# [time-nuts] Sidereal time

Bruce Griffiths bruce.griffiths at xtra.co.nz
Sat Jan 16 03:13:59 UTC 2010

```Magnus Danielson wrote:
> 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
>
> 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
>
> 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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>
Hej Magnus

No one bothers with such gear ratios for a modern telescope as its
cheaper to use a computer than have a set of custom gears made.
In any case, direct drive of the axes is sometimes used - no gears:
http://www.halfmann-teleskoptechnik.com/e_index.htm

Calculating the time is just the beginning if you want to point to
Saturn for which the RA and DEC vary over time and the simple model
isn't very accurate:
http://ssd.jpl.nasa.gov/horizons.cgi

Bruce

```