All Gaia data processed by the Data Processing and Analysis Consortium
comes tagged with a solution identifier. This is a numeric field
attached to each table row that can be used to unequivocally identify
the version of all the subsystems that where used in the generation of
the data as well as the input data used. It is mainly for internal DPAC
use but is included in the published data releases to enable end users
to examine the provenance of processed data products. To decode a given
solution ID visit
A unique single numerical identifier of the source.
For the contents of Gaia DR1, which does not include Solar System
objects, the source ID consists consists of a 64-bit integer, least
significant bit = 1 and most significant bit = 64, comprising:
- a HEALPix index number (sky pixel) in bits 36 - 63; by definition
the smallest HEALPix index number is zero.
- a 2-bit Data Processing Centre code in bits 34 - 35; for example
MOD(sourceId / 4294967296, 8) can be used to distinguish between
sources initialised via the Initial Gaia Source List by the Torino
DPC (code = 0) and sources otherwise detected and assigned by Gaia
observations (code >0)
- a 25-bit plus 7 bit sequence number within the HEALPix pixel in bits
1 - 32 split into:
- a 25 bit running number in bits 8 – 32; the running numbers are
defined to be positive, i.e. never zero (except in the case of
forced empty windows)
- a 7-bit component number in bits 1 – 7
- one spare bit in bit 33
This means that the HEALpix index level 12 of a given source is
contained in the most significant bits. HEALpix index of 12 and lower
levels can thus be retrieved as follows:
- HEALpix level 12 = source_id / 34359738368
- HEALpix level 11 = source_id / 137438953472
- HEALpix level 10 = source_id / 549755813888
- HEALpix level n = source_id / 2 ^ 35 * 4 ^ (12 - level).
Additional details can be found in the Gaia DPAC public document Source
Identifiers — Assignment and Usage throughout DPAC (document code
GAIA–C3–TN–ARI–BAS–020) available from
Random index which can be used to select smaller subsets of the data
that are still representative. The column contains a random permutation
of the numbers from 0 to N-1, where N is the number of rows.
The random index can be useful for validation (testing on 10 different
random subsets), visualization (displaying 1% of the data), and
statistical exploration of the data, without the need to download all
the data.
Reference epoch to which the astrometic source parameters are referred,
expressed as a Julian Year in TCB.
Barycentric right ascension \alpha of the source in ICRS at the
reference epoch refEpoch
Standard error \sigma_{\alpha *} \equiv \sigma_\alpha\cos\delta of the
right ascension of the source in ICRS at the reference epoch refEpoch.
Barycentric declination \delta of the source in ICRS at the reference
epoch refEpoch
Standard error \sigma_\delta of the declination of the source in ICRS at
the reference epoch refEpoch
Absolute barycentric stellar parallax \varpi of the soure at the
reference epoch refEpoch
Standard error \sigma_\varpi of the stellar parallax at the reference
epoch refEpoch
Proper motion in right ascension \mu_{\alpha *} of the source in ICRS at
the reference epoch refEpoch. This is the projection of the proper
motion vector in the direction of increasing right ascension.
Standard error \sigma_{\mu\alpha *} of the proper motion vector in right
ascension at the reference epoch refEpoch
Proper motion in declination \mu_\delta of the source at the reference
epoch refEpoch. This is the projection of the proper motion vector in
the direction of increasing declination.
Standard error \sigma_{\mu\delta} of the proper motion in declination at
the reference epoch refEpoch
Correlation between right ascension and declination, in dimensionless
units [-1:+1]
Correlation between right ascension and parallax, in dimensionless units
[-1:+1]
Correlation between right ascension and proper motion in right
ascension, in dimensionless units [-1:+1]
Correlation between right ascension and proper motion in declination, in
dimensionless units [-1:+1]
Correlation between declination and parallax, in dimensionless units
[-1:+1]
Correlation between declination and proper motion in right ascension, in
dimensionless units [-1:+1]
Correlation between declination and proper motion in declination, in
dimensionless units [-1:+1]
Correlation between parallax and proper motion in right ascension, in
dimensionless units [-1:+1]
Correlation between parallax and proper motion in declination, in
dimensionless units [-1:+1]
Correlation between proper motion in right ascension and proper motion
in declination, in dimensionless units [-1:+1]
Total number of AL observations (= CCD transits) used in the astrometric
solution of the source, independent of their weight. Note that some
observations may be strongly downweighted (see astrometricNBadObsAl).
Total number of AC observations (= CCD transits) used in the astrometric
solution of the source, independent of their weight. Note that some
observations may be strongly downweighted (see astrometricNBadObsAc).
Nearly all sources having G <13 will have AC observations from 2d
windows, while fainter than that limit only \sim1% of stars (the
so–called ‘calibration faint stars’) are assigned 2d windows resulting
in AC observations.
Number of AL observations (= CCD transits) that were not strongly
downweighted in the astrometric solution of the source. Strongly
downweighted observations (with downweighting factor w<0.2) are instead
counted in astrometricNBadObsAl. The sum of astrometricNGoodObsAl and
astrometricNBadObsAl equals astrometricNObsAl, the total number of AL
observations used in the astrometric solution of the source.
Number of AC observations (= CCD transits) that were not strongly
downweighted in the astrometric solution of the source. Strongly
downweighted observations (with downweighting factor w<0.2) are instead
counted in astrometricNBadObsAc. The sum of astrometricNGoodObsAc and
astrometricNBadObsAc equals astrometricNObsAc, the total number of AC
observations used in the astrometric solution of the source.
Number of AL observations (= CCD transits) that were strongly
downweighted in the astrometric solution of the source, and therefore
contributed little to the determination of the astrometric parameters.
An observation is considered to be strongly downweighted if its
downweighting factor w<0.2, which means that the absolute value of the
astrometric residual exceeds 4.83 times the total uncertainty of the
observation, calculated as the quadratic sum of the centroiding
uncertainty, excess source noise, and excess attitude noise.
Number of AC observations (= CCD transits) that were strongly
downweighted in the astrometric solution of the source, and therefore
contributed little to the determination of the astrometric parameters.
An observation is considered to be strongly downweighted if its
downweighting factor w<0.2, which means that the absolute value of the
astrometric residual exceeds 4.83 times the total uncertainty of the
observation, calculated as the quadratic sum of the centroiding
uncertainty, excess source noise, and excess attitude noise.
In the TGAS solution \tt astrometricDeltaQ (\Delta Q) indicates the
discrepancy between the Hipparcos proper motion and the TGAS proper
motion. A large value of \tt deltaQ could indicate non-linear motion
(e.g. in a binary).
The precise definition is
\Delta Q =
\begin{bmatrix}
\Delta\mu_{\alpha *} & \Delta\mu_{\delta}
\end{bmatrix}
\left(\vec{C}_\text{pm,\,T}+\vec{C}_\text{pm,\,H}\right)^{-1}
\begin{bmatrix}
\Delta\mu_{\alpha *} \\ \Delta\mu_{\delta}
\end{bmatrix}
where \Delta\mu_{\alpha *} = \mu_{\alpha *,\rm T}-\mu_{\alpha *,\rm H},
\Delta\mu_{\delta} = \mu_{\delta,\rm T}-\mu_{\delta,\rm H}, with T and H
indicating values from the Gaia DR1 (TGAS) solution and Hipparcos
catalogue. \vec{C}_\text{pm,\,T} and \vec{C}_\text{pm,\,H} are the
corresponding 2\times 2 covariance matrices.
In order to compute \Delta Q the two sets of proper motions must use the
same reference frame and the same reference epoch. Thus, the proper
motion components as given in the Hipparcos catalogue were rotated to
the Gaia DR1 reference frame, and then propagated to the Gaia reference
epoch.
This is the excess noise \epsilon_i of the source. It measures the
disagreement, expressed as an angle, between the observations of a
source and the best-fitting standard astrometric model (using five
astrometric parameters). The assumed observational noise in each
observation is quadratically increased by \epsilon_i in order to
statistically match the residuals in the astrometric solution. A value
of 0 signifies that the source is astrometrically well-behaved, i.e.
that the residuals of the fit statistically agree with the assumed
observational noise. A positive value signifies that the residuals are
statistically larger than expected.
The significance of \epsilon_i is given by \tt
astrometricExcessNoiseSig (D). If D\le 2 then \epsilon_i is probably not
significant, and the source may be astrometrically well-behaved even if
\epsilon_i is large.
The excess noise \epsilon_i may absorb all kinds of modelling errors
that are not accounted for by the observational noise (image centroiding
error) or the excess attitude noise. Such modelling errors include LSF
and PSF calibration errors, geometric instrument calibration errors, and
part of the high-frequency attitude noise. These modelling errors are
particularly important in the early data releases, but should decrease
as the astrometric modelling of the instrument and attitude improves
over the years.
Additionally, sources that deviate from the standard five-parameter
astrometric model (e.g. unresolved binaries, exoplanet systems, etc.)
may have positive \epsilon_i. Given the many other possible
contributions to the excess noise, the user must study the empirical
distributions of \epsilon_i and D to make sensible cutoffs before
filtering out sources for their particular application.
In Gaia DR1, the excess source noise has the same interpretation as
described above for both the primary (TGAS) and secondary data sets. It
measures the disagreement between the five-parameter model and the
observations, augmented by the different priors used. Thus, in TGAS the
excess noise may be increased if the proper motion seen during the 14
months of Gaia observations are not in agreement with the proper motion
inferred from the Tycho-2/Gaia comparison. In the secondary solution the
excess noise may be increased if the Gaia observations indicate a proper
motion or parallax several times larger than the prior uncertainty.
The excess source noise is further explained in Sects. 3.6 and 5.1.2 of
Lindegren et al. (2012).
Lindegren, L., U. Lammers, D. Hobbs, O’MullaneW., U. Bastian, and J.
Hernandez. 2012. “The Astrometric Core Solution for the Gaia Mission.
Overview of Models, Algorithms, and Software Implementation.” Astronomy
and Astrophysics 538 (February).
A dimensionless measure (D) of the significance of the calculated \tt
astrometricExcessNoise (\epsilon_i). A value D>2 indicates that the
given \epsilon_i is probably significant.
For good fits in the limit of a large number of observations, D should
be zero in half of the cases and approximately follow the positive half
of a normal distribution with zero mean and unit standard deviation for
the other half. Consequently, D is expected to be greater than 2 for
only a few percent of the sources with well-behaved astrometric
solutions.
In the early data releases \epsilon_i will however include instrument
and attitude modelling errors that are statistically significant and
could result in large values of \epsilon_i and D. The user must study
the empirical distributions of these statistics and make sensible
cutoffs before filtering out sources for their particular application.
The excess noise significance is further explained in Sect. 5.1.2 of
Lindegren et al. (2012).
Lindegren, L., U. Lammers, D. Hobbs, O’MullaneW., U. Bastian, and J.
Hernandez. 2012. “The Astrometric Core Solution for the Gaia Mission.
Overview of Models, Algorithms, and Software Implementation.” Astronomy
and Astrophysics 538 (February).
Flag indicating if this source was used as a primary source (\tt true)
or secondary source (\tt false). Only primary sources contribute to the
estimation of attitude, calibration, and global parameters. The
estimation of source parameters is otherwise done in exactly the same
way for primary and secondary sources.
Relegation factor of the source calculated as per Eq. (118) in Lindegren
et al. (2012) used for the primary selection process.
Lindegren, L., U. Lammers, D. Hobbs, O’MullaneW., U. Bastian, and J.
Hernandez. 2012. “The Astrometric Core Solution for the Gaia Mission.
Overview of Models, Algorithms, and Software Implementation.” Astronomy
and Astrophysics 538 (February).
Mean astrometric weight of the source in the AL direction.
The mean astrometric weight of the source is calculated as per Eq. (119)
in Lindegren et al. (2012).
Lindegren, L., U. Lammers, D. Hobbs, O’MullaneW., U. Bastian, and J.
Hernandez. 2012. “The Astrometric Core Solution for the Gaia Mission.
Overview of Models, Algorithms, and Software Implementation.” Astronomy
and Astrophysics 538 (February).
Mean astrometric weight of the source in the AC direction
The mean astrometric weight of the source is calculated as per Eq. (119)
in Lindegren et al. (2012).
Lindegren, L., U. Lammers, D. Hobbs, O’MullaneW., U. Bastian, and J.
Hernandez. 2012. “The Astrometric Core Solution for the Gaia Mission.
Overview of Models, Algorithms, and Software Implementation.” Astronomy
and Astrophysics 538 (February).
Type of prior used in the astrometric solution:
- 0: No prior used
- 1: Galaxy Bayesian Prior for parallax and proper motion
- 2: Galaxy Bayesian Prior for parallax and proper motion relaxed by
factor 10
- 3: Hipparcos prior for position
- 4: Hipparcos prior for position and proper motion
- 5: Tycho2 prior for position
- 6: Quasar prior for proper motion
The Galaxy Bayesian Prior is defined in , where it is denoted
\sigma_{\varpi,F90} (for the parallax) and
\sigma_{\mu,F90}={\cal R}\sigma_{\varpi,F90}, with {\cal
R}=10 yr^{-1} (for proper motion). The Galaxy Bayesian Prior relaxed by
a factor 10 is 10\sigma_{\varpi,F90} and 10\sigma_{\mu,F90},
respectively.
For Gaia DR1 the only types of priors used are 2 (for the secondary data
set), 3 (for the Hipparcos subset of the primary data set), or 5 (for
the non-Hipparcos subset of the primary data set). Type 6 was used for
internal calibration purposes and alignment of the reference frame, but
the corresponding astrometric results are in general not published.
This field indicates the number of observations (detection transits)
that have been matched to a given source during the last internal
crossmatch revision.
During data processing, this source happened to been duplicated and one
source only has been kept. This may indicate observational,
cross-matching or processing problems, or stellar multiplicity, and
probable astrometric or photometric problems in all cases. In DR1, for
close doubles with separations below some 2 arcsec, truncated windows
have not been processed, neither in astrometry and photometry. The
transmitted window is centred on the brighter part of the acquired
window, so the brighter component has a better chance to be selected,
even when processing the fainter transit. If more than two images are
contained in a window, the result of the image parameter determination
is un-predictable in the sense that it might refer to either (or
neither) image, and no consistency is assured.
The scanDirectionStrength and scanDirectionMean quantify the
distribution of AL scan directions across the source.
scanDirectionStrength[k-1] (k=1,2,3,4) is the absolute value of the
trigonometric moments m_k=\langle\exp(ik\theta)\rangle, where \theta is
the position angle of the scan and the mean value is taken over the
nObs[0] AL observations contributing to the astrometric parameters of
the source. \theta is defined in the usual astronomical sense: \theta=0
when the FoV is moving towards local North, and \theta=90^\circ towards
local East.
The scanDirectionStrength is a number between 0 and 1, where 0 means
that the scan directions are well spread out in different directions,
while 1 means that they are concentrated in a single direction (given by
scanAngleMean).
The different orders k are statistics of the scan directions modulo
360^\circ/k. For example, at first order (k=1), \theta=10^\circ and
\theta=190^\circ count as different directions, but at second order
(k=2) they are the same. Thus, scanDirectionStrength[0] is the degree of
concentration when the sense of direction is taken into account, while
scanDirectionStrength[1] is the degree of concentration without regard
to the sense of direction. A large value of scanDirectionStrength[3]
indicates that the scans are concentrated in two nearly orthogonal
directions.
The scanDirectionStrength and scanDirectionMean quantify the
distribution of AL scan directions across the source.
scanDirectionStrength[k-1] (k=1,2,3,4) is the absolute value of the
trigonometric moments m_k=\langle\exp(ik\theta)\rangle, where \theta is
the position angle of the scan and the mean value is taken over the
nObs[0] AL observations contributing to the astrometric parameters of
the source. \theta is defined in the usual astronomical sense: \theta=0
when the FoV is moving towards local North, and \theta=90^\circ towards
local East.
The scanDirectionStrength is a number between 0 and 1, where 0 means
that the scan directions are well spread out in different directions,
while 1 means that they are concentrated in a single direction (given by
scanAngleMean).
The different orders k are statistics of the scan directions modulo
360^\circ/k. For example, at first order (k=1), \theta=10^\circ and
\theta=190^\circ count as different directions, but at second order
(k=2) they are the same. Thus, scanDirectionStrength[0] is the degree of
concentration when the sense of direction is taken into account, while
scanDirectionStrength[1] is the degree of concentration without regard
to the sense of direction. A large value of scanDirectionStrength[3]
indicates that the scans are concentrated in two nearly orthogonal
directions.
The scanDirectionStrength and scanDirectionMean quantify the
distribution of AL scan directions across the source.
scanDirectionStrength[k-1] (k=1,2,3,4) is the absolute value of the
trigonometric moments m_k=\langle\exp(ik\theta)\rangle, where \theta is
the position angle of the scan and the mean value is taken over the
nObs[0] AL observations contributing to the astrometric parameters of
the source. \theta is defined in the usual astronomical sense: \theta=0
when the FoV is moving towards local North, and \theta=90^\circ towards
local East.
The scanDirectionStrength is a number between 0 and 1, where 0 means
that the scan directions are well spread out in different directions,
while 1 means that they are concentrated in a single direction (given by
scanAngleMean).
The different orders k are statistics of the scan directions modulo
360^\circ/k. For example, at first order (k=1), \theta=10^\circ and
\theta=190^\circ count as different directions, but at second order
(k=2) they are the same. Thus, scanDirectionStrength[0] is the degree of
concentration when the sense of direction is taken into account, while
scanDirectionStrength[1] is the degree of concentration without regard
to the sense of direction. A large value of scanDirectionStrength[3]
indicates that the scans are concentrated in two nearly orthogonal
directions.
The scanDirectionStrength and scanDirectionMean quantify the
distribution of AL scan directions across the source.
scanDirectionStrength[k-1] (k=1,2,3,4) is the absolute value of the
trigonometric moments m_k=\langle\exp(ik\theta)\rangle, where \theta is
the position angle of the scan and the mean value is taken over the
nObs[0] AL observations contributing to the astrometric parameters of
the source. \theta is defined in the usual astronomical sense: \theta=0
when the FoV is moving towards local North, and \theta=90^\circ towards
local East.
The scanDirectionStrength is a number between 0 and 1, where 0 means
that the scan directions are well spread out in different directions,
while 1 means that they are concentrated in a single direction (given by
scanAngleMean).
The different orders k are statistics of the scan directions modulo
360^\circ/k. For example, at first order (k=1), \theta=10^\circ and
\theta=190^\circ count as different directions, but at second order
(k=2) they are the same. Thus, scanDirectionStrength[0] is the degree of
concentration when the sense of direction is taken into account, while
scanDirectionStrength[1] is the degree of concentration without regard
to the sense of direction. A large value of scanDirectionStrength[3]
indicates that the scans are concentrated in two nearly orthogonal
directions.
The scanDirectionStrength and scanDirectionMean quantify the
distribution of AL scan directions across the source.
scanDirectionMean[k-1] (k=1,2,3,4) is 1/k times the argument of the
trigonometric moments m_k=\langle\exp(ik\theta)\rangle, where \theta is
the position angle of the scan and the mean value is taken over the
nObs[0] AL observations contributing to the astrometric parameters of
the source. \theta is defined in the usual astronomical sense: \theta=0
when the FoV is moving towards local North, and \theta=90^\circ towards
local East.
scanDirectionMean[k-1] is an angle between -180^\circ/k and
+180^\circ/k, giving the mean position angle of the scans at order k.
The different orders k are statistics of the scan directions modulo
360^\circ/k. For example, at first order (k=1), \theta=10^\circ and
\theta=190^\circ count as different directions, but at second order
(k=2) they are the same. Thus, scanDirectionMean[0] is the mean
direction when the sense of direction is taken into account, while
scanDirectionMean[1] is the mean direction without regard to the sense
of the direction. For example, scanDirectionMean[0] = 0 means that the
scans preferentially go towards North, while scanDirectionMean[1] = 0
means that they preferentially go in the North-South direction, and
scanDirectionMean[4] = 0 that they preferentially go either in the
North-South or in the East-West direction.
The scanDirectionStrength and scanDirectionMean quantify the
distribution of AL scan directions across the source.
scanDirectionMean[k-1] (k=1,2,3,4) is 1/k times the argument of the
trigonometric moments m_k=\langle\exp(ik\theta)\rangle, where \theta is
the position angle of the scan and the mean value is taken over the
nObs[0] AL observations contributing to the astrometric parameters of
the source. \theta is defined in the usual astronomical sense: \theta=0
when the FoV is moving towards local North, and \theta=90^\circ towards
local East.
scanDirectionMean[k-1] is an angle between -180^\circ/k and
+180^\circ/k, giving the mean position angle of the scans at order k.
The different orders k are statistics of the scan directions modulo
360^\circ/k. For example, at first order (k=1), \theta=10^\circ and
\theta=190^\circ count as different directions, but at second order
(k=2) they are the same. Thus, scanDirectionMean[0] is the mean
direction when the sense of direction is taken into account, while
scanDirectionMean[1] is the mean direction without regard to the sense
of the direction. For example, scanDirectionMean[0] = 0 means that the
scans preferentially go towards North, while scanDirectionMean[1] = 0
means that they preferentially go in the North-South direction, and
scanDirectionMean[4] = 0 that they preferentially go either in the
North-South or in the East-West direction.
The scanDirectionStrength and scanDirectionMean quantify the
distribution of AL scan directions across the source.
scanDirectionMean[k-1] (k=1,2,3,4) is 1/k times the argument of the
trigonometric moments m_k=\langle\exp(ik\theta)\rangle, where \theta is
the position angle of the scan and the mean value is taken over the
nObs[0] AL observations contributing to the astrometric parameters of
the source. \theta is defined in the usual astronomical sense: \theta=0
when the FoV is moving towards local North, and \theta=90^\circ towards
local East.
scanDirectionMean[k-1] is an angle between -180^\circ/k and
+180^\circ/k, giving the mean position angle of the scans at order k.
The different orders k are statistics of the scan directions modulo
360^\circ/k. For example, at first order (k=1), \theta=10^\circ and
\theta=190^\circ count as different directions, but at second order
(k=2) they are the same. Thus, scanDirectionMean[0] is the mean
direction when the sense of direction is taken into account, while
scanDirectionMean[1] is the mean direction without regard to the sense
of the direction. For example, scanDirectionMean[0] = 0 means that the
scans preferentially go towards North, while scanDirectionMean[1] = 0
means that they preferentially go in the North-South direction, and
scanDirectionMean[4] = 0 that they preferentially go either in the
North-South or in the East-West direction.
The scanDirectionStrength and scanDirectionMean quantify the
distribution of AL scan directions across the source.
scanDirectionMean[k-1] (k=1,2,3,4) is 1/k times the argument of the
trigonometric moments m_k=\langle\exp(ik\theta)\rangle, where \theta is
the position angle of the scan and the mean value is taken over the
nObs[0] AL observations contributing to the astrometric parameters of
the source. \theta is defined in the usual astronomical sense: \theta=0
when the FoV is moving towards local North, and \theta=90^\circ towards
local East.
scanDirectionMean[k-1] is an angle between -180^\circ/k and
+180^\circ/k, giving the mean position angle of the scans at order k.
The different orders k are statistics of the scan directions modulo
360^\circ/k. For example, at first order (k=1), \theta=10^\circ and
\theta=190^\circ count as different directions, but at second order
(k=2) they are the same. Thus, scanDirectionMean[0] is the mean
direction when the sense of direction is taken into account, while
scanDirectionMean[1] is the mean direction without regard to the sense
of the direction. For example, scanDirectionMean[0] = 0 means that the
scans preferentially go towards North, while scanDirectionMean[1] = 0
means that they preferentially go in the North-South direction, and
scanDirectionMean[4] = 0 that they preferentially go either in the
North-South or in the East-West direction.
Number of observations (CCD transits) that contributed to the G mean
flux and mean flux error.
Mean flux in the G-band.
Error on the mean flux in the G-band.
Mean magnitude in the G band. This is computed from the G-band mean flux
applying the magnitude zero-point in the Vega scale.
Flag indicating if variability was identified in the photometric G band:
- source not processed and/or exported to catalogue
- Source not identified as variable
- source identified and processed as variable, see tables
PhotVariableSummary, PhotVariableTimeSeriesGfov,
PhotVariableTimeSeriesGfovStatisticalParameters, and Cepheid or
Rrlyrae for more details.
Note that for this data release only a small subset of (variable)
sources was processed and/or exported, so for many (known) variable
sources this flag is set to “NOT AVAILABLE”. No “CONSTANT” sources were
exported either.
Galactic Longitude of the object at reference epoch refEpoch, see ESA,
1997, ’The Hipparcos and Tycho Catalogues’, ESA SP-1200, Volume 1,
Section 1.5.3, for the conversion details.
Galactic Latitude of the object at reference epoch refEpoch, see ESA,
1997, ’The Hipparcos and Tycho Catalogues’, ESA SP-1200, Volume 1,
Section 1.5.3, for the conversion details.
Ecliptic Longitude of the object at reference epoch refEpoch, see ESA,
1997, ’The Hipparcos and Tycho Catalogues’, ESA SP-1200, Volume 1,
Section 1.5.3, for the conversion details.
Ecliptic Latitude of the object at reference epoch refEpoch, see ESA,
1997, ’The Hipparcos and Tycho Catalogues’, ESA SP-1200, Volume 1,
Section 1.5.3, for the conversion details.