rotations.jl

Astrometry.SOFA.ee00 — Function

ee00(day1::Float64, day2::Float64, ϵA::Float64, ψ::Float64)

The equation of the equinoxes, compatible with IAU 2000 resolutions, given the nutation in longitude and the mean obliquity.

Input

day1 – TT as Julian Date (Note 1)
day2 – ... as Julian Date
epsa – mean obliquity (Note 2)
dpsi – nutation in longitude (Note 3)

Output

ee – equation of the equinoxes (Note 4)

Note

The TT date day1+day2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:
```
   date1          date2

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.
The obliquity, in radians, is mean of date.
The result, which is in radians, operates in the following sense:
Greenwich apparent ST = GMST + equation of the equinoxes
The result is compatible with the IAU 2000 resolutions. For further details, see IERS Conventions 2003 and Capitaine et al. (2002).

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

source

Astrometry.SOFA.ee00a — Function

ee00a(day1::Float64, day2::Float64)

Equation of the equinoxes, compatible with IAU 2000 resolutions.

Input

day1 – TT as Julian Date (Note 1)
day2 – ... as Julian Date

Output

ee – equation of the equinoxes (Note 2)

Note

The TT date day1+day2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:
```
   date1          date2

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.
The result, which is in radians, operates in the following sense:
Greenwich apparent ST = GMST + equation of the equinoxes
The result is compatible with the IAU 2000 resolutions. For further details, see IERS Conventions 2003 and Capitaine et al. (2002).

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003).

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004).

source

Astrometry.SOFA.ee00b — Function

ee00b(day1::Float64, day2::Float64)

Equation of the equinoxes, compatible with IAU 2000 resolutions but using the truncated nutation model IAU 2000B.

Input

day1 – TT as Julian Date (Note 1)
day2 – ... as Julian Date

Output

ee – equation of the equinoxes (Note 2)

Note

The TT date day1+day2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:
```
   date1          date2

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.
The result, which is in radians, operates in the following sense:
Greenwich apparent ST = GMST + equation of the equinoxes
The result is compatible with the IAU 2000 resolutions except that accuracy has been compromised (1 mas) for the sake of speed. For further details, see McCarthy & Luzum (2003), IERS Conventions 2003 and Capitaine et al. (2003).

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003)

McCarthy, D.D. & Luzum, B.J., "An abridged model of the precession-nutation of the celestial pole", Celestial Mechanics & Dynamical Astronomy, 85, 37-49 (2003)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

source

Astrometry.SOFA.ee06a — Function

ee06a(day1::Float64, day2::Float64)

Equation of the equinoxes, compatible with IAU 2000 resolutions and IAU 2006/2000A precession-nutation.

Input

day1 – TT as Julian Date (Note 1)
day2 – ... as Julian Date

Output

ee – equation of the equinoxes (Note 2)

Note

The TT date day1+day2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:
```
   date1          date2

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.
The result, which is in radians, operates in the following sense:
Greenwich apparent ST = GMST + equation of the equinoxes

References

McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003), IERS Technical Note No. 32, BKG

source

Astrometry.SOFA.eect00 — Function

eect00(day1::Float64, day2::Float64)

Equation of the equinoxes complementary terms, consistent with IAU 2000 resolutions.

Input

day1 – TT as Julian Date (Note 1)
day2 – ... as Julian Date

Output

eect – complementary terms (Note 2)

Note

The TT date day1+day2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:
```
   date1          date2

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.
The "complementary terms" are part of the equation of the equinoxes (EE), classically the difference between apparent and mean Sidereal Time:
GAST = GMST + EE
with:
EE = dpsi * cos(eps)
where dpsi is the nutation in longitude and eps is the obliquity of date. However, if the rotation of the Earth were constant in an inertial frame the classical formulation would lead to apparent irregularities in the UT1 timescale traceable to side- effects of precession-nutation. In order to eliminate these effects from UT1, "complementary terms" were introduced in 1994 (IAU, 1994) and took effect from 1997 (Capitaine and Gontier, 1993):
GAST = GMST + CT + EE
By convention, the complementary terms are included as part of the equation of the equinoxes rather than as part of the mean Sidereal Time. This slightly compromises the "geometrical" interpretation of mean sidereal time but is otherwise inconsequential.
The present function computes CT in the above expression, compatible with IAU 2000 resolutions (Capitaine et al., 2002, and IERS Conventions 2003).

References

Capitaine, N. & Gontier, A.-M., Astron.Astrophys., 275, 645-650 (1993)

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astron.Astrophys., 406, 1135-1149 (2003)

IAU Resolution C7, Recommendation 3 (1994)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

source

Astrometry.SOFA.eqeq94 — Function

eqeq94(day1::Float64, day2::Float64)

Equation of the equinoxes, IAU 1994 model.

Input

day1 – TDB date (Note 1)
day2 – TDB date

Output

ee – equation of the equinoxes (Note 2)

Note

The date day1+day2 is a Julian Date, apportioned in any convenient way between the two arguments. For example, JD(TT)=2450123.7 could be expressed in any of these ways, among others:
```
   date1          date2

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 method is best matched to the way the argument is handled internally and will deliver the optimum resolution. The MJD method and the date & time methods are both good compromises between resolution and convenience.
The result, which is in radians, operates in the following sense:
Greenwich apparent ST = GMST + equation of the equinoxes

References

IAU Resolution C7, Recommendation 3 (1994).

Capitaine, N. & Gontier, A.-M., 1993, Astron.Astrophys., 275, 645-650.

source

Astrometry.SOFA.era00 — Function

era00(day1::Float64, day2::Float64)

Earth rotation angle (IAU 2000 model).

Input

day1 – UT1 as Julian Date (see note)
day2 – ... as Julian Date

Output

era – Earth rotation angle (radians), range 0-2pi

Note

The UT1 date dj1+dj2 is a Julian Date, apportioned in any convenient way between the arguments dj1 and dj2. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:
```
    dj1            dj2

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. The date & time method is best matched to the algorithm used: maximum precision is delivered when the dj1 argument is for 0hrs UT1 on the day in question and the dj2 argument lies in the range 0 to 1, or vice versa.
The algorithm is adapted from Expression 22 of Capitaine et al.
1. The time argument has been expressed in days directly, and,
to retain precision, integer contributions have been eliminated. The same formulation is given in IERS Conventions (2003), Chap. 5, Eq. 14.

References

Capitaine N., Guinot B. and McCarthy D.D, 2000, Astron. Astrophys., 355, 398-405.

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

source

Astrometry.SOFA.gmst00 — Function

gmst00(ut1::Float64, ut2::Float64, tt1::Float64, tt2::Float64)

Greenwich mean sidereal time (model consistent with IAU 2000 resolutions).

Input

uta – UT1 as Julian Date (Notes 1,2)
utb – ... as Julian Date
tta – TT as Julian Date (Notes 1,2)
ttb – ... as Julian Date

Output

gmst – Greenwich mean sidereal time (radians)

Note

The UT1 and TT dates uta+utb and tta+ttb respectively, are both Julian Dates, apportioned in any convenient way between the argument pairs. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:
```
   Part A         Part B

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable (in the case of UT; the TT is not at all critical in this respect). The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth Rotation Angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.
Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to predict the effects of precession. If UT1 is used for both purposes, errors of order 100 microarcseconds result.
This GMST is compatible with the IAU 2000 resolutions and must be used only in conjunction with other IAU 2000 compatible components such as precession-nutation and equation of the equinoxes.
The result is returned in the range 0 to 2pi.
The algorithm is from Capitaine et al. (2003) and IERS Conventions

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

source

Astrometry.SOFA.gmst06 — Function

gmst06(ut1::Float64, ut2::Float64, tt1::Float64, tt2::Float64)

Greenwich mean sidereal time (consistent with IAU 2006 precession).

Input

uta – UT1 as Julian Date (Notes 1,2)
utb – ... as Julian Date
tta – TT as Julian Date (Notes 1,2)
ttb – ... as Julian Date

Output

gmst – Greenwich mean sidereal time (radians)

Note

The UT1 and TT dates uta+utb and tta+ttb respectively, are both Julian Dates, apportioned in any convenient way between the argument pairs. For example, JD=2450123.7 could be expressed in any of these ways, among others:
```
   Part A        Part B

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable (in the case of UT; the TT is not at all critical in this respect). The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth rotation angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.
Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to predict the effects of precession. If UT1 is used for both purposes, errors of order 100 microarcseconds result.
This GMST is compatible with the IAU 2006 precession and must not be used with other precession models.
The result is returned in the range 0 to 2pi.

References

Capitaine, N., Wallace, P.T. & Chapront, J., 2005, Astron.Astrophys. 432, 355

source

Astrometry.SOFA.gmst82 — Function

gmst82(day1::Float64, day2::Float64)

Universal Time to Greenwich mean sidereal time (IAU 1982 model).

Input

day1 – UT1 Julian Date (see note)
day2 – ... Julian Date

Output

gmst – Greenwich mean sidereal time (radians)

Note

The UT1 date dj1+dj2 is a Julian Date, apportioned in any convenient way between the arguments dj1 and dj2. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:
```
    dj1            dj2

2450123.7          0          (JD method)
 2451545        -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5         0.2         (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. The date & time method is best matched to the algorithm used: maximum accuracy (or, at least, minimum noise) is delivered when the dj1 argument is for 0hrs UT1 on the day in question and the dj2 argument lies in the range 0 to 1, or vice versa.
The algorithm is based on the IAU 1982 expression. This is always described as giving the GMST at 0 hours UT1. In fact, it gives the difference between the GMST and the UT, the steady 4-minutes-per-day drawing-ahead of ST with respect to UT. When whole days are ignored, the expression happens to equal the GMST at 0 hours UT1 each day.
In this function, the entire UT1 (the sum of the two arguments dj1 and dj2) is used directly as the argument for the standard formula, the constant term of which is adjusted by 12 hours to take account of the noon phasing of Julian Date. The UT1 is then added, but omitting whole days to conserve accuracy.

References

Transactions of the International Astronomical Union, XVIII B, 67 (1983).

Aoki et al., Astron.Astrophys., 105, 359-361 (1982).

source

Astrometry.SOFA.gst00a — Function

gst00a(ut1::Float64, ut2::Float64, tt1::Float64, tt2::Float64)

Greenwich apparent sidereal time (consistent with IAU 2000 resolutions).

Input

uta – UT1 as Julian Date (Notes 1,2)
utb – ... as Julian Date
tta – TT as Julian Date (Notes 1,2)
ttb – ... as Julian Date

Output

gst – Greenwich apparent sidereal time (radians)

Note

The UT1 and TT dates uta+utb and tta+ttb respectively, are both Julian Dates, apportioned in any convenient way between the argument pairs. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:
```
    uta            utb

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable (in the case of UT; the TT is not at all critical in this respect). The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth Rotation Angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.
Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to predict the effects of precession-nutation. If UT1 is used for both purposes, errors of order 100 microarcseconds result.
This GAST is compatible with the IAU 2000 resolutions and must be used only in conjunction with other IAU 2000 compatible components such as precession-nutation.
The result is returned in the range 0 to 2pi.
The algorithm is from Capitaine et al. (2003) and IERS Conventions

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

source

Astrometry.SOFA.gst00b — Function

gst00b(ut1::Float64, ut2::Float64)

Greenwich apparent sidereal time (consistent with IAU 2000 resolutions but using the truncated nutation model IAU 2000B).

Input

uta – UT1 as Julian Date (Notes 1,2)
utb – ... as Julian Date

Output

gst – Greenwich apparent sidereal time (radians)

Note

The UT1 date uta+utb is a Julian Date, apportioned in any convenient way between the argument pair. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:
```
    uta            utb

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth Rotation Angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.
The result is compatible with the IAU 2000 resolutions, except that accuracy has been compromised for the sake of speed and convenience in two respects:
. UT is used instead of TDB (or TT) to compute the precession component of GMST and the equation of the equinoxes. This results in errors of order 0.1 mas at present.
. The IAU 2000B abridged nutation model (McCarthy & Luzum, 2003) is used, introducing errors of up to 1 mas.
This GAST is compatible with the IAU 2000 resolutions and must be used only in conjunction with other IAU 2000 compatible components such as precession-nutation.
The result is returned in the range 0 to 2pi.
The algorithm is from Capitaine et al. (2003) and IERS Conventions

References

Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to implement the IAU 2000 definition of UT1", Astronomy & Astrophysics, 406, 1135-1149 (2003)

McCarthy, D.D. & Luzum, B.J., "An abridged model of the precession-nutation of the celestial pole", Celestial Mechanics & Dynamical Astronomy, 85, 37-49 (2003)

McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003), IERS Technical Note No. 32, BKG (2004)

source

Astrometry.SOFA.gst06 — Function

gst06(ut1a::Float64, ut1b::Float64, tta::Float64, ttb::Float64,
      r::Matrix{Float64})

Greenwich apparent sidereal time, IAU 2006, given the NPB matrix.

Input

uta – UT1 as Julian Date (Notes 1,2)
utb – ... as Julian Date
tta – TT as Julian Date (Notes 1,2)
ttb – ... as Julian Date
rnpb – nutation x precession x bias matrix

Output

gst – Greenwich apparent sidereal time (radians)

Note

The UT1 and TT dates uta+utb and tta+ttb respectively, are both Julian Dates, apportioned in any convenient way between the argument pairs. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:
```
    uta            utb

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable (in the case of UT; the TT is not at all critical in this respect). The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth rotation angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.
Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to predict the effects of precession-nutation. If UT1 is used for both purposes, errors of order 100 microarcseconds result.
Although the function uses the IAU 2006 series for s+XY/2, it is otherwise independent of the precession-nutation model and can in practice be used with any equinox-based NPB matrix.
The result is returned in the range 0 to 2pi.

References

Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

source

Astrometry.SOFA.gst06a — Function

gst06a(ut1::Float64, ut2::Float64, tt1::Float64, tt2::Float64)

Greenwich apparent sidereal time (consistent with IAU 2000 and 2006 resolutions).

Input

uta – UT1 as Julian Date (Notes 1,2)
utb – ... as Julian Date
tta – TT as Julian Date (Notes 1,2)
ttb – ... as Julian Date

Output

gst – Greenwich apparent sidereal time (radians)

Note

The UT1 and TT dates uta+utb and tta+ttb respectively, are both Julian Dates, apportioned in any convenient way between the argument pairs. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:
```
    uta            utb

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable (in the case of UT; the TT is not at all critical in this respect). The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth rotation angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.
Both UT1 and TT are required, UT1 to predict the Earth rotation and TT to predict the effects of precession-nutation. If UT1 is used for both purposes, errors of order 100 microarcseconds result.
This GAST is compatible with the IAU 2000/2006 resolutions and must be used only in conjunction with IAU 2006 precession and IAU 2000A nutation.
The result is returned in the range 0 to 2pi.

References

Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981

source

Astrometry.SOFA.gst94 — Function

gst94(ut1::Float64, ut2::Float64)

Greenwich apparent sidereal time (consistent with IAU 1982/94 resolutions).

Input

uta – UT1 as Julian Date (Notes 1,2)
utb – ... as Julian Date

Output

gst – Greenwich apparent sidereal time (radians)

Note

The UT1 date uta+utb is a Julian Date, apportioned in any convenient way between the argument pair. For example, JD(UT1)=2450123.7 could be expressed in any of these ways, among others:
```
    uta            utb

2450123.7           0.0       (JD method)
2451545.0       -1421.3       (J2000 method)
2400000.5       50123.2       (MJD method)
2450123.5           0.2       (date & time method)
```
The JD method is the most natural and convenient to use in cases where the loss of several decimal digits of resolution is acceptable. The J2000 and MJD methods are good compromises between resolution and convenience. For UT, the date & time method is best matched to the algorithm that is used by the Earth Rotation Angle function, called internally: maximum precision is delivered when the uta argument is for 0hrs UT1 on the day in question and the utb argument lies in the range 0 to 1, or vice versa.
The result is compatible with the IAU 1982 and 1994 resolutions, except that accuracy has been compromised for the sake of convenience in that UT is used instead of TDB (or TT) to compute the equation of the equinoxes.
This GAST must be used only in conjunction with contemporaneous IAU standards such as 1976 precession, 1980 obliquity and 1982 nutation. It is not compatible with the IAU 2000 resolutions.
The result is returned in the range 0 to 2pi.

References

Explanatory Supplement to the Astronomical Almanac, P. Kenneth Seidelmann (ed), University Science Books (1992)

IAU Resolution C7, Recommendation 3 (1994)

source