0,44 arcmin per year. The Gregorian correction was used for
comparision value rather than a tabulated value, but I was lazy to get a
quick back-off-envelope type of result.
My point being that fairly simple approximate "gears" could be used to
give a good-enought result such that remaining drift can be compensated
using regular observation. Pointing towards known fix-stars for
calibration of local position, local pointing error and clock offset would
end up as a single correction factor of pointing angle correction.
The only thing one wants is that date, time and position sets the local
sidreal time close enought for manual correction to be a matter of minor
adjustments.
To convert the day (D) of a year into a sidreal day (DS) one gets
DS = D*366,25/365,25 = D + D/365,25
For hours we would use the relation HS = 24*DS, D = DI + H/24 and used
modulo 24
HS = 24*D + 24*D/365,25 = 24*DI + H + 24*D/365,25 = H + 24*D/365,25
Thus, the time of day is adjusted with the date, but there is no need to
calculate the full number of seconds. Similarly may the time of day be
converted to degrees.
AS = 360*DS mod 360 = 360*D + D*360/365,25 mod 360
= 360*DI + 15*H + DI*360/365,25 + H*15/365,25 mod 360
= 15*H + H*15/365,25 + DI*360/365,25 mod 360
H is then broken into HI, MI and SI for normal wall-clock representation.
This approximate convertion on the back-of-envelope level has silently
ignored the phase error, but retracing to the USNO webpage should allow a
more thorough calculation of a suitable offset.
The remaining mod 360 operation needs to handle the addition of three
0-360 degree ranges, so the range only needs to extend over 1080 degrees.
From the above formula it becomes apparent that the pointing needs an
adjustment of about a degree every day and about 2,464 arcmin every hour.
So, a very coarse calculation could be good enought. A fairly trivial
calculation with a correction from date and fine-correction for hour and
minute may provide enought pointing precission. It is trivial to correct
for local offset from the UTC time using the GPS position.
Should be doable even for a tiny processor. Should be not too hard to
include into a motor control to keep the scope pointed to the right point.
Cheers,
Magnus
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