I. X-ray astronomy will play an increasingly important role in studies of the early universe and large scale structure, but these studies are ultimately limited by sparse photon numbers. There is a need to develop progressively larger collecting area telescopes under increasingly severe mass constraints.
II. The challenge is greater in the X-ray band than optical, as X-ray telescopes reflect X-rays twice, requiring reflectors two orders of magnitude larger than the effective aperture. Large mass is currently problematic for Constellation-X mission.
III. Looking beyond Constellation, a radically different approach is needed based on super lightweight reflectors and perhaps in situ assembly of the telescope. This could enable an ultra high throughput X-
Differentiation between Global and Local Datum from Different aspect Nzar Braim
Differentiation between Global and Local Datum from Different aspect
Spatial professionals are required to deal with an increasingly wide range
of positioning information obtained from various sources including
terrestrial surveying, Global Navigation Satellite System (GNSS)
observations and online GNSS processing services. These positions refer
to a multitude of local, national, and global datums. A clear understanding
of the different coordinate reference systems and datums in use today and
the appropriate transformations between these are therefore essential to
ensure rigorous consideration of reference frame variations to
produce high-quality outcomes in spatial data analysis tasks.
Two temperate Earth-mass planets orbiting the nearby star GJ 1002Sérgio Sacani
We report the discovery and characterisation of two Earth-mass planets orbiting in the habitable zone of the nearby M-dwarf GJ 1002 based on
the analysis of the radial-velocity (RV) time series from the ESPRESSO and CARMENES spectrographs. The host star is the quiet M5.5 V star
GJ 1002 (relatively faint in the optical, V ∼ 13.8 mag, but brighter in the infrared, J ∼ 8.3 mag), located at 4.84 pc from the Sun.
We analyse 139 spectroscopic observations taken between 2017 and 2021. We performed a joint analysis of the time series of the RV and full-width
half maximum (FWHM) of the cross-correlation function (CCF) to model the planetary and stellar signals present in the data, applying Gaussian
process regression to deal with the stellar activity.
We detect the signal of two planets orbiting GJ 1002. GJ 1002 b is a planet with a minimum mass mp sin i of 1.08 ± 0.13 M⊕ with an orbital period
of 10.3465 ± 0.0027 days at a distance of 0.0457 ± 0.0013 au from its parent star, receiving an estimated stellar flux of 0.67 F⊕. GJ 1002 c is a
planet with a minimum mass mp sin i of 1.36 ± 0.17 M⊕ with an orbital period of 20.202 ± 0.013 days at a distance of 0.0738 ± 0.0021 au from
its parent star, receiving an estimated stellar flux of 0.257 F⊕. We also detect the rotation signature of the star, with a period of 126 ± 15 days. We
find that there is a correlation between the temperature of certain optical elements in the spectrographs and changes in the instrumental profile that
can affect the scientific data, showing a seasonal behaviour that creates spurious signals at periods longer than ∼ 200 days.
GJ 1002 is one of the few known nearby systems with planets that could potentially host habitable environments. The closeness of the host star
to the Sun makes the angular sizes of the orbits of both planets (∼ 9.7 mas and ∼ 15.7 mas, respectively) large enough for their atmosphere to be
studied via high-contrast high-resolution spectroscopy with instruments such as the future spectrograph ANDES for the ELT or the LIFE mission.
An Earth-sized exoplanet with a Mercury-like compositionSérgio Sacani
Earth, Venus, Mars and some extrasolar terrestrial planets1
have a mass and radius that is consistent with a mass fraction
of about 30% metallic core and 70% silicate mantle2
. At the
inner frontier of the Solar System, Mercury has a completely
different composition, with a mass fraction of about 70%
metallic core and 30% silicate mantle3
. Several formation or
evolution scenarios are proposed to explain this metal-rich
composition, such as a giant impact4, mantle evaporation5
or the depletion of silicate at the inner edge of the protoplanetary
disk6. These scenarios are still strongly debated.
Here, we report the discovery of a multiple transiting planetary
system (K2-229) in which the inner planet has a radius
of 1.165 ± 0.066 Earth radii and a mass of 2.59 ± 0.43 Earth
masses. This Earth-sized planet thus has a core-mass fraction
that is compatible with that of Mercury, although it was
expected to be similar to that of Earth based on host-star
chemistry7
. This larger Mercury analogue either formed with
a very peculiar composition or has evolved, for example, by
losing part of its mantle. Further characterization of Mercurylike
exoplanets such as K2-229 b will help to put the detailed
in situ observations of Mercury (with MESSENGER and
BepiColombo8) into the global context of the formation and
evolution of solar and extrasolar terrestrial planets.
Refined parameters of the HD 22946 planetary system and the true orbital peri...Sérgio Sacani
Multi-planet systems are important sources of information regarding the evolution of planets. However, the long-period
planets in these systems often escape detection. These objects in particular may retain more of their primordial characteristics compared
to close-in counterparts because of their increased distance from the host star. HD 22946 is a bright (G = 8.13 mag) late F-type star
around which three transiting planets were identified via Transiting Exoplanet Survey Satellite (TESS) photometry, but the true orbital
period of the outermost planet d was unknown until now.
Aims. We aim to use the Characterising Exoplanet Satellite (CHEOPS) space telescope to uncover the true orbital period of HD 22946d
and to refine the orbital and planetary properties of the system, especially the radii of the planets.
Methods. We used the available TESS photometry of HD 22946 and observed several transits of the planets b, c, and d using CHEOPS.
We identified two transits of planet d in the TESS photometry, calculated the most probable period aliases based on these data, and
then scheduled CHEOPS observations. The photometric data were supplemented with ESPRESSO (Echelle SPectrograph for Rocky
Exoplanets and Stable Spectroscopic Observations) radial velocity data. Finally, a combined model was fitted to the entire dataset in
order to obtain final planetary and system parameters.
Results. Based on the combined TESS and CHEOPS observations, we successfully determined the true orbital period of the planet d
to be 47.42489 ± 0.00011 days, and derived precise radii of the planets in the system, namely 1.362 ± 0.040 R⊕, 2.328 ± 0.039 R⊕, and
2.607 ± 0.060 R⊕ for planets b, c, and d, respectively. Due to the low number of radial velocities, we were only able to determine 3σ
upper limits for these respective planet masses, which are 13.71 M⊕, 9.72 M⊕, and 26.57 M⊕. We estimated that another 48 ESPRESSO
radial velocities are needed to measure the predicted masses of all planets in HD 22946. We also derived stellar parameters for the host
star.
Conclusions. Planet c around HD 22946 appears to be a promising target for future atmospheric characterisation via transmission
spectroscopy. We can also conclude that planet d, as a warm sub-Neptune, is very interesting because there are only a few similar
confirmed exoplanets to date. Such objects are worth investigating in the near future, for example in terms of their composition and
internal structure.
The Surprising Evolution of the Shadow on the TW Hya DiskSérgio Sacani
We report new total-intensity visible-light high-contrast imaging of the TW Hya disk taken with the Space
Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope. This represents the first published
images of the disk with STIS since 2016, when a moving shadow on the disk surface was reported. We continue
to see the shadow moving in a counterclockwise fashion, but in these new images the shadow has evolved into
two separate shadows, implying a change in behavior for the occulting structure. Based on radiative-transfer
models of optically thick disk structures casting shadows, we infer that a plausible explanation for the change is
that there are now two misaligned components of the inner disk. The first of these disks is located between 5 and
6 au with an inclination of 5.5° and position angle (PA) of 170°, and the second between 6 and 7 au with
an inclination of 7° and PA of 50°. Finally, we speculate on the implications of the new shadow structure
and determine that additional observations are needed to disentangle the nature of TW Hya’s inner-disk
architecture.
50 Years of the Astronomy Centre at the University of SussexPeter Coles
This summarizes about 50 research papers and other notable events, approximately one for each year of existence of the Astronomy Centre at the University of Sussex (1966-2016). Shown at a special event on 15th October 2016. to mark the 50th Anniversary
We present the 2020 version of the Siena Galaxy Atlas (SGA-2020), a multiwavelength optical and infrared
imaging atlas of 383,620 nearby galaxies. The SGA-2020 uses optical grz imaging over ≈20,000 deg2 from the
Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys Data Release 9 and infrared imaging in
four bands (spanning 3.4–22 μm) from the 6 year unWISE coadds; it is more than 95% complete for galaxies larger
than R(26) ≈ 25″ and r < 18 measured at the 26 mag arcsec−2 isophote in the r band. The atlas delivers precise
coordinates, multiwavelength mosaics, azimuthally averaged optical surface-brightness profiles, model images and
photometry, and additional ancillary metadata for the full sample. Coupled with existing and forthcoming optical
spectroscopy from the DESI, the SGA-2020 will facilitate new detailed studies of the star formation and mass
assembly histories of nearby galaxies; enable precise measurements of the local velocity field via the Tully–Fisher
and fundamental plane relations; serve as a reference sample of lasting legacy value for time-domain and
multimessenger astronomical events; and more.
A smack model_of_colliding_planetesimals_and_dust_in_the_beta_pictoris_debris...Sérgio Sacani
Uma nova simulação de supercomputador da NASA do planeta e do disco de detritos ao redor da estrela Beta Pictoris revela que o movimento do planeta dirige ondas espirais através do disco, um fenômeno que gera colisões entre os detritos em órbita. Padrões nas colisões e a poeira resultante parece ser responsável por muitas feições observadas que pesquisas anteriores tinham sido incapazes de serem explicadas completamente.
Large-Scale Inference in Time Domain AstrophysicsJoshua Bloom
Presented at the 2014 Workshop on Algorithms for Modern Massive Data Sets (MMDS 2014), June 19, 2014 (Berkeley, CA):
The scientific promise of modern astrophysical surveys - from exoplanets to gravity waves - is palpable. Yet extracting insight from the data deluge is neither guaranteed nor trivial: existing paradigms for analysis are already beginning to breakdown under the data velocity. I will describe our efforts to apply statistical machine learning to large-scale astronomy datasets both in batch and streaming mode. From the discovery of supernovae to the characterization of tens of thousands of variable stars such approaches are leading the way to novel inference. Specific discoveries concerning precision distance measurements and using LSST as a pseudo-spectrograph will be discussed.
Differentiation between Global and Local Datum from Different aspect Nzar Braim
Differentiation between Global and Local Datum from Different aspect
Spatial professionals are required to deal with an increasingly wide range
of positioning information obtained from various sources including
terrestrial surveying, Global Navigation Satellite System (GNSS)
observations and online GNSS processing services. These positions refer
to a multitude of local, national, and global datums. A clear understanding
of the different coordinate reference systems and datums in use today and
the appropriate transformations between these are therefore essential to
ensure rigorous consideration of reference frame variations to
produce high-quality outcomes in spatial data analysis tasks.
Two temperate Earth-mass planets orbiting the nearby star GJ 1002Sérgio Sacani
We report the discovery and characterisation of two Earth-mass planets orbiting in the habitable zone of the nearby M-dwarf GJ 1002 based on
the analysis of the radial-velocity (RV) time series from the ESPRESSO and CARMENES spectrographs. The host star is the quiet M5.5 V star
GJ 1002 (relatively faint in the optical, V ∼ 13.8 mag, but brighter in the infrared, J ∼ 8.3 mag), located at 4.84 pc from the Sun.
We analyse 139 spectroscopic observations taken between 2017 and 2021. We performed a joint analysis of the time series of the RV and full-width
half maximum (FWHM) of the cross-correlation function (CCF) to model the planetary and stellar signals present in the data, applying Gaussian
process regression to deal with the stellar activity.
We detect the signal of two planets orbiting GJ 1002. GJ 1002 b is a planet with a minimum mass mp sin i of 1.08 ± 0.13 M⊕ with an orbital period
of 10.3465 ± 0.0027 days at a distance of 0.0457 ± 0.0013 au from its parent star, receiving an estimated stellar flux of 0.67 F⊕. GJ 1002 c is a
planet with a minimum mass mp sin i of 1.36 ± 0.17 M⊕ with an orbital period of 20.202 ± 0.013 days at a distance of 0.0738 ± 0.0021 au from
its parent star, receiving an estimated stellar flux of 0.257 F⊕. We also detect the rotation signature of the star, with a period of 126 ± 15 days. We
find that there is a correlation between the temperature of certain optical elements in the spectrographs and changes in the instrumental profile that
can affect the scientific data, showing a seasonal behaviour that creates spurious signals at periods longer than ∼ 200 days.
GJ 1002 is one of the few known nearby systems with planets that could potentially host habitable environments. The closeness of the host star
to the Sun makes the angular sizes of the orbits of both planets (∼ 9.7 mas and ∼ 15.7 mas, respectively) large enough for their atmosphere to be
studied via high-contrast high-resolution spectroscopy with instruments such as the future spectrograph ANDES for the ELT or the LIFE mission.
An Earth-sized exoplanet with a Mercury-like compositionSérgio Sacani
Earth, Venus, Mars and some extrasolar terrestrial planets1
have a mass and radius that is consistent with a mass fraction
of about 30% metallic core and 70% silicate mantle2
. At the
inner frontier of the Solar System, Mercury has a completely
different composition, with a mass fraction of about 70%
metallic core and 30% silicate mantle3
. Several formation or
evolution scenarios are proposed to explain this metal-rich
composition, such as a giant impact4, mantle evaporation5
or the depletion of silicate at the inner edge of the protoplanetary
disk6. These scenarios are still strongly debated.
Here, we report the discovery of a multiple transiting planetary
system (K2-229) in which the inner planet has a radius
of 1.165 ± 0.066 Earth radii and a mass of 2.59 ± 0.43 Earth
masses. This Earth-sized planet thus has a core-mass fraction
that is compatible with that of Mercury, although it was
expected to be similar to that of Earth based on host-star
chemistry7
. This larger Mercury analogue either formed with
a very peculiar composition or has evolved, for example, by
losing part of its mantle. Further characterization of Mercurylike
exoplanets such as K2-229 b will help to put the detailed
in situ observations of Mercury (with MESSENGER and
BepiColombo8) into the global context of the formation and
evolution of solar and extrasolar terrestrial planets.
Refined parameters of the HD 22946 planetary system and the true orbital peri...Sérgio Sacani
Multi-planet systems are important sources of information regarding the evolution of planets. However, the long-period
planets in these systems often escape detection. These objects in particular may retain more of their primordial characteristics compared
to close-in counterparts because of their increased distance from the host star. HD 22946 is a bright (G = 8.13 mag) late F-type star
around which three transiting planets were identified via Transiting Exoplanet Survey Satellite (TESS) photometry, but the true orbital
period of the outermost planet d was unknown until now.
Aims. We aim to use the Characterising Exoplanet Satellite (CHEOPS) space telescope to uncover the true orbital period of HD 22946d
and to refine the orbital and planetary properties of the system, especially the radii of the planets.
Methods. We used the available TESS photometry of HD 22946 and observed several transits of the planets b, c, and d using CHEOPS.
We identified two transits of planet d in the TESS photometry, calculated the most probable period aliases based on these data, and
then scheduled CHEOPS observations. The photometric data were supplemented with ESPRESSO (Echelle SPectrograph for Rocky
Exoplanets and Stable Spectroscopic Observations) radial velocity data. Finally, a combined model was fitted to the entire dataset in
order to obtain final planetary and system parameters.
Results. Based on the combined TESS and CHEOPS observations, we successfully determined the true orbital period of the planet d
to be 47.42489 ± 0.00011 days, and derived precise radii of the planets in the system, namely 1.362 ± 0.040 R⊕, 2.328 ± 0.039 R⊕, and
2.607 ± 0.060 R⊕ for planets b, c, and d, respectively. Due to the low number of radial velocities, we were only able to determine 3σ
upper limits for these respective planet masses, which are 13.71 M⊕, 9.72 M⊕, and 26.57 M⊕. We estimated that another 48 ESPRESSO
radial velocities are needed to measure the predicted masses of all planets in HD 22946. We also derived stellar parameters for the host
star.
Conclusions. Planet c around HD 22946 appears to be a promising target for future atmospheric characterisation via transmission
spectroscopy. We can also conclude that planet d, as a warm sub-Neptune, is very interesting because there are only a few similar
confirmed exoplanets to date. Such objects are worth investigating in the near future, for example in terms of their composition and
internal structure.
The Surprising Evolution of the Shadow on the TW Hya DiskSérgio Sacani
We report new total-intensity visible-light high-contrast imaging of the TW Hya disk taken with the Space
Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope. This represents the first published
images of the disk with STIS since 2016, when a moving shadow on the disk surface was reported. We continue
to see the shadow moving in a counterclockwise fashion, but in these new images the shadow has evolved into
two separate shadows, implying a change in behavior for the occulting structure. Based on radiative-transfer
models of optically thick disk structures casting shadows, we infer that a plausible explanation for the change is
that there are now two misaligned components of the inner disk. The first of these disks is located between 5 and
6 au with an inclination of 5.5° and position angle (PA) of 170°, and the second between 6 and 7 au with
an inclination of 7° and PA of 50°. Finally, we speculate on the implications of the new shadow structure
and determine that additional observations are needed to disentangle the nature of TW Hya’s inner-disk
architecture.
50 Years of the Astronomy Centre at the University of SussexPeter Coles
This summarizes about 50 research papers and other notable events, approximately one for each year of existence of the Astronomy Centre at the University of Sussex (1966-2016). Shown at a special event on 15th October 2016. to mark the 50th Anniversary
We present the 2020 version of the Siena Galaxy Atlas (SGA-2020), a multiwavelength optical and infrared
imaging atlas of 383,620 nearby galaxies. The SGA-2020 uses optical grz imaging over ≈20,000 deg2 from the
Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys Data Release 9 and infrared imaging in
four bands (spanning 3.4–22 μm) from the 6 year unWISE coadds; it is more than 95% complete for galaxies larger
than R(26) ≈ 25″ and r < 18 measured at the 26 mag arcsec−2 isophote in the r band. The atlas delivers precise
coordinates, multiwavelength mosaics, azimuthally averaged optical surface-brightness profiles, model images and
photometry, and additional ancillary metadata for the full sample. Coupled with existing and forthcoming optical
spectroscopy from the DESI, the SGA-2020 will facilitate new detailed studies of the star formation and mass
assembly histories of nearby galaxies; enable precise measurements of the local velocity field via the Tully–Fisher
and fundamental plane relations; serve as a reference sample of lasting legacy value for time-domain and
multimessenger astronomical events; and more.
A smack model_of_colliding_planetesimals_and_dust_in_the_beta_pictoris_debris...Sérgio Sacani
Uma nova simulação de supercomputador da NASA do planeta e do disco de detritos ao redor da estrela Beta Pictoris revela que o movimento do planeta dirige ondas espirais através do disco, um fenômeno que gera colisões entre os detritos em órbita. Padrões nas colisões e a poeira resultante parece ser responsável por muitas feições observadas que pesquisas anteriores tinham sido incapazes de serem explicadas completamente.
Large-Scale Inference in Time Domain AstrophysicsJoshua Bloom
Presented at the 2014 Workshop on Algorithms for Modern Massive Data Sets (MMDS 2014), June 19, 2014 (Berkeley, CA):
The scientific promise of modern astrophysical surveys - from exoplanets to gravity waves - is palpable. Yet extracting insight from the data deluge is neither guaranteed nor trivial: existing paradigms for analysis are already beginning to breakdown under the data velocity. I will describe our efforts to apply statistical machine learning to large-scale astronomy datasets both in batch and streaming mode. From the discovery of supernovae to the characterization of tens of thousands of variable stars such approaches are leading the way to novel inference. Specific discoveries concerning precision distance measurements and using LSST as a pseudo-spectrograph will be discussed.
EXTINCTION AND THE DIMMING OF KIC 8462852Sérgio Sacani
To test alternative hypotheses for the behavior of KIC 8462852, we obtained measurements of the star
over a wide wavelength range from the UV to the mid-infrared from October 2015 through December
2016, using Swift, Spitzer and at AstroLAB IRIS. The star faded in a manner similar to the longterm
fading seen in Kepler data about 1400 days previously. The dimming rate for the entire period
reported is 22.1 ± 9.7 milli-mag yr−1
in the Swift wavebands, with amounts of 21.0 ± 4.5 mmag in
the groundbased B measurements, 14.0 ± 4.5 mmag in V , and 13.0 ± 4.5 in R, and a rate of 5.0 ± 1.2
mmag yr−1 averaged over the two warm Spitzer bands. Although the dimming is small, it is seen at
& 3 σ by three different observatories operating from the UV to the IR. The presence of long-term
secular dimming means that previous SED models of the star based on photometric measurements
taken years apart may not be accurate. We find that stellar models with Tef f = 7000 - 7100 K and
AV ∼ 0.73 best fit the Swift data from UV to optical. These models also show no excess in the
near-simultaneous Spitzer photometry at 3.6 and 4.5 µm, although a longer wavelength excess from
a substantial debris disk is still possible (e.g., as around Fomalhaut). The wavelength dependence of
the fading favors a relatively neutral color (i.e., RV & 5, but not flat across all the bands) compared
with the extinction law for the general ISM (RV = 3.1), suggesting that the dimming arises from
circumstellar material
UV and Hα HST observations of 6 GASP jellyfish galaxiesSérgio Sacani
Star-forming, Hα-emitting clumps are found embedded in the gaseous tails of galaxies undergoing
intense ram pressure stripping in galaxy clusters, so-called jellyfish galaxies. These clumps offer a
unique opportunity to study star formation under extreme conditions, in the absence of an underlying
disk and embedded within the hot intracluster medium. Yet, a comprehensive, high spatial resolution
study of these systems is missing. We obtained UVIS/HST data to observe the first statistical sample
of clumps in the tails and disks of six jellyfish galaxies from the GASP survey; we used a combination
of broad-band (UV to I) filters and a narrow-band Hα filter. HST observations are needed to study
the sizes, stellar masses and ages of the clumps and their clustering hierarchy. These observations will
be used to study the clump scaling relations, the universality of the star formation process and verify
whether a disk is irrelevant, as hinted by jellyfish galaxy results. This paper presents the observations,
data reduction strategy, and some general results based on the preliminary data analysis. The UVIS
high spatial resolution gives an unprecedented sharp view of the complex structure of the inner regions
of the galaxies and of the substructures in the galaxy disks. We found clear signatures of stripping
in regions very close in projection to the galactic disk. The star-forming regions in the stripped tails
are extremely bright and compact while we did not detect a significant number of star-forming clumps
outside those detected by MUSE. The paper finally presents the development plan for the project.
47. The Telescope Optics
The most familiar type of X-ray optics in astronomy is the double coni-
cal telescope, especially the Wolter Type 1 telescope. This optic has been
employed in every X-ray telescope mission to date and in all those awaiting
launch. A Wolter telescope can be segmented and this is, in fact, being con-
sidered for the European XEUS telescope.
Kirkpatrick-Baez Mirror
Segmentation can also be applied, perhaps more eectively to the Kirkpatrick-
Baez (K-B) array of stacked orthogonal parabolic re
ectors (Figure A). As
shown in Figure B, a large K-B mirror can be segmented into rectangular
modules of equal size and shape.
A segmented K-B telescope has the advantage of being highly modular
on several levels. All segments are rectangular boxes with the same outer
dimensions. Along a column, the segments are nearly identical and many
are interchangeable with each other. All re
ectors deviate from
atness only
slightly after the
48. gures are imparted. On the other hand theWolter re
ectors
are highly curved in the azimuthal direction and the curvature varies over a
wide range. Furthermore, within a segment, the K-B re
ectors themselves
can be segmented along the direction of the optical axis. As shown in Figure
C, a K-B mirror system can be folded more easily than the Wolter mirror
into a compact volume for launch and deployment in space.
9
49. Figure A. Kirkpatrick-Baez mirror consisting of orthogonal stacks of re
ectors. Each re-
ector is a parabola in one dimension.
Figure B. A large K-B mirror can be segmented into rectangular modules of equal size
and shape.
10
50. Figure C. Mirror folded for launch (upper) and unfolded in situ (lower).
11
53. rst shows a segmented telescope (as a Kirkpatrick-Baez type mirror
assembly) situated on its own spacecraft. At a distance equal to the focal
length (about 300 m) are a group of spacecrafts containing detectors of vari-
ous dierent types, i.e. high resolution, wide
54. eld, spectroscopy, etc. Usually
only one detector is active and precisely stationed at the focus. With the
aid of its own sensors and signals sent from the telescope that spacecraft
performs station keeping to maintain that distance equal to the focal length
with a few milimeters.
In the second
55. gure the target is changed. Only the active detector which
may not be the same one of the previous
56. gure has changed position to take
up the focal plane station. The others can stay put until they go into service.
The third
57. gure shows an alignment of three satellites whichmay be needed
for certain very high resolution dispersive spectroscopy measurements.
12