B.1.21 Times

Functions for conversion of time values between various forms. The forms used are

Modified Julian Date (MJD)

A continuous measure in days since midnight at the start of 17 November 1858. Based on UTC.

Julian Day (JD)

MJD plus a fixed offset of 2400000.5. The number of days since the notional creation of the universe, midday on 1 Jan 4713 BC.

ISO 8601

A string representation of the form yyyy-mm-ddThh:mm:ss.s, where the T is a literal character (a space character may be used instead). Based on UTC.

Julian Epoch

A continuous measure based on a Julian year of exactly 365.25 days. For approximate purposes this resembles the fractional number of years AD represented by the date. Sometimes (but not here) represented by prefixing a 'J'; J2000.0 is defined as 2000 January 1.5 in the TT timescale.

Besselian Epoch

A continuous measure based on a tropical year of about 365.2422 days. For approximate purposes this resembles the fractional number of years AD represented by the date. Sometimes (but not here) represented by prefixing a 'B'.

Decimal Year

Fractional number of years AD represented by the date. 2000.0, or equivalently 1999.99recurring, is midnight at the start of the first of January 2000. Because of leap years, the size of a unit depends on what year it is in.

Therefore midday on the 25th of October 2004 is 2004-10-25T12:00:00 in ISO 8601 format, 53303.5 as an MJD value, 2004.81588 as a Julian Epoch and 2004.81726 as a Besselian Epoch.

Currently this implementation cannot be relied upon to better than a millisecond.

isoToMjd( isoDate )

Converts an ISO8601 date string to Modified Julian Date. The basic format of the isoDate argument is yyyy-mm-ddThh:mm:ss.s, though some deviations from this form are permitted:

• The 'T' which separates date from time can be replaced by a space
• The seconds, minutes and/or hours can be omitted
• The decimal part of the seconds can be any length, and is optional
• The 'mm-dd' part may be replaced by a 3-digit day of year 'ddd'
• A 'Z' (which indicates UTC) may be appended to the time

Some legal examples are therefore: "1994-12-21T14:18:23.2", "1968-01-14", "2112-05-25 16:45Z", and "1987-172T22:12".

• Parameters:
  • isoDate (String): date in ISO 8601 format
• Return value
  • (floating point): modified Julian date corresponding to isoDate
• Examples:
  • isoToMjd("2004-10-25T18:00:00") = 53303.75
  • isoToMjd("1970-01-01") = 40587.0

dateToMjd( year, month, day, hour, min, sec )

Converts a calendar date and time to Modified Julian Date.

• Parameters:
  • year (integer): year AD
  • month (integer): index of month; January is 1, December is 12
  • day (integer): day of month (the first day is 1)
  • hour (integer): hour (0-23)
  • min (integer): minute (0-59)
  • sec (floating point): second (0<=sec<60)
• Return value
  • (floating point): modified Julian date corresponding to arguments
• Example:
  • dateToMjd(1999, 12, 31, 23, 59, 59.) = 51543.99998

dateToMjd( year, month, day )

Converts a calendar date to Modified Julian Date.

• Parameters:
  • year (integer): year AD
  • month (integer): index of month; January is 1, December is 12
  • day (integer): day of month (the first day is 1)
• Return value
  • (floating point): modified Julian date corresponding to 00:00:00 of the date specified by the arguments
• Example:
  • dateToMjd(1999, 12, 31) = 51543.0

decYearToMjd( decYear )

Converts a Decimal Year to a Modified Julian Date.

• Parameters:
  • decYear (floating point): decimal year
• Return value
  • (floating point): modified Julian Date
• Example:
  • decYearToMjd(2000.0) = 51544.0

isoToUnixSec( isoDate )

Converts an ISO8601 date string to seconds since 1970-01-01. The basic format of the isoDate argument is yyyy-mm-ddThh:mm:ss.s, though some deviations from this form are permitted:

• The 'T' which separates date from time can be replaced by a space
• The seconds, minutes and/or hours can be omitted
• The decimal part of the seconds can be any length, and is optional
• The 'mm-dd' part may be replaced by a 3-digit day of year 'ddd'
• A 'Z' (which indicates UTC) may be appended to the time

Some legal examples are therefore: "1994-12-21T14:18:23.2", "1968-01-14", "2112-05-25 16:45Z and "1987-172T22:12".

• Parameters:
  • isoDate (String): date in ISO 8601 format
• Return value
  • (floating point): seconds since the Unix epoch
• Examples:
  • isoToUnixSec("2004-10-25T18:00:00") = 1098727200
  • isoToUnixSec("1970-01-01") = 0

decYearToUnixSec( decYear )

Converts a Decimal Year to seconds since 1970-01-01.

• Parameters:
  • decYear (floating point): decimal year
• Return value
  • (floating point): seconds since the Unix epoch
• Examples:
  • decYearToUnixSec(2000.0) = 946684800
  • decYearToUnixSec(1970) = 0

mjdToUnixSec( mjd )

Converts a Modified Julian Date to seconds since 1970-01-01.

• Parameters:
  • mjd (floating point): modified Julian date
• Return value
  • (floating point): seconds since the Unix epoch

jdToUnixSec( jd )

Converts a Julian day to seconds since 1970-01-01.

• Parameters:
  • jd (floating point): Julian day
• Return value
  • (floating point): seconds since the Unix epoch

mjdToIso( mjd )

Converts a Modified Julian Date value to an ISO 8601-format date-time string. The output format is yyyy-mm-ddThh:mm:ss. If the result predates the Common Era, the string "(BCE)" is prepended.

• Parameters:
  • mjd (floating point): modified Julian date
• Return value
  • (String): ISO 8601 format date corresponding to mjd
• Example:
  • mjdToIso(53551.72917) = "2005-06-30T17:30:00"

mjdToDate( mjd )

Converts a Modified Julian Date value to an ISO 8601-format date string. The output format is yyyy-mm-dd. If the result predates the Common Era, the string "(BCE)" is prepended.

• Parameters:
  • mjd (floating point): modified Julian date
• Return value
  • (String): ISO 8601 format date corresponding to mjd
• Example:
  • mjdToDate(53551.72917) = "2005-06-30"

mjdToTime( mjd )

Converts a Modified Julian Date value to an ISO 8601-format time-only string. The output format is hh:mm:ss.

• Parameters:
  • mjd (floating point): modified Julian date
• Return value
  • (String): ISO 8601 format time corresponding to mjd
• Example:
  • mjdToTime(53551.72917) = "17:30:00"

mjdToDecYear( mjd )

Converts a Modified Julian Date to Decimal Year.

• Parameters:
  • mjd (floating point): modified Julian Date
• Return value
  • (floating point): decimal year
• Example:
  • mjdToDecYear(0.0) = 1858.87671

formatMjd( mjd, format )

Converts a Modified Julian Date value to a date using a customisable date format. The format is as defined by the java.text.SimpleDateFormat class. The default output corresponds to the string "yyyy-MM-dd'T'HH:mm:ss"

Note that the output from certain formatting characters (such as MMM for month, EEE for day of week) is dependent on your locale (system language settings). The output time zone however always corresponds to UTC.

• Parameters:
  • mjd (floating point): modified Julian date
  • format (String): formatting patttern
• Return value
  • (String): custom formatted time corresponding to mjd
• Examples:
  • formatMjd(50000.3, "EEE dd, MMM, yy") = "Tue 10 Oct, 95"
  • formatMjd(50000.1234, "'time 'H:mm:ss.SSS") = "time 2:57:41.760"

jdToMjd( jd )

Converts a Julian Day to Modified Julian Date. The calculation is simply jd-2400000.5.

• Parameters:
  • jd (floating point): Julian day number
• Return value
  • (floating point): MJD value

mjdToJd( mjd )

Converts a Modified Julian Date to Julian Day. The calculation is simply jd+2400000.5.

• Parameters:
  • mjd (floating point): MJD value
• Return value
  • (floating point): Julian day number

mjdToJulian( mjd )

Converts a Modified Julian Date to Julian Epoch. For approximate purposes, the result of this routine consists of an integral part which gives the year AD and a fractional part which represents the distance through that year, so that for instance 2000.5 is approximately 1 July 2000.

• Parameters:
  • mjd (floating point): modified Julian date
• Return value
  • (floating point): Julian epoch
• Example:
  • mjdToJulian(0.0) = 1858.87885

julianToMjd( julianEpoch )

Converts a Julian Epoch to Modified Julian Date. For approximate purposes, the argument of this routine consists of an integral part which gives the year AD and a fractional part which represents the distance through that year, so that for instance 2000.5 is approximately 1 July 2000.

• Parameters:
  • julianEpoch (floating point): Julian epoch
• Return value
  • (floating point): modified Julian date
• Example:
  • julianToMjd(2000.0) = 51544.5

mjdToBesselian( mjd )

Converts Modified Julian Date to Besselian Epoch. For approximate purposes, the result of this routine consists of an integral part which gives the year AD and a fractional part which represents the distance through that year, so that for instance 1950.5 is approximately 1 July 1950.

• Parameters:
  • mjd (floating point): modified Julian date
• Return value
  • (floating point): Besselian epoch
• Example:
  • mjdToBesselian(0.0) = 1858.87711

besselianToMjd( besselianEpoch )

Converts Besselian Epoch to Modified Julian Date. For approximate purposes, the argument of this routine consists of an integral part which gives the year AD and a fractional part which represents the distance through that year, so that for instance 1950.5 is approximately 1 July 1950.

• Parameters:
  • besselianEpoch (floating point): Besselian epoch
• Return value
  • (floating point): modified Julian date
• Example:
  • besselianToMjd(1950.0) = 33281.92346

unixMillisToMjd( unixMillis )

Converts from milliseconds since the Unix epoch (1970-01-01T00:00:00) to a modified Julian date value

• Parameters:
  • unixMillis (long integer): milliseconds since the Unix epoch
• Return value
  • (floating point): modified Julian date

mjdToUnixMillis( mjd )

Converts from modified Julian date to milliseconds since the Unix epoch (1970-01-01T00:00:00).

• Parameters:
  • mjd (floating point): modified Julian date
• Return value
  • (long integer): milliseconds since the Unix epoch

MJD_OFFSET

JD value for MJD = 0 (=2400000.5).