THE HIPPARCOS SOLAR SYSTEM OBJECTS ANNEXES D. Hestroffer

THE HIPPARCOS SOLAR SYSTEM OBJECTS ANNEXES

D. Hestro er

Astrophysics Division, ESTEC, NL-2200AG No ordwijk, The Netherlands

Bec-Borsenb erger 1997. The observations of plane- ABSTRACT

tary satellites relative to the background stars yield,

in an indirect manner, accurate p ositions of the grav-

Astrometric and photometric measurements of a

itating ma jor planet's centre of mass Morrison et al.

numb er of solar system ob jects were p erformed by the

1997; Fienga et al. 1997. Photometric observations

Hipparcos satellite in b oth the Hipparcos main mis-

of asteroids provides information ab out their rota-

sion and the Tycho exp eriment. The sp eci c asp ects

tional prop erties such as shap e and spin-vector orien-

of the Hipparcos observations and reduction pro cess

tation, and the scattering prop erties of their surface.

implemented for the solar system ob jects are pre-

Hence observations of such primordial ob jects yield

sented. Sp ecial attention is paid to the error budget

insight on their collisional evolution, and on the early

of the reduction which is accurate to the mas milli-

solar system.

arcsecond level for the Hipparcos main mission. The

contents of the Hipparcos Solar System Ob jects Cat-

The Hipparcos satellite successfully observed the so-

alogues is describ ed. Comparison b etween the results

lar system ob jects during its almost 4 years mission

derived from the two Consortia FAST and NDAC, as

duration. Hence it provides astrometric as well as

well as comparison with ground-based observations,

photometric information on these relatively bright

are given.

ob jects. The retained ob jects and the geometry of

the Hipparcos observations are brie y presented in

Section 2. The information gathered by the star

mapp er constitutes the Tycho Catalogue, while the

Key words: Astrometry, photometry, solar system.

Hipparcos Catalogue is derived from the observations

made through the main grid. The reduction of the

solar system ob jects observations follows the pro ce-

1. INTRODUCTION

dure retained for the stars on the rst stages, and

is adapted to these rapidly moving and eventually

resolved ob jects. The data are of di erent nature

Among the thousands of stars, the Hipparcos pro-

and precision and are presented separately in Sec-

gramme included a selection of solar system ob jects

tions 3 and 4. All astrometric p ositions are given in

ma jor planets, planetary satellites and asteroids.

the ICRS, and the transformation is presented in Sec-

The primary motivation is to provide highly accurate

tion 5. Comparison with ground-based observations

p ositions for the link of the dynamical reference sys-

and calculated places, and between the NDAC and

tem to the International Celestial Reference System

FAST p ositions, are given in Section 6.

ICRS, but also to enable dynamical and physical

studies of these ob jects. The value of astrometric

observations of asteroids, relatively to the reference

frame de ned by the stars, for the establishmentof

2. HIPPARCOS OBSERVATIONS

the dynamical reference frame, was rst suggested by

Dyson 1928. These ob jects were thought to con-

siderably enhance the results obtained from observa-

2.1. Observing Programme

tions of the Sun or ma jor planets. Nonetheless, this

metho d encountered some limitations; hence such ob-

Initially two satellites Europa and Titan and 63

servations of minor planets enter for instance in the

asteroids were retained in the Hipparcos main mis-

solution derived by Fricke 1982 for the FK5 with

sion programme. Positions of the solar system ob-

a relatively mo dest weight. Hipparcos should dra-

jects were entered in the Input Catalogue by means

matically improve the situation e.g. Hestro er et al.

of their ephemerides Bec-Borsenb erger 1985. Since

1995; Bec-Borsenb erger et al. 1995, and yield a link

the p ositions had to b e known a priori with a preci-

between the dynamical system and the ICRS with a

sion b etter than 1 arcsec, a ground-based campaign of

precision of the same order of magnitude as the b est

observations of these asteroids was started in 1983 in

result obtained so far Folkner et al. 1994.

order to improve the accuracy of their ephemerides.

High precision measures of the p ositions of asteroids

The numb er of retained asteroids was reduced to 48

enables to improve their ephemerides but also in par-

after consideration of the numb er of their predicted

ticular cases of very close encounters to determine the

transits during the scheduled nominal mission dura-

mass of some of them e.g. Viateau 1997; Bange &

tion. The Saturnian satellite S8 Iap etus was added

to the observation programme during the mission. for Venus, Mars, Jupiter and Saturn. Next, the ob-

A priori ephemerides of the 48 Hipparcos asteroids, jects brighter than V 10 and with sucientnum-

the four Galilean satellites, Titan, Venus and planets b er of observations were retained; the list is given in

Mars through Neptune were also calculated as part of Table 1. When available, the photometry is provided

the Tycho Input Catalogue of 3 million stars. Never- in the Tycho B and V passbands which, although

T T

theless, not all of these solar system ob jects were re- not identical, are close to the Johnson B and V . Over

tained for the Catalogue output see Section 3; their the range 0:2 < B V < 1:8, the following lin-

inclusion was necessary for technical reasons Bastian ear formulae yield transformations b etween the two

&Wagner 1997. photometric systems accurate to 0.05 mag:

V V = 0:09 B V

T J T

2.2. A Scanning Satellite

B V = 0:85 B V

J T

Since the Hipparcos satellite was scanning the whole

sky in a regular manner, no p ointing to a sp eci c ob-

ject was p ossible; but an observation o ccurred dur-

Moreover the

ing its transit across the eld of view. Star motion

spin axis of the satellite was precessing with a con-

stant angle of 43 around the direction towards the

45 o

enabling a complete and optimal coverage of

Sun, w

the celestial sphere. On the other hand, solar sys-

tem ob jects are gravitating around the Sun in a band

20'

near the ecliptic, thus observations of these ob jects

are spread around the quadratures see Figure 1, i.e.

when the solar phase angle is maximal. Also the total

0"91 0"91 5"63

numb er of observations is varied b etween the di er-

Figure2. Schematic view of the star mapper slits system.

ent observed ob jects from roughly 15 to 125 tran-

All slits have the same width in the direction of the w

sits. The same remark applies for the distribution

axis. The inclined and vertical slits are spaced, in the

of these transits in time or along the planet's tra jec-

tory. The Hipparcos and Tycho observations are of

direction of a star's motion, with distance ratio 2:3:1 of

course almost simultaneous; a transit across the star

the step s = 5 :63 arcsec. The ` ducial lines', which can

mapp er o ccurs a few seconds b efore the transit across

be thought as the centres of gravity of the four slits in each

the main grid.

group, are shown as dashed lines.

Quadrature

Table 1. Solar system objects of the Tycho Catalogue. (2) (3)

asteroid (1)

Name Photometry Astrometry Rotation

axis Minor planets:

p p

1 Ceres p

(1) p

2 Pallas

p p esta

86° 4 V

p p

6 Heb e

p p

Sun 7 Iris Satellite Satellites:

(2) p

J I I I{Ganymede {

J IV{Callisto {

p p S VI{Titan

(3)

Ma jor planets:

Uranus {

Neptune {

Figure 1. Schematic view of the Hipparcos satel lite's

scanning law. The observations of solar system objects

are made around the quadratures.

The magnitudes in the twochannels are derived, in

the same way as for the stars, from the amplitude

3. TYCHO

of the convolved signal and are calculated by a sim-

pli ed calibration pro cedure. The magnitude pro-

vided for each transit corresp onds to the mean of the

The data gathered by the star mapp er constitute the

measure for each slits group crossing. No magnitude

Tycho Catalogue. Aschematic view of the grid sys-

is provided for ob jects larger in apparent size than

tem is given in Figure 2. The Tycho observations are

the width of the slits 0.91 arcsec. For ob jects that

not adapted to ob jects larger in apparent size than

were not substantially smaller than the slit's width,

the smallest separation b etween two slits 5.63 arc-

systematic errors may o ccur. Finally, no standard er-

sec. At least for this reason no data can b e provided

rors are provided for the estimation of the B and V

T T

magnitudes; they are of the order of 0.1 mag for an ; , the standard errors ; and the corre-

ob ject of magnitude V 8 and 0.35 mag for V 10.

lation between the two co ordinates . To enable

future systematic correction of the data, esp ecially

Since the transits across each slits group yield in-

for the large ma jor planets, the p osition angle ,

formation in two directions, one can derive a con-

the inclined-slit ag signz , and the standard errors

ventional two-dimensional p osition on the celestial

; are provided as additional data. All p ositions

1 2

sphere for each transit. The displacement of the so-

are referred to the ICRS system see Section 5. It is

lar system ob ject b etween the crossing of the ducial

stressed that phase, shap e or alb edo corrections are

lines of the slit groups in a time interval up to ab out

not taken into account. The p osition corresp onds to

10 s is known with sucient accuracy to enable such

the photo centre for the smallest ob jects. For Uranus,

a construction. The primary astrometric information

Neptune and to a lesser extent the twoJovian satel-

is the time when an ob ject crosses the ducial line as

lites, whose angular diameters are larger than the

derived in the detection and estimation pro cess. The

slit width, the p osition on the surface of the body

di erence b etween the observed and predicted cross-

dep ends highly on its alb edo distribution and the

ing time for each slit group is converted into an along-

scanning geometry. More accurate correction to the

scan residual on p osition. Next the two along-scan

centre of gure can b e applied by a simulation of the

residuals u ; u are transformed into residuals

1 2

Tycho photon counts and convolution with the slit

in the two orthogonal directions w and z asso ciated to

resp onse. A general description of the pro cedure to

the fo cal plane of the telescop e. This transformation

follow is given in the Hipparcos Catalogue Hg &

P dep ends on the sign of the z co ordinate, whether

Makarov 1997.

the transit o ccurs in the upp er part sgnz = +1

or the lower part sgnz =1 of the inclined slits.

The orientation of the w; z frame on the celestial

4. HIPPARCOS

sphere is given by the p osition angle . The observed

p osition, at the|arbitrarily chosen|reference ep o ch

t , is thus derived from an a priori calculated p osi-

In contrast to the star mapp er, the main grid is

tion close to the true p osition and the along-scan

made of `vertical' slits, and hence only provides a

residuals by:

one-dimensional p osition, i.e. the observed p osition

lo cus in the direction p erp endicular to the slits. As-

2 1

= R P 1

trometry is provided for ob jects brighter than V 13

2 2

and smaller in apparent size than 1 arcsec, i.e. 48

asteroids, the planetary satellites J2 Europa, S6 Ti-

where = cos , and where:

tan and S8 Iap etus unfortunately only a very few

observations are available for Iap etus.

sin cos

R =

cos sin

The primary astrometric and photometric informa-

tion is obtained from the Fourier expansion of the

0 1

mo dulated signal:

P =

signz signz

S t = I [1 + M cos!t + '

The second-order terms arising from the transfor-

mation between the tangent plane and the celestial

+ N cos2!t +2] 2

sphere are neglected. Intro ducing the diagonal ma-

trix of the standard error of the measurements:

where ! is the fundamental angular frequency. This

reduces for a p oint-like source to:

S t = I [1 + M cos!t + '

o o

the variance matrix of the derived co ordinates is

+ N cos2!t +2' ] 3

o o

given by:

0 1

where M ;N are calibrated mo dulation co ecients,

o o

and the mo dulation phases are indep endent of the

2 0 0

@ A

= R P P R

harmonic rank ' = = ' . The astrometry is

given at this stage by an abscissa v as derived from

the mo dulation phases '; within FAST, and the

This matrix is no longer diagonal, re ecting the fact

phase ', of the rst harmonic only, within NDAC.

that|dep ending on the p osition angle and the ra-

For a p oint-like or relatively small source typically

tio = |the principal axis of the asso ciated error

with a diameter 0:05 arcsec, the FAST and

1 2

ellipse do es not coincide with the N,E directions to-

NDAC abscissae have the same exp ectancy since the

ward the northern celestial p ole and the east. The

calibrated phases ' and are almost equal. For

along-scan standard errors are derived from an error

a larger extended source, the di erence b etween the

mo del adequate for stellar images and do not corre-

FAST and NDAC abscissa dep ends on the physical

sp ond to a Gaussian noise. Moreover, the signals for

prop erties of the minor planet or planetary satellite

planets are broader and more at at the top than the

such as apparent diameter, solar phase angle, alb edo

signals of p oint-like sources. Thus the derived quan-

distribution over the visible surface and scanning ge-

2 2

ometry.

tities and should preferably be regarded as

indicators of the quality of a single measure.

In contrast to the stars, the FAST and NDAC so-

For each transit, the astrometric observation is de- lutions have not b een merged into a single p osition.

ned by the reference epoch t , the co ordinates The FAST reduction pro cedure is not adapted to the 2

observations of the largest ob jects J2 Europa and the apparent magnitude Hp and Hp are derived

dc ac

S6 Titan, thus only the NDAC p ositions are provided. from the co ecients I; IM; IN . The apparent mag-

For smaller ob jects, b oth pro cedures are valid; but as nitude Hp is directly given by the mean intensity

noted b efore, the FAST and NDAC p ositions lo ci do I corrected for background noise. The second esti-

not strictly sp eaking corresp ond to the same p oint mator Hp is derived from the amplitude IM; IN

on the surface of the ob ject. Hence, in order to avoid of the mo dulation. It is stressed that the Hp esti-

intro ducing additional errors, no merging of the data mator, given as additional data, is of lower precision

was p erformed. Nevertheless, for the smallest b o dies and biased. Wehave, in a rst approximation, for a

relatively to the grid step, b oth FAST and NDAC spherical ob ject of apparent diameter :

lo ci corresp ond as a rst approximation to the p osi-

2 4

tion of the photo centre Hestro er & Mignard 1997.

Hp Hp a + o +o

ac dc

The displacement on the sky of an asteroid or a plan-

where a > 0 is a scalar and is the solar phase

etary satellite during the 17 seconds it takes to

angle. The transformation from the Hp system to

cross the main grid, can b e calculated with sucient

standard magnitudes are given by Mignard et al.

accuracy to enable the construction of a normal p o-

1997. The Hp and V bands have more or less

sition lo cus for each transit. A linear regression is

the same e ectivewavelength, they can b e related in

p erformed over the transit in order to determine the

a go o d approximation for solar system ob jects with

< <

average o set between the calculated and observed

0:5 B V 1:5 by a relation involving the

abscissae. This o set is given by a weighted mean

B V colour index in the Johnson system Mignard,

within NDAC L2 t and by the median within

private communication:

FAST L1 t. The reference epochs, the standard

error asso ciated to these two estimators and the great

Hp V 0:304 B V 0:202 B V

circle on which the p ositions are pro jected are di er-

3 4

ent.

+0:107 B V 0:045 B V

The apparent p ositions are corrected for ab erration,

The Hipparcos solar system ob jects photometric cat-

gravitational light b ending by the Sun, and for the

alogue is completed, for convenience, with some ad-

Hipparcos satellite's parallax the geo centric p osition

ditional calculated asp ect data: the distance to the

was provided with an accuracy of 2 km by the

Sun, the distance to the satellite and the solar phase

satellite orbit determination p erformed at ESOC.

angle.

The epoch of observation is also corrected for the

rst order light-time di erence due to the geo centric

orbit. Hence the published p osition corresp onds to

5. TRANSFORMATION TO THE ICRS

the astrometric direction at time t , where t is the

published ep o ch of observation and is the light-time

delay to the geo centre. The astrometric direction

After the sphere reduction stage, all Hipparcos or

for each transit is supplied by means of a reference

Tycho solar system ob jects astrometric p ositions are

p oint ; and the direction of the straight line

0 0

related to intermediary reference frames P called

v = constant in the tangent plane asso ciated with

F37.3 for FAST, N37.5 for NDAC and for historical

this reference p oint see Figure 3. The reference

reasons N18 for TDAC. However the p ositions have

p oint is constructed in such a way that it has the

to b e given in the system of the nal Hipparcos Cat-

same observed abscissa on the reference great circle,

alogue, i.e. the optical counter part of the ICRS. All

and a ordinate given by the calculated ephemeris.

the reference frames P are de ned by the stars and

All p ositions are referred to the ICRS system see

the asso ciated sphere construction; they are related

Section 5, it is stressed that phase, shap e or alb edo

to the single sphere solution H37C Lindegren et al.

corrections are not taken into account.

1997. This latter reference frame is next aligned to

the frame of the ICRS by a small time-dep endent

+ N

valevsky 1997:

z rotation Ko

" !

Observed "

"t=" +t T !

RGC " 0 places 0 P w w

where T = J1991:25 is the reference ep o ch.

(α , δ ) 0 0 0 (α , δ ) E 0 0

v ICRS

rotation is accurate to 0.6 mas for the orien- y This

Ω i RGC

and 0.25 mas/year for the spin comp onents

x tation

valevsky et al. 1997. Zoom in the tangent plane Ko

slit motion

The Hipparcos astrometry of solar system ob jects is

uni-dimensional. It is completely characterised by

the abscissa and the orientation of the great circle

Figure3. Referencepoint and transformation to the tan-

on which the planet p osition is pro jected. Hence the

gent plane.

published data determine the equation of the straight

line v = constant, in the tangent plane centred at the

The photometry is provided only within FAST for reference p oint ; . The great circle is de ned

0 0

the 48 asteroids of the mission in the Hipparcos Hp with resp ect to the stars and hence to the intermedi-

broad-band photometric system. No photometry is ary frame P. The origin for the abscissa of the p osi-

available for the planetary satellites since the di u- tion lo cus is at the ascending no de of the great circle

sion of the light of their resp ective planets p erturb ed with the reference frame P.Thus the transformation

considerably the measurements. Two estimators of to the ICRS is given by application of an in nitesimal

rotation to the reference p oint, the change on the p o-

sition angle b eing negligible. The transformation

for the Tycho and Hipparcos p ositions of solar system

h t is given by:

ob jects at ep o c 0.5

1 0

1 " t " t y

z 0

C B

" t 1 " t

u t u t= x

z -0.5

P ICRS

A @

t " t 1

" -1

y x

1990 1991 1992 1993

where u is the astrometric direction of either the

t or the Tycho observed p o- Hipparcos reference p oin 1

sition:

cos

cos 0.5

u = sin cos

P sin 0

-0.5

For the Tycho data the spin comp onents b etween the

two reference frames are of the order of 1 mas/year

-1

are negligible. Zonal and temp oral systematic

and 1990 1991 1992 1993

errors of larger size up to 6 mas were also neglected

with regard to the random error of a single transit.

Figure4. Residuals for the Tycho and Carlsbergpositions

of Uranus relative to the DE200 ephemeris. Each point

corresponds to a single transit across each instrument.

6. COMPARISONS AND PRECISIONS

The Tycho p ositions have some similarities to the co-

ordinates obtained by meridian circles observations.

0.5

The number of transits per apparition may how-

ever be considerably smaller, and since these o ccur

0.4

around the quadratures, they are complementary to

unit variance

the ground-based measurements. Figure 4 shows the

0.3 Gaussian

Hipparcos residuals obtained for Uranus with resp ect

These are given

to the widely used DE200 ephemeris. 0.2

together with the residuals obtained with the Carls-

tatLaPalma Morisson, private com-

b erg instrumen 0.1

munication. Both observational data are in good

t; in particular they show the systematic

agreemen 0

in right ascension of the DE200 solution and

error -6 -4 -2 0 2 4 6

the improvement obtained with the DE403 solution.

It was noted in Section 3. that the precisions for Ty-

Figure 5. Normalised di erence between the FAST and

cho observations are more indicative of the quality

NDAC positions. The histogram is constructed from a

of the astrometric measures. As can b e seen on the

disp ersion of the residuals, the Tycho p ositions are

subset of 39 minor planets and a total of 1967 transits in

of the same order of precision than the ground-based

common to the NDAC and FAST catalogues.

observations carried out with vertical circles.

The FAST and NDAC astrometry have b een ob-

tained by indep endent means. They di er mainly by

the fact that they have not b een derived for the same

epoch, neither do they corresp ond to pro jections on

The precision of the Hipparcos photometric and as-

the same great circle, and as stated b efore, they do

trometric data at the transit level dep end on the

not corresp ond to the same p oint on the surface of

magnitude of the ob ject at the observation epoch.

the asteroid see Section 4.. If we consider the sub-

The standard errors for the Hipparcos astrometry are

given in Figure 6. With an average of 10 15 mas,

set of the 39 asteroids of size smaller than 0.2 arcsec ,

Hipparcos measures, which are directly related to the

the correlation factor of 0.85 between the abscissae

ICRS, surpass the ground-based meridian telescop es

and the scaling of the standard errors as derived from

observations by a factor 10. The average precision

faint stars Arenou, private communication, we nd

for the photometric dc comp onentis0:02 0:03 mag.

the distribution of the normalised di erence v=

Since the dc and ac comp onent are indep endent, a

given in Figure 5. As exp ected, this distribution is

more precise estimator can b e constructed by taking

an almost centered Gaussian of unit variance with a

the weighted mean of the Hp and Hp values;

ac dc

mean hv i < 1 mas, so that no signi cant system-

it is however stressed that such a construction in-

atic o set is presentbetween the FAST and NDAC

tro duces systematic errors when the ob ject's angular

p ositions for this subset of observations.

size is not negligible i.e. when the mo dulation co ef-

cients are such that M >M and/or N >N , see

Excluding the nine asteroids 1 Ceres to 7 Iris, 10 Hy-

o o

giea and 324 Bamb erga. Section 4.

of asteroids and also stars, leading for the rst time

to 1 the determination of their diameter in the op-

tical domain, and 2 to a basis of comparison to the

extensive results obtained in the IR domain by the

IRAS satellite.

ACKNOWLEDGMENTS

The author is indebted to the late Bruno Morando,

who initially guided him in this work, for his sup-

p ort and assistance. This work is the result of a

collab oration between many memb ers of the di er-

ent Consortia INCA, FAST, NDAC, TDAC, it is a

great pleasure to acknowledge their dedicated contri-

bution. The author is supp orted by a research grant

from the Europ ean Space Agency.

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man 1996 within the the context of ESA's `Horizon

The Hipparcos and Tycho Catalogues, ESA SP{

2000 Plus' programme would allow astrometric ob-

1200, Vol 3.

servations on the sub-milli-arcsecond level of a few

Morrison, L.V., Hestro er, D., Taylor D.B., van

hundreds of small asteroids Hestro er & Morando

Leeuwen, F., 1997, ESA SP{402, this volume

1995. It would also provide high precision photom-

etry in a way similar to Hipparcos. In contrast to

Viateau, B., Rapap ort, M., 1997, this volume

Hipparcos, GAIA would b e able to resolvehundreds