Index: /trunk/doc/pslib/psLibADD.tex =================================================================== --- /trunk/doc/pslib/psLibADD.tex (revision 1617) +++ /trunk/doc/pslib/psLibADD.tex (revision 1618) @@ -1,3 +1,3 @@ -%%% $Id: psLibADD.tex,v 1.30 2004-08-24 19:32:18 eugene Exp $ +%%% $Id: psLibADD.tex,v 1.31 2004-08-25 04:36:56 price Exp $ \documentclass[panstarrs]{panstarrs} @@ -694,17 +694,227 @@ Correct time representation is critical in astronomical software. -PSLib uses the \code{psTime} structure to represent all time values. -This structure represents a time which is consists of seconds and -fractions of seconds in a time system defined by the \code{psTimeType} -element \code{type}. Two possible time systems are currently -available: TAI and UTC. Both are defined in terms of the reference -epoch 1970-01-01T00:00:00Z, but with minor modifications for -leap-seconds as needed. The first represenatation, TAI (International -Atomic Time), has seconds of uniform length and no leap seconds. The -exact zero reference is 1970/01/01,00:00:10 UTC. The second -representations is UTC, which has seconds of uniform length and -leap-seconds as needed to adjust it to remain within 0.9 seconds of -the Earth's rotation. It has a zero-point of exactly -1970/01/01,00:00:00 UTC. +PSLib uses the \code{psTime} structure to represent time values. This +structure represents a time which is consists of seconds and fractions +of seconds in a time system defined by the \code{psTimeType} element +\code{type}. Two possible time systems are currently available: TAI +and UTC. Both are defined in terms of the reference epoch +1970-01-01T00:00:00Z, but with minor modifications for leap seconds as +needed. The first represenatation, TAI (International Atomic Time), +has seconds of uniform length and no leap seconds. The exact zero +reference is 1970/01/01,00:00:10 UTC. The second representation is +UTC, which has seconds of uniform length and leap seconds as needed to +adjust it to remain within 0.9 seconds of the Earth's rotation. It +has a zero-point of exactly 1970/01/01,00:00:00 UTC. + + +The conversion from a time and longitude to local mean sidereal time +is performed using the SLALib function \code{sla_GMST}. +\paragraph{Coordinated Universal Time (UTC)} + +Coordinated Univeral Time (UTC) is a system of time with SI length +seconds but attempts to stay within 1s of UT1. This is done by the +insertion of leap second whenever UTC-UT1 $\ge$ 0.9s. By definition +UTC-TAI is an integer number of seconds. UTC went into effect on +"1972-01-01T00:00:00" and is defined as being UTC-TAI = 10s on that +date. For dates prior to 1972-01-01 a fixed offset of +10s relative +to TAI will be assumed. + +\begin{equation} +UTC = TAI + 10s + leapseconds +\end{equation} + +Leapseconds are declared by the International Earth Rotation and +Reference Systems Service (IERS). Leapseconds only occur in the UTC +time system and cannot be accurately predicted due to variations in +the Earth's rotational period. To determine the number of leapsecond +in a given UTC date a table of leapseconds as annouced by the IERS +must be consulted. This table will have to be updated each time a new +leapsecond occurs. + +For ease of conversion, UTC should be represented as the number of +seconds since the UNIX epoch of "1970-01-01T00:00:00". + +\paragraph{International Atomic Time (TAI)} + +International Atomic Time or Temps Atomique International (TAI) is a +system of time defined by the Bureau International des Poids et +Mesures (BIPM) with SI length seconds as measured at sea level. To +convert from UTC to TAI subtract the base delta of $10s$ and all of +the accumulated leapsecons since 1972-01-01 up until the UTC date +being converted. + +\begin{equation} +{\rm TAI} = {\rm UTC} - 10{\rm s} - {\rm leapseconds} +\end{equation} + +For ease of conversion, TAI should be represented as the number of +seconds since the UNIX epoch of "1970-01-01T00:00:00". + +\paragraph{Leap seconds} + +Leap seconds keep UTC within 0.9s of UT1. The offset between TAI and +UTC must be looked up from tables. Jumps in the offset correspond to +leap seconds. + +\begin{verbatim} + 1972 JUL 1 =JD 2441499.5 TAI-UTC= 11.0 S + (MJD - 41317.) X 0.0 S + 1973 JAN 1 =JD 2441683.5 TAI-UTC= 12.0 S + (MJD - 41317.) X 0.0 S + 1974 JAN 1 =JD 2442048.5 TAI-UTC= 13.0 S + (MJD - 41317.) X 0.0 S + 1975 JAN 1 =JD 2442413.5 TAI-UTC= 14.0 S + (MJD - 41317.) X 0.0 S + 1976 JAN 1 =JD 2442778.5 TAI-UTC= 15.0 S + (MJD - 41317.) X 0.0 S + 1977 JAN 1 =JD 2443144.5 TAI-UTC= 16.0 S + (MJD - 41317.) X 0.0 S + 1978 JAN 1 =JD 2443509.5 TAI-UTC= 17.0 S + (MJD - 41317.) X 0.0 S + 1979 JAN 1 =JD 2443874.5 TAI-UTC= 18.0 S + (MJD - 41317.) X 0.0 S + 1980 JAN 1 =JD 2444239.5 TAI-UTC= 19.0 S + (MJD - 41317.) X 0.0 S + 1981 JUL 1 =JD 2444786.5 TAI-UTC= 20.0 S + (MJD - 41317.) X 0.0 S + 1982 JUL 1 =JD 2445151.5 TAI-UTC= 21.0 S + (MJD - 41317.) X 0.0 S + 1983 JUL 1 =JD 2445516.5 TAI-UTC= 22.0 S + (MJD - 41317.) X 0.0 S + 1985 JUL 1 =JD 2446247.5 TAI-UTC= 23.0 S + (MJD - 41317.) X 0.0 S + 1988 JAN 1 =JD 2447161.5 TAI-UTC= 24.0 S + (MJD - 41317.) X 0.0 S + 1990 JAN 1 =JD 2447892.5 TAI-UTC= 25.0 S + (MJD - 41317.) X 0.0 S + 1991 JAN 1 =JD 2448257.5 TAI-UTC= 26.0 S + (MJD - 41317.) X 0.0 S + 1992 JUL 1 =JD 2448804.5 TAI-UTC= 27.0 S + (MJD - 41317.) X 0.0 S + 1993 JUL 1 =JD 2449169.5 TAI-UTC= 28.0 S + (MJD - 41317.) X 0.0 S + 1994 JUL 1 =JD 2449534.5 TAI-UTC= 29.0 S + (MJD - 41317.) X 0.0 S + 1996 JAN 1 =JD 2450083.5 TAI-UTC= 30.0 S + (MJD - 41317.) X 0.0 S + 1997 JUL 1 =JD 2450630.5 TAI-UTC= 31.0 S + (MJD - 41317.) X 0.0 S + 1999 JAN 1 =JD 2451179.5 TAI-UTC= 32.0 S + (MJD - 41317.) X 0.0 S +\end{verbatim} + +For the present time, it should be assumed that this table resides on +local disk in a known location (i.e., there is no need that it is +downloaded from the internet by PSLib). Later, the location of this +file will be made configurable. + +This data is available from +\code{http://hpiers.obspm.fr/eop-pc/earthor/utc/TAI-UTC_tab.html} + +\paragraph{Gregorian dates to seconds} + +The below algorithm converts from Gregorian-formatted dates to +seconds since the UNIX epoch. + +\begin{verbatim} + Given year, month, day. + + ### Make month in range 3..14 (treat Jan & Feb as months 13..14 of prev year): + if ( month <= 2 ) + { + year -= ( temp = ( 14 - month ) / 12 ) + month += 12 * temp + } + else if ( month > 14 ) + { + year += ( temp = ( month - 3 ) / 12 ) + month -= 12 * temp + } + + ### make year positive + if ( year < 0 ) + { + day -= 146097 * ( temp = ( 399 - year ) / 400 ) + year += 400 * temp + } + + ### add: day of month, days of previous 0-11 month period that began + ### w/March, days of previous 0-399 year period that began w/March + ### of a 400-multiple year), days of any 400-year periods before + ### that, and 306 days to adjust from Mar 1, year 0-relative to Jan + ### 1, year 1-relative + day += ( month * 367 - 1094 ) / 12 + year % 100 * 1461 / 4 + + ( year / 100 * 36524 + year / 400 ) - 306 + + unix = ( ( day - 1 ) * 86400 ) - 62135596800 + utc = unix - leapseconds(unix) +\end{verbatim} + +To go the other way: + +\begin{verbatim} + unix = utc + leapseconds(utc) + day = ( unix + 62135596800 ) / 86400 + temp = 0 + + ### add 306 days to make relative to Mar 1, 0; also adjust day to be + ### within a range (1..2**28-1) where our calculations will work + ### with 32bit ints + if ( day > 2**28 - 307 ) + { + ### avoid overflow if day close to maxint + temp = ( day - 146097 + 306 ) / 146097 + 1 + day -= temp * 146097 - 306 + } + else if ( ( day += 306 ) <= 0 ) + { + temp = -( -day / 146097 + 1 ) ### avoid ambiguity in C division of negatives + day -= temp * 146097 + } + + cent = ( day * 4 - 1 ) / 146097 ### calc number of centuries day is after 29 Feb of yr 0 + day -= cent * 146097 / 4 ### (4 centuries = 146097 days) + year = ( day * 4 - 1 ) / 1461 ### calc number of years into the century, + day -= year * 1461 / 4 ### again March-based (4 yrs =~ 146[01] days) + month = ( day * 12 + 1093 ) / 367 ### get the month (3..14 represent March through + day -= ( month * 367 - 1094 ) / 12 ### February of following year) + year += cent * 100 + temp * 400 ### get the real year, which is off by + if ( month > 12 ) ### one if month is January or February + { + year++ + month -= 12 + } + + + Output year, month, day. +\end{verbatim} + +(Above taken from \code{DateTime.pm} (C) 2003 Dave Rolsky, available +from \code{datetime.perl.org}.) + + + +\paragraph{Universal Time (UT1)} +\label{sec:ut1} + +Univseral Time is a measure of the rotation angle of the Earth. When +corrected for polar motion it is referred to as UT1. This is distict +from UT0 which does not involve corrections for polar motion. + +The offset of UTC from UT1, $\Delta$ UT1 = UTC - UT1, may be +determined from the following site in real time: + +\code{ftp://maia.usno.navy.mil/ser7/finals.all} + +\noindent with explanatory guide at + +\code{ftp://maia.usno.navy.mil/ser7/readme.finals} + +See also the web page \code{http://maia.usno.navy.mil/}. The most +significant accuracy requirements are for the current value when +calculating the LST. For this purpose, the table above +(\code{ser7.dat}), which provides predictions over a 2 month period, +must be made available locally to PSLib and updated regularly. + +For the present time, it should be assumed that this table resides on +local disk in a known location (i.e., there is no need that it is +downloaded from the internet by PSLib). Later, the location of this +file will be made configurable. + +For dates within the range of the table, the value for the offset +between UTC and UT1 shall be derived from linear interpolation between +the nearest entries in the table. For dates earlier the range of the +above table, a warning shall be generated, and the values calculated +from a different table (an estimate, instead of observations), +obtained from: + +\code{http://hpiers.obspm.fr/eoppc/eop/eopc01/eopc01.1900-2004} + +Dates outside the ranges of the above tables shall generate an error. + +These tables shall be read in only when required by the user, and +shall remain in memory until the termination of the program. An +additional function, \code{psTimeTableReset} should be provided in +order to force the reloading of the time tables. + +\paragraph{Julian Day and Modified Julian Day} Julian Day (JD) and Modified Julian Day (MJD) are both continuous time @@ -716,65 +926,87 @@ \begin{verbatim} -mjd = psTime.tv_sec/86400.0 + psTime.tv_usec/86400000000.0 + 40587.0; - jd = psTime.tv_sec/86400.0 + psTime.tv_usec/86400000000.0 + 2440587.5; +mjd = psTime.sec/86400.0 + psTime.usec/86400000000.0 + 40587.0; + jd = psTime.sec/86400.0 + psTime.usec/86400000000.0 + 2440587.5; \end{verbatim} -The entry below gives the current relationship between JD, MJD, UTC, -and TAI, and comes from the reference at -\code{http://tycho.usno.navy.mil/leapsec.html} - -\begin{verbatim} - 1961 JAN 1 =JD 2437300.5 TAI-UTC= 1.4228180 S + (MJD - 37300.) X 0.001296 S - 1961 AUG 1 =JD 2437512.5 TAI-UTC= 1.3728180 S + (MJD - 37300.) X 0.001296 S - 1962 JAN 1 =JD 2437665.5 TAI-UTC= 1.8458580 S + (MJD - 37665.) X 0.0011232S - 1963 NOV 1 =JD 2438334.5 TAI-UTC= 1.9458580 S + (MJD - 37665.) X 0.0011232S - 1964 JAN 1 =JD 2438395.5 TAI-UTC= 3.2401300 S + (MJD - 38761.) X 0.001296 S - 1964 APR 1 =JD 2438486.5 TAI-UTC= 3.3401300 S + (MJD - 38761.) X 0.001296 S - 1964 SEP 1 =JD 2438639.5 TAI-UTC= 3.4401300 S + (MJD - 38761.) X 0.001296 S - 1965 JAN 1 =JD 2438761.5 TAI-UTC= 3.5401300 S + (MJD - 38761.) X 0.001296 S - 1965 MAR 1 =JD 2438820.5 TAI-UTC= 3.6401300 S + (MJD - 38761.) X 0.001296 S - 1965 JUL 1 =JD 2438942.5 TAI-UTC= 3.7401300 S + (MJD - 38761.) X 0.001296 S - 1965 SEP 1 =JD 2439004.5 TAI-UTC= 3.8401300 S + (MJD - 38761.) X 0.001296 S - 1966 JAN 1 =JD 2439126.5 TAI-UTC= 4.3131700 S + (MJD - 39126.) X 0.002592 S - 1968 FEB 1 =JD 2439887.5 TAI-UTC= 4.2131700 S + (MJD - 39126.) X 0.002592 S - 1972 JAN 1 =JD 2441317.5 TAI-UTC= 10.0 S + (MJD - 41317.) X 0.0 S - 1972 JUL 1 =JD 2441499.5 TAI-UTC= 11.0 S + (MJD - 41317.) X 0.0 S - 1973 JAN 1 =JD 2441683.5 TAI-UTC= 12.0 S + (MJD - 41317.) X 0.0 S - 1974 JAN 1 =JD 2442048.5 TAI-UTC= 13.0 S + (MJD - 41317.) X 0.0 S - 1975 JAN 1 =JD 2442413.5 TAI-UTC= 14.0 S + (MJD - 41317.) X 0.0 S - 1976 JAN 1 =JD 2442778.5 TAI-UTC= 15.0 S + (MJD - 41317.) X 0.0 S - 1977 JAN 1 =JD 2443144.5 TAI-UTC= 16.0 S + (MJD - 41317.) X 0.0 S - 1978 JAN 1 =JD 2443509.5 TAI-UTC= 17.0 S + (MJD - 41317.) X 0.0 S - 1979 JAN 1 =JD 2443874.5 TAI-UTC= 18.0 S + (MJD - 41317.) X 0.0 S - 1980 JAN 1 =JD 2444239.5 TAI-UTC= 19.0 S + (MJD - 41317.) X 0.0 S - 1981 JUL 1 =JD 2444786.5 TAI-UTC= 20.0 S + (MJD - 41317.) X 0.0 S - 1982 JUL 1 =JD 2445151.5 TAI-UTC= 21.0 S + (MJD - 41317.) X 0.0 S - 1983 JUL 1 =JD 2445516.5 TAI-UTC= 22.0 S + (MJD - 41317.) X 0.0 S - 1985 JUL 1 =JD 2446247.5 TAI-UTC= 23.0 S + (MJD - 41317.) X 0.0 S - 1988 JAN 1 =JD 2447161.5 TAI-UTC= 24.0 S + (MJD - 41317.) X 0.0 S - 1990 JAN 1 =JD 2447892.5 TAI-UTC= 25.0 S + (MJD - 41317.) X 0.0 S - 1991 JAN 1 =JD 2448257.5 TAI-UTC= 26.0 S + (MJD - 41317.) X 0.0 S - 1992 JUL 1 =JD 2448804.5 TAI-UTC= 27.0 S + (MJD - 41317.) X 0.0 S - 1993 JUL 1 =JD 2449169.5 TAI-UTC= 28.0 S + (MJD - 41317.) X 0.0 S - 1994 JUL 1 =JD 2449534.5 TAI-UTC= 29.0 S + (MJD - 41317.) X 0.0 S - 1996 JAN 1 =JD 2450083.5 TAI-UTC= 30.0 S + (MJD - 41317.) X 0.0 S - 1997 JUL 1 =JD 2450630.5 TAI-UTC= 31.0 S + (MJD - 41317.) X 0.0 S - 1999 JAN 1 =JD 2451179.5 TAI-UTC= 32.0 S + (MJD - 41317.) X 0.0 S -\end{verbatim} - -The conversion from a time and longitude to local mean sidereal time -is performed using the SLA Lib function \code{sla_GMST}. This -function requires the value $\Delta$ UT1 = UTC - UT1. The value of -$\Delta$ UT1 may be determined from the following site in real time: - -\code{ftp://maia.usno.navy.mil/ser7/ser7.dat} - -In addition, the long-term values may be determined from the table -found at: \code{ftp://maia.usno.navy.mil/ser7/finals.all}. See also -the web page \code{http://maia.usno.navy.mil/}. The most significant -accuracy requirements are for the current value when calculating the -LST. For this purpose, the table above (\code{ser7.dat}), which -provides predictions over a 2 month period, must be made available -locally to PSLib and updated regularly. +$2451545.0$ JD $= 51544.5$ MJD is equivalent to "2000-01-01T00:00:00". + +\begin{equation} +{\rm JD} = {\rm MJD} + 2400000.5 +\end{equation} + +\paragraph{Terrestrial Dynamical Time (TDT)} + +Terrestrial Dynamical Time (TDT) is defined as a fixed offset from +TAI. Its only purpose as far as we are concerned is for its utility +in obtaining the GMST. + +\begin{equation} +{\rm TDT} = {\rm TAI} + 32.184{\rm s} +\end{equation} + +\paragraph{TDT as Julian Centuries since J2000.0} + +The algorithm for calulating GMST requires TDT formated in Julian centruies +since the J2000.0 epoch. + +\begin{equation} +t_u = \frac{{\rm JD} - 2451545.0}{36525} +\end{equation} + +\paragraph{UT1 as Julian Centuries since J2000.0} + +The algorithm for calulating GMST requires UT1 be formated in Julian +centuries since the J2000.0 epoch. + +\begin{equation} +t = \frac{{\rm JD} - 2451545.0}{36525} +\end{equation} + +\paragraph{Greenwich Mean Sidereal Time (GMST)} + +Greenwich Mean Sidereal Time (GMST) is caclulated from UT1 and TDT. +This algorithm requires that both time inputs are expressed as Julian +centuries since J2000.0. + +Here $t_u$ is UT1 expressed in Julian centuries since J2000.0, and $t$ +is TDT expressed in Julian centuries since J2000.0. + +\begin{eqnarray} +{\rm GMST00}(t_u, t) & = & UT1 + 24110.5493771\\ +& & + 8639877.3173760\, t_u + 307.4771600\, t\\ +& & + 0.0931118\, t^2 - 0.0000062\, t^3\\ +& & + 0.0000013\, t^4 +\end{eqnarray} + +Gives $GMST00$ in seconds. + +\paragraph{Longitude} + +Longitudes are often expressed in the form of decimal degrees while the +algorithm for calculating GMST outputs seconds. + +\begin{equation} +1\degree = 240s +\end{equation} + +\paragraph{Local Mean Sidereal Time (LMST)} + +Local Mean Sidereal Time (LMST) is Greenwich Mean Sideral Time (GMST) +plus the observer's location in East longitude. Calculating LMST +requires the input of Universal Time (UT1), Terrestrial Dynamical Time +(TDT) and a longitude (measured East of Greenwich). + +\begin{equation} +LMST = GMST00(t_u, t) + longitude +\end{equation} + +Gives $LMST$ in seconds. + +\paragraph{Polar Coordinates} + +The polar coordinates, $x_p$ and $y_p$, required for \code{SLA_AOPPA} +(and hence the \code{psGrommit}s), may be calculated in a similar +manner as for the offset of UT1 from UTC (\S\ref{sec:ut1}). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%