ecliptic.jl

eceq06(day1::Float64, day2::Float64, lon::Float64, lat::Float64)

Transformation from ecliptic coordinates (mean equinox and ecliptic of date) to ICRS RA,Dec, using the IAU 2006 precession model.

Input

• day1 – TT as a 2-part Julian date
• day2 – ... Julian date (Note 1)
• lon – ecliptic longitude (radians)
• lat – ecliptic latitude (radians)

Output

• ras – ICRS right ascension (radians)
• dec – ICRS declination (radians)

Note

1. 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:

      day1          day2
   
   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.

2. No assumptions are made about whether the coordinates represent starlight and embody astrometric effects such as parallax or aberration.

3. The transformation is approximately that from ecliptic longitude and latitude (mean equinox and ecliptic of date) to mean J2000.0 right ascension and declination, with only frame bias (always less than 25 mas) to disturb this classical picture.

ecm06(day1::Float64, day2::Float64)

ICRS equatorial to ecliptic rotation matrix, IAU 2006.

Input

• day1 – TT as a 2-part Julian date (Note 1)
• day2 – ...Julian date (Note 1)

Output

• r – ICRS to ecliptic rotation matrix

Note

1. 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:

      day1          day2
   
   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.

2. The matrix is in the sense

   Eep = rm x PICRS,

   where PICRS is a vector with respect to ICRS right ascension and declination axes and Eep is the same vector with respect to the (inertial) ecliptic and equinox of date.

3. P_ICRS is a free vector, merely a direction, typically of unit magnitude, and not bound to any particular spatial origin, such as the Earth, Sun or SSB. No assumptions are made about whether it represents starlight and embodies astrometric effects such as parallax or aberration. The transformation is approximately that between mean J2000.0 right ascension and declination and ecliptic longitude and latitude, with only frame bias (always less than 25 mas) to disturb this classical picture.

eqec06(day1::Float64, day2::Float64, ras::Float64, dec::Float64)

Transformation from ICRS equatorial coordinates to ecliptic coordinates (mean equinox and ecliptic of date) using IAU 2006 precession model.

Input

• day1 – TT as a 2-part Julian date (Note 1)
• day2 – ... Julian date (Note 1)
• ras – ICRS right ascension (radians)
• dec – ICRS declination (radians)

Output

• lon – ecliptic longitude (radians)
• lat – ecliptic latitude (radians)

Note

1. The TT date date1+date2 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.

2. No assumptions are made about whether the coordinates represent starlight and embody astrometric effects such as parallax or aberration.

3. The transformation is approximately that from mean J2000.0 right ascension and declination to ecliptic longitude and latitude (mean equinox and ecliptic of date), with only frame bias (always less than 25 mas) to disturb this classical picture.

lteceq(epoch::Float64, lon::Float64, lat::Float64)

Transformation from ecliptic coordinates (mean equinox and ecliptic of date) to ICRS RA,Dec, using a long-term precession model.

Input

• epoch – Julian epoch (TT)
• lon – ecliptic longitude (radians)
• lat – ecliptic latitude (radians)

Output

• ras – ICRS right ascension (radians)
• dec – ICRS declination (radians)

Note

1. No assumptions are made about whether the coordinates represent starlight and embody astrometric effects such as parallax or aberration.

2. The transformation is approximately that from ecliptic longitude and latitude (mean equinox and ecliptic of date) to mean J2000.0 right ascension and declination, with only frame bias (always less than 25 mas) to disturb this classical picture.

3. The Vondrak et al. (2011, 2012) 400 millennia precession model agrees with the IAU 2006 precession at J2000.0 and stays within 100 microarcseconds during the 20th and 21st centuries. It is accurate to a few arcseconds throughout the historical period, worsening to a few tenths of a degree at the end of the +/- 200,000 year time span.

References

Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession expressions, valid for long time intervals, Astron.Astrophys. 534, A22

Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession expressions, valid for long time intervals (Corrigendum), Astron.Astrophys. 541, C1

ltecm(epoch::Float64)

ICRS equatorial to ecliptic rotation matrix, long-term.

Input

• epoch – Julian epoch (TT)

Output

• r – ICRS to ecliptic rotation matrix

Note

1. The matrix is in the sense

   Eep = rm x PICRS,

   where PICRS is a vector with respect to ICRS right ascension and declination axes and Eep is the same vector with respect to the (inertial) ecliptic and equinox of epoch epj.

2. P_ICRS is a free vector, merely a direction, typically of unit magnitude, and not bound to any particular spatial origin, such as the Earth, Sun or SSB. No assumptions are made about whether it represents starlight and embodies astrometric effects such as parallax or aberration. The transformation is approximately that between mean J2000.0 right ascension and declination and ecliptic longitude and latitude, with only frame bias (always less than 25 mas) to disturb this classical picture.

3. The Vondrak et al. (2011, 2012) 400 millennia precession model agrees with the IAU 2006 precession at J2000.0 and stays within 100 microarcseconds during the 20th and 21st centuries. It is accurate to a few arcseconds throughout the historical period, worsening to a few tenths of a degree at the end of the +/- 200,000 year time span.

References

Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession expressions, valid for long time intervals, Astron.Astrophys. 534, A22

Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession expressions, valid for long time intervals (Corrigendum), Astron.Astrophys. 541, C1

lteqec(epoch::Float64, ras::Float64, dec::Float64)

Transformation from ICRS equatorial coordinates to ecliptic coordinates (mean equinox and ecliptic of date) using a long-term precession model.

Input

• epoch – Julian epoch (TT)
• ras – ICRS right ascension (radians)
• dec – ICRS declination (radians)

Output

• lon – ecliptic longitude (radians)
• lat – ecliptic latitude (radians)

Note

1. No assumptions are made about whether the coordinates represent starlight and embody astrometric effects such as parallax or aberration.

2. The transformation is approximately that from mean J2000.0 right ascension and declination to ecliptic longitude and latitude (mean equinox and ecliptic of date), with only frame bias (always less than 25 mas) to disturb this classical picture.

3. The Vondrak et al. (2011, 2012) 400 millennia precession model agrees with the IAU 2006 precession at J2000.0 and stays within 100 microarcseconds during the 20th and 21st centuries. It is accurate to a few arcseconds throughout the historical period, worsening to a few tenths of a degree at the end of the +/- 200,000 year time span.

References

Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession expressions, valid for long time intervals, Astron.Astrophys. 534, A22

Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession expressions, valid for long time intervals (Corrigendum), Astron.Astrophys. 541, C1