We review what could be astronomy from the Moon in the next decades in the visible domain. After a short review observational approaches, from photometry to high contrast and high angular resolution imaging, We essentially focus on some promising scientific objectives, from Solar System to the extragalactic domain. At the end, I add a proposal to use the Earth-Moon system to test fundamental physics. Since this meeting is dedicated to the next decades of Astronomy from the Moon, we consider projects and science objectives for several decades from now.

1. Phil. Trans. R. Soc. A.
doi:10.1098/not yet assigned
Astronomy from the Moon: From Exoplanets to Cosmology and Beyond in Visible Light
Jean Schneider and Antoine Labeyrie
Insert
affiliations here, include: Department, Institution, Address, City, Area and Code,
Country, ORCID ID"
Keywords: solar system - exoplanets - stellar physics – cosmology - quantum
physics
Abstract
We review what could be astronomy from the Moon in the next decades in the visible domain.
After a short review observational approaches, from photometry to high contrast and high angular
resolution imaging, We essentially focus on some promising scientific objectives, from Solar
System to the extragalactic domain. At the end, I add a proposal to use the Earth-Moon system to
test fundamental physics. Since this meeting is dedicated to the next decades of Astronomy from
the Moon, we consider projects and science objectives for several decades from now.
1. Introduction
The Moon offers exceptional conditions for astronomy since it accumulates the advantages of
ground based and space based observational conditions. Without atmosphere, it has the same sky
quality than telescopes on satellites and access to all wavelengths. It will also permit the same
Jean Schneider (jean.schneider@obspm.fr)
Paris Observatory, Luth UMR 8102, Meudon, 92190, France
ORCID 0000-0002-3136-6537
Antoine Labeyrie (anlabeyrie@orange.fr)
Observatoire de La Côte d’Azue, Nice, 06000 , France

2. upgrade and reparation possibilities than on Earth. In addition, lunar observatories offer
conditions which are specific to the Moon: 1/ since the Moon rotates 28 slower than Earth, it
permits longer observations of an object than ground based telescopes 2/ since they see the sky
through an angle different than the view from Earth, they allow some observations impossible
from Earth. Another advantage of lunar telescopes compared to space telescopes is that the latter
have a limited lifetime due to fuel consumption, although there are projects to refurbish
spacecrafts with spatializes fuel tankers1
Here we restrict ourselves to optical astronomy in the
visible wavelengths, infrared astronomy being discussed by Maillard (2023 ALLURE project [1]).
In section 2 we list instrumental approaches: spectrophotometry, spectropolarimetry and
interferometry. In section 3 we review the main logistic issues. In section 4 we provide a, non
exhaustive, sometimes nonstandard, panorama of science objectives, in the spirit of [2]. Finally, in
section 5 we propose a 1-5 meter telescope as a common precursor of different large projects.
2. Instrumental approaches
2.1 Spectro-photometry and spectro-polarimetry
A priori, any telescope can make both of them. The 1,000 m2
array of 6.5 m telescopes at the
lunar pole (Life Finder Telescope At Lunar Poles LFTALP) project is an array dedicated to
transits [3]. It is a lunar extension of the ground-based LFAST project (Large Fiber Array
Spectroscopic Telescope [4]). The LOUVE project (Lunar Optical UV Explorer - [5]) is a 30 cm
project to take advantage of the absence of lunar atmosphere to make spectrophotometry of bright
sources in the UV.
2.2 Direct imaging
2.2.1 Moderate size telescopes. As presented in this issue, the Loupe telescope is
a one meter class telescope devoted to observe the Earth ([6], |7]). In the section 4
we extend its original goal to other scientific purposes.
2.2.2 Large telescopes
Large telescopes provide both high angular resolution and photometric sensitivity.
They present less difficulty to manoeuvre than large terrestrial telescopes since the
lunar gravity is smaller than on Earth and there is no wind on the Moon. Theble:
OWL-Moon project is a 50 or more meter class proposed telescope |8] equipped
with a coronagraph for very high contrast imaging with multiple sciences cases,
from exoplanets to cosmology.
2.3 Very high angular resolution
2.3.1 Standard interferometer
1For instance the Orbit Fab company is preparing tanker refuelling mission :
https://www.orbitfab.com/

3. A standard interferometer project, similar to the Gravity interferometer at the
european VLT [9] has recently been proposed for the Moon [10]. It could have a
several kilometre baseline. Since with its 28 days orbit around the Earth and its
locked orbit the Moon rotates more slowly than Earth, for a given observation time
the delay lines must be 28 times shorter than for a ground based telescope.
2.3.2 Hypertelescope
A hypertelescope is a 2D array with many sub-pupill mirrors where, at the
recombined focus, there is a “pupill densifier” which directly provides 2D images
instead of complicated fringed images for extended sources. One introduces a FOV
limitation, that does not depend on the geometry of the array but only on the beam
combination scheme. This field is referred to as Direct Imaging FOV (DIF), that is,
the FOV inside which an image of a source can be formed directly [36]. If s is the
spacing of two adjacent mirrors (assume larger than the mirror sizes), the “Direct
Imaging FOV” (DIF) angular size θDIF = λ/s and diameter of the interference
peak θpeak= λ/D imply that the DIF can contain a grid of nr = (D/s)2
= N adjacent
resolution elements (resels) . But the residual halos surrounding the interference
peak in the image of each point source become incoherently added in the image,
thus degrading the image contrast. If the DIF size is configured to match that of the
planet's image, thus containing N resels, the resulting halo level grows as N and
therefore reaches that of the interference peaks. Deconvolution techniques such as
modified for hypertelescopic images are more efficient and can even reconstruct
sources located beyond the DIF, while still in the Fizeau envelope [11]. A ground-
based demonstrator is under construction in the south of France [34]. On the Moon,
the array may be a classical interferometer with delay lines to compensate the
Moon rotation. Due to the slow orbital revolution of the Moon around the Earth
compared to the 24 hour Earth rotation, for a 3 hour observation 1 meter delay
lines are sufficient, compared to 30 meters delay lines at the VLTI. To avoid delay
lines, the mirrors could be installed on a paraboloid in a lunar crater (Figure 1).
The pixels on a 2D objects have, at a wavelength λ , an angular resolution
λ/s where s is the spacing of sub-pupills.

4. Figure 1 Sketch at approximate scale of a Crater-Nested Lunar Hypertelescope with its focal
receiver suspended from cables and movable along the focal surface (fine dotted arc). The locus
of the mirror array (fat dotted arc) is either paraboloidal actively deformable by applying small
tip-tilt piston corrections on its segments, or fixed and spherical if a corrector of spherical
aberration is added in the focal optics. No delay lines are needed but the “meta-mirror” size is
limited to about 20 km by the maximal 6 km depth of impact craters for an effective meta-
aperture of 5–10 km. The mirror elements are either carried by separate fixed tripods or by a
hammock-like cable netting. The figure at right shows how the focal instruments can be moved to
follow the target or go to another target [12].
Another solution would be to attach the small mirrors to the crater cliff, with focal
instruments on the opposite point of the cliff summit (Figure 2). It would avoid yje
need for a long cable carrying the focal instruments, but the pointing range
visibility would be very limited.
Figure 2 Hypertelescope with mirrors on a cliff of the crater
2.3.3 Intensity Interferometry
Intensity interferometry [35], with two telescopes measures the factor |γ 12|
defined by
<Δ I1(t ,r1)Δ I2(t ,r2)>=(<I (r1,t)>< I (r2 ,)>)(1+|γ12|
2
) (1)

5. where γ12 is the mutual coherence function of light between locations r1 and r2
and < > means the time average. For three telescopes The relation becomes
<Δ I1(t ,r1)Δ I2(t ,r2)Δ I3(t ,r3)>=(< I (r1,t)>< I(r2 ,t)><I (r3 ,t)>).(1+| γ12|
2
| γ23|
2
| γ31|
2
+2ℜ(γ12 γ23 γ31))
etc for N telescopes [13].
For two telescopes, the signal to noise ratio is
(S/N)RM S=A·α ·n·γ12(r)
2
·Δ f
1/2
·(T /2)
1/2
(2)
where A is the geometric mean of the areas (not diameters) of the two
telescopes, α is the quantum efficiency of the optics plus detector system, n is
the flux of the source in photons per unit optical bandwidth per unit area per
unit time; ∆f is the bandwidth of the detector and T is the integration time [13].
The correlation leads to an angular resolution up to λ /L for a wavelength λ
and a baseline L. But, to achieve a S/N ratio of 3, the relation (2) shows that it
requires a very narrow wave band with a very fast (pico to femto second time
resolution) detector and a large number of collected photons to reach a 3 sigma
SNR. A large collecting area is thus required. A 50 meter OWL-Moon like
telescope on the Moon and some 30-40 meter class ground-based telescopes are
suited for that purpose. For N telescopes with non-redundant baselines, the number
of baselines is N(N-1)/2. A large number of baselines allows for the construction of
2D images of extended objects with an angular resolution λ/L where L is the
mean separation of two telescopes. For an Earth-Moon intensity interferometer one
can combine all future lunar optical telescopes, in particular the 1,000 m2
array of
6.5 m telescopes at the lunar pole [3] and ground optical telescopes and the
multiplication of baselines provided by the Earth orbit around the Sun and the
Moon orbit around the Earth to explore the (u, v) Fourier transform plane. In
addition to a few very large ground telescopes, it has been proposed to use the
collaboration of many amateur ground telescopes [14]. They would add terrestrial
baselines and contribute to the total collecting area A used in the formula (2).
3. Issues
3.1 Dust
There are and will be two main sources of lunar dust, meteoritic impacts and
human activities. They will essentially degrade the reflectivity or transparency of
optical surfaces. Several projects intend to measure its properties, e.g. [15] It is
thus important to take countermeasures to eliminate its impacts on instrumentation.
For instance, electromagnetic removal has been proposed [16].
3.2 Lunar seismology

6. As analysed in [17], the seismic activity of the Moon may be an issue for lunar
interferometers. But, as noted by the authors, a “Moon-based version could be
considered in the long term when a human presence would permit maintenance
and upgrading leading to a longer lifetime with continuous performance
enhancement”. Indeed, in the long term humans will be able to equip
interferometers with acoustic filters, similarly to what is done for terrestrial
gravitational wave detectors. There is thus no show stop here.
3.3 Location
The best location of a lunar telescope depends on two factors: the physical
conditions of the location (temperature, soil quality, solar illumination) and and
and its scientific objectives. For instances, telescopes looking in the Earth direction
have to be located on the near side of the Moon. From the point of view of target
observability they can be placed almost anywhere. At the lunar poles, only half the
sky is visible, but all the time. At the lunar equator, all sky is visible, but only half
time.
For LOUPE the optimum is not far from the lunar equator. For LOUVE, three
possible possible locations can be considered on the two lunar north and southern
hemispheres and near the equator since it should be a mow-cost telescope.
4. Main Science Objectives
4.1 Solar System
4.1.1 Observations towards the Earth
4.1.1.1 Observations of the Earth itself
The Loupe project is intended to observe the Earth as en exoplanet |6], [7]. It
will in particular determine its polarimetric properties as a function of the phase
angle of the reflected Sun light along its orbit around the Sun. In section 4.1.1.2
another application is described.
EUSO (Extreme Universe Space Observatory) will detect the cosmic ray
showers in the Earth atmosphere from balloons and circum-terrestrial satellites
[18] (Figure 3). A lunar EUSO will have a more global view than satellite-
based EUSOs

7. Figure 3 Different versions of a balloon or in-orbit EUSO. Available at the
EUSO website https://www.jemeuso.org/missions/overview/
4.1.1.2 Solar eclipses
As seen from the Moon, the Earth is 3.8 times as large than the Sun and than
the Moon as seen from the Earth. Therefore, solar eclipses of the Sun by the
Earth as seen from the Moon last 3.8 times longer than solar eclipses by the
Moon as seen from the Earth and will see the far outer regions of the solar
corona (Figure 4).
In addition, it provides a way to probe the whole Earth atmosphere by
transmission spectroscopy of the Sun during the ingress and egress of the
eclipses. And, while Soho and Parker will have a limited lifetime, a lunar
telescope will have a longer lifetime and looking at the Sun will provide long
term observations.

8. Figure 4 Solar far corona seen from the Moon during a solar eclipse by the Earth
4.1.1.3 Stellar observations through Earth’s atmosphere
When a star is on the line joining a lunar telescope to the center of Earth or
very close to it, the Earth atmosphere acts as Earth-sized converging lens [19].
The light rays coming from the star are refracted under different angles,
depending on their wave length and the altitude of their path in the Earth
atmosphere. Some will exactly converge at the Moon surface (Figure 5),
leading to a magnification up to 50,000 |19]. This type of lens is not suited to
imaging, but, its magnification can make it helpful for the photometric
detection of very faint optical sources. For instance, with the help of a high
speed photometer it can detect new optical pulsars. In addition, the
spectroscopic monitoring of these stellar observations will allow to follow the
modifications of the terrestrial atmosphere with meteorology, seasons and solar
eruptions for instance.
Figure 5 Stellar image seen on the Moon through the global Earth atmosphere as a lense.
4.1.1.4 Sun + Earth gravitational deviation
According to General Relativity, a light ray passing at a distance r from an
object of mass M is deviated by an angle α=GM /rc2
=RScharz /r ( RScharz is
the Schwarzschild radius of the object).

9. Since the solar eclipses last 3.8 longer as seen from Earth, and since stellar
positions seen from the Moon will not suffer from atmospheric perturbations,
the precision of measurements will be better than from Earth.
A light ray passing at 2 solar radii from the Sun is deviated by an angle αSul
= 0.5 arcsec. A light ray passing at 1.05 Earth radius from the Earth is deviated
by an angle α Earth = 0.3 mas. A 0.1 mas angular precision is achieved at 0.5
micron by a 25 meter lunar telescope, which would therefore detect from the
Moon the gravitational deflection of a star by the Earth at a 3 sigma level. If, as
seen from the Moon, the Earth is approximately close to the Sun (or even
eclipsing the Sun), the two deviations add (when the star is seen on the same
side of the Sun and the Earth) or subtract themselves (when the star is seen
from the Moon between the Earth and the Sun). Since General relativity is a
non linear theory, the two deviation will only add in first order. The Post
Newtonian formalism adds an additional term O( αSun α Earth ) to the linear
theory. Since the Einstein theory of the two-body Earth-Sun system is not
linear, the global deviation will not be the sum αSun+α Earth
4.1.2 .Stellar occultation by solar systems objects.
Such occultations, if observed from the Moon will generally not be also
observable from Earth. And thanks to the fact that Moon’s rotation is 28 times
longer than Earth’s, stellar occultation could last 28 times longer than seen
from the Earth, depending on the Moon-asteroid-occulted star configuration.
Unfortunately, the probability that the occultation by a given object of the same
star seen from Earth and, before or later, from the Moon is only
(REarth /DEM )
2
=2.10
−4
where REarth and DEM are the Earth radius and
the Earth-Moon distance.
4.2 Exoplanets
4.2.1 Transits light curves and spectroscopy
The 1200 m2 array project at the lunar pole [3] and an OWL-Moon like 50-meter
telescope [8] will make precise measurements of planet radii, Transit Time
Variations (leading to the detection of additional planets and of exo-moons) and
search for the chemical composition of exoplanet atmospheres, potentially
providing biosignatures.
4.2.2 Microlensing Detection
With a lunar telescope one can make coordinated Earth-Moon parallax
observations. Gravitational microlensing generates a circular “Einstein ring” when
the background source is exactly aligned with a circular foreground lens. If the

10. foreground lens is a binary point system, the Einstein ring becomes a non circular
caustics. The background source has a maximum amplification when its line-of-
sight as seen from the Earth crosses the caustics. When the background star is seen
from outside of Earth, it crosses the caustics at different times. This has been
observed with the Spitzer space telescope for OGLE-2016-BLG-1093Lb (Figure 6 -
[20]). Since from the Moon the microlensing event is seen under an angle different
from Earth, it will provide a better 2D characterization of the planet location
respective to its parent star.
Figure 6 Coordinated Earth-Spitzer
microlensing parallax for OGLE-2016-
BLG-1093Lb [20].
4.2.3 Direct imaging
4.2.2.1 Standard
angular resolution
Figure 6 Coordinated Earth-Spitzer microlensing parallax for OGLE-2016-BLG-1093Lb
[20].
A 50 meter OWL-Moon like telescope will provide the detection and make
spectroscopic observations of 300-500 Earth-like planets in 20 years [8]. The

11. follow-up of the planet observations will provide the 3D planet orbits and
seasonal effects.
4.2.2.2 Very high angular resolution
The multipixel observation of exoplanet’s morphology has already been
described in [12]. Here we add other sciences cases.
4.2.2.2.1 Specular reflection of oceans
McCullough [32] and Williams & Gaidos [33] have proposed to detect the
specular reflection of the parent star on oceans of exoplanets (Figure 7). For
example, the glint of terrestrial oceans has been detected with the LCROSS
mission [21]. The follow-up along the planet rotation of the specular reflection
will help to shape the non-reflective parts of the planets, that is their continents.
Figure 7 Simulation of the solar glint by Earth ocean [60]
4.2.2.2.2 Very high resolution imaging of transits
The spectro-imaging of planetary transits of transits can be made with a
hyptertelescope. If RΔ is the spatial resolution on the stellar surface, one
gains a factor R* /RΔ in the SNR compared to transits seen without
resolving the stellar surface, where R* is the stellar radius (Figure 8).

12. Figure 8 Multipixel imaging of planetary transits
Exo-rings and exo-moons can also be detected with Intensity Interferometry
(Figure 9 ).
Figure 9 Simulation of transits of a giant planet with rings and moons seen
by a 2 km intensity interferometry array [13].

13. 4.2.2.2.3 Mountains and volcanoes on planets
Let us go further about very high resolution imaging. Whereas
several of the above science topics can be addressed with a
single OWL on the Moon, some questions require the
extremely high angular resolution afforded by an Earth–Moon
Intensity Interferometer. Once an OWL-type telescope is
installed on the Moon, or even a 10 m lunar precursor, one could
readily address optical Intensity Interferometry with
unprecedented baselines and angular resolution. For instance
it could measure the heights of mountains on transiting
exoplanets. This is an important problem for the geophysics of
planets. Weisskopf [22] has shown that there is a relationship
between the maximum height of mountains on a planet and
its mass and the mechanical characteristics of its crust. The
issue of the detectability of the mountains has already been
addressed for transiting planets [23]. Here we propose a
significant improvement, based on the principle of the
detection of the silhouette of ringed planets by Intensity
Interferometry as developed in [19]. With a 60 m resolution at
the 1.4 pc distance of alpha Cen, for transiting planets,
mountains, down to 500 meter height, will appear at the
border of the planet silhouette during the transit (in case of a
transparent atmosphere with no clouds). These observations
will require very long exposures. During the exposure, the
planet is rotating around its axis, leading to a washing-out of
the features that we are looking at. But the planet rotation
period will be well known from the periodicity of its
photometric data [6]. Therefore, the mountain silhouette will
appear in a two-dimensional Fourier transform of a long
series of short exposure images at the planet rotation
frequency. Moreover, volcanoes, generally associated with
high mountains, can be detected as a temporary excess of red
emission of the planet.
4.3 Stellar physics

14. 4.3.1 Pulsar pulse echoes
Pulsars are generally surrounded by a nebula, gaseous and/or dusty. We
propose to detect the optical echo of the pulse on nearby opaque clumps of
the nebulae with a high speed high angular resolution. The time delay
between the direct pulse and its echoes give the 3D geometry of the
configuration. For the Crab pulsar at 2.5 kpc, with a visible
magnitude 17, assuming clumps at 10 AU from the pulsar
with a 10% reflectivity, and a size 1 AU, the echoes would
have a magnitude m=17−2.5log10 (1/(10∗2π))=22 , still
detectable with a large telescope.
4.3.2 Stellar gravitational lensing
When two stars are on the same line of sight, the foreground star acts as a
gravitational lens on the background star, leading to an ring-like image of the
background star (Einstein ring) with a radius RE=√RSchwarz DS DL/ DLS ,
where RSchwarz is the foreground star Schwarzschild radius, DS and DL the
source and lens distances and DSL the lens-source distance, and a surface
brightness equal to that of the background star. If its angular size is larger than
the foreground star, one can mask the foreground star by a coronagraph and see
only the Einstein ring. If the two stars are not exactly on the same line of sight,
the Einstein ring breaks into two arcs (see Figure 11). For instance, the Einstein
ring of a star at 8 kpc, lensed by a 1 M star at 6 pc has a radius of 70µas |
⊙
24]. See the Figure 10.
Figure 10 Simulation of the Einstein ring of a star at 8 kpc, lensed by a 1 M star at 6 pc. The
⊙
foreground star is occulted by a coronagraph. The radius of the Einstein ring is 70µas [24]

15. 4.4 Extragalactic domain
4.4.1 Gravitational lensing of quasars.
Very high angular resolution gives access to very detailed images, for example in
the case of quasar microlensing. When a background quasar is slightly off the
galaxy line of sight, its Einstein ring breaks into a larger and a smaller arc. The
figure 11 shows the configuration for the Double Quasar 0957+561 (mV = 17).
Very high resolution images will measure the length and width of these arc, and
their curvature will constrain the shape of the lensing galaxy.
Figure 11 Geometry of a lensed quasar, adapted from [25] for the double quasar QSO 0957+561.
RS and DS are the radius and the distance of the quasar source, ML and DL are the mass and the
distance of the lensing galaxy. The figure is not on scale, and the lens galaxy is supposed to be
spherical.
4.4.2 Dark matter distribution
Einstein rings can be disrupted by anomalies in dark matter distribution in the case
where dark matter is made of axions, beyond the standard particle model [26]
(Figure 12).

16. Figure 12 Left: Einstein ring in case of dark matter distributed smoothly in Weakly Interacting
Massive ParticleS (WIMPS). Right: Einstein ring modulated by fluctuations in dark matter
distribution (after [26]).
4.5 Quantum Physics
In the quantum mechanical theory of observation, the problem is the following. The
quantum entanglement between pairs of photons (correlations of photon polarisation)
can, theoretically, go up to infinity. It has been proposed to test this statement for
Earth-Moon distances ([27], [28]): the two photon detectors would be placed one on
Earth and the other on the on the Moon. Recently a variant implementation has been
proposed [29]. The source of photons pairs would be at the Earth-Sun L4 or L5
Lagrange point and one detector on the Earth and the other on the Moon (Figure 13).
Actually, both experiments should be implemented since, given our ignorance of what
could be beyond standard quantum mechanics, one does not know if a variation of
entanglement with distance depends on the length of photon passes or on the distance
between detectors.
Figure 13 A source of entangled photons pairs at the Earth-Sun L4 or L5 Lagrange point
and one detector on the Earth and the other on the Moon [29].

17. One may wonder if there can be a priori theoretical estimates for a distance scale D
or a speed of propagation V of non standard correlations. Playing only with the
usual fundamental constants h, c and G can only give V = c or V = ∞ and D =
Planck length 10-33 cm. Playing in addition with less fundamental constants like
the quark mass Mquark allows to multiply these values by any arbitrary power N of
the dimensionless constant G Mquark
2
/hc ~ 10-39
. For small values of N like -1 or
+1 one gets V = 10+/-39
c and D = 10-33/+39
cm. Another source of a priori estimates
for the distance scale D could come from possible non standard theories or
phenomena like short-scale « fifth » force (D= a few cm to a few meter), the
MOND theory as an alternative theory to dark matter (D ~ 10kpc, [30]), the
Pioneer Anomaly (D ~ 10 AU) or the distance D = cT = 100 kpc derived from the
time scale T = 108 yr for the « spontaneous collapse» [31]. As one can see, the
span of possible a priori predictions has no solid constraint and only experiment
may eventually provide a constraint.
5 A precursor
Among the several facilities described in this meeting, some of them could have a
common one to few meter-class telescope precursor with different focal detectors, from
UV to infrared, in order to explore the different logistic problems. These are LOUVE,
LOUPE, LFTALP, ALLURE, and OWL-Moon. The science case of LOUPE requires a
location from where the Earth is visible, therefore not the far side of the Moon. The
compatibility with other projects has to be discussed further. Although interferometer
need several telescopes, they would also profit from the logistics lessons provided by. a
single aperture small precursor.
Additional Information
Authors' Contributions
Antoine Labeyrie has conceived and described the lunar hypertelescope. Jean Schneider has
provided science cases.
Competing Interests
The authors declare they have no competing interests.
Funding Statement
Jean Schneider is funded by the Paris Observatory/PSL. Antoine Labeyrie is funded by the
Collège de France
Acknowledgements

18. Jean Schneider is grateful to Roger Angel, Dainis Dravins, Alain Grimaud, Bruno Lacamp and
Jean-Pierre Maillard for discussions.
Data Accessibility
This article has no data.
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