[time-nuts] Sidereal time

[jmfranke]

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" <magnus at rubidium.dyndns.org>
Sent: Friday, January 15, 2010 9:47 PM
To: <jfor at quik.com>; "Discussion of precise time and frequency measurement" 
<time-nuts at 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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