Our knowledge of the physical and dynamical properties of the small body populations in the solar system is constantly improving, thanks to new Earth- and space-based observations, space missions as well as theoretical advances, and the appearance of the first interstellar objects. The goal of this session is to highlight recent results that are providing fundamental clues about the early stages of the solar and extrasolar systems.
Previous work has demonstrated orbital stability for 100 Myr of initially near-circular and coplanar small bodies in a region termed the 'Earth–Mars belt' from 1.08 au<a<1.28 au. Via numerical integration of 3000 particles, we studied orbits from 1.04–1.30 au for the age of the Solar system. We show that on this time scale, except for a few locations where mean-motion resonances with Earth affect stability, only a narrower 'Earth–Mars belt' covering a∼(1.09,1.17) au, e<0.04, and I<1◦ has over half of the initial orbits survive for 4.5 Gyr. In addition to mean-motion resonances, we are able to see how the ν3, ν4, and ν6 secular resonances contribute to long-term instability in the outer (1.17–1.30 au) region on Gyr time scales. We show that all of the (rather small) near-Earth objects (NEOs) in or close to the Earth–Mars belt appear to be consistent with recently arrived transient objects by comparing to a NEO steady-state model. Given the <200m scale of these NEOs, we estimated the Yarkovsky effect drift rates in semimajor axis, and use these to estimate that a diameter of ∼100km or larger would allow primordial asteroids in the Earth–Mars belt to likely survive. We conclude that only a few 100 km scale asteroids could have been present in the belt’s region at the end of the terrestrial planet formation.
How to cite:
Huang, Y. and Gladman, B.: Primordial Stability of the Earth–Mars Belt, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-164, https://doi.org/10.5194/epsc2020-164, 2020.
Long-period comets coming from the Oort cloud are thought to beplanetesimals formed in the planetary region on the ecliptic plane.We have investigated the orbital evolution of these bodiesdue to the Galactic tide.We extended Higuchi et al. (2007) and derived theanalytical solutions to the Galactic longitude and latitude ofthe direction of aphelion, L and B.Using the analytical solutions,we show that the ratio of the periods of the evolution of L and B is very close to either 2 or ∞ for initial eccentricities ei∼1,as is true for the Oort cloud comets.From the relation between L and B, we predict that Oort cloud comets returning to the planetary region concentrate on the ecliptic planeand a second plane, which we call the "empty ecliptic".This consists in a rotation of 180° of the ecliptic around the Galactic pole. Our numerical integrations confirm that the radial component of the Galactic tide, which is neglected in the derivation of the analytical solutions,is not strong enough to break the relation between L and B derived analytically. Brief examination of observational data showsthat there are concentrations near both the ecliptic and the empty ecliptic. We also show that the anomalies of the distribution of B of long-period comets mentioned by several authors are explained by the concentrations on the two planes more consistently than the previous explanation.
How to cite:
Higuchi, A.: Anisotropy of long-period comets explained by their formation process, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-265, https://doi.org/10.5194/epsc2020-265, 2020.
It is widely accepted that the theoretical framework of the so-called Lidov-Kozai oscillation was established independently in the early 1960s by a Soviet Union dynamicist (Michail L'vovich Lidov) and by a Japanese celestial mechanist (Yoshihide Kozai). A large variety of studies has stemmed from the original works by Lidov and Kozai, now having the prefix of "Lidov-Kozai" or "Kozai-Lidov." However, from a survey of past literature published in late nineteenth to early twentieth century, we have confirmed that there already existed a pioneering work using a similar analysis of this subject established in that period. This was accomplished by a Swedish astronomer, Edvard Hugo von Zeipel. In this presentation we make a brief summary of von Zeipel's work on this subject in contrast to the works of Lidov and Kozai, and show that von Zeipel's achievements in the early twentieth century (written and published in French under the title "Sur l’application des séries de M. Lindstedt à l’étudedu mouvement des comètes périodiques") already comprehended most of the fundamental and necessary formulations that the Lidov-Kozai oscillation requires. By comparing the works of Lidov, Kozai, and von Zeipel along this line of studies, we assert that the prefix "von Zeipel-Lidov-Kozai" should be used for designating this theoretical framework, and not just Lidov-Kozai or Kozai-Lidov.
How to cite:
Ito, T. and Ohtsuka, K.: The Lidov-Kozai oscillation and Hugo von Zeipel, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-269, https://doi.org/10.5194/epsc2020-269, 2020.
Youssef Moulane, Emmanuel Jehin, Francisco José Pozuelos, Jean Manfroid, Zouhair Benkhaldoun, and Bin Yang
Long Period Comets (LPCs) have orbital periods longer than 200 years, perturbed from their resting place in the Oort cloud. Such gravitational influences may send these icy bodies on a path towards the center of the Solar system in highly elliptical orbits. In this work, we present the activity and composition evolution of several LPCs observed with both TRAPPIST telescopes (TS and TN) during the period of 2019-2020. These comets include: C/2017 T2 (PANSTARRS), C/2018 Y1 (Iwamoto), C/2018 W2 (Africano), and disintegrated comet C/2019 Y4 (ATLAS). We monitored the OH, NH, CN, C2 and C3 production rates evolution and their chemical mixing ratios with respect to their distances to the Sun as well as the dust production rate proxy (A(0)fp) during the journey of these comets into the inner Solar system.
C/2017 T2 (PANSTARRS) is a very bright comet which was discovered on October 2, 2017 when it was 9.20 au from the Sun. We started observing this comet with TS at the beginning of August 2019 when it was at 3.70 au. The comet made the closest approach to the Earth on December 28, 2019 at a distance of 1.52 au and it passed the perihelion on May 4, 2020 at 1.61 au. The water production rate of the comet reached a maximum of (4,27±0,12)1028 molecules/s and its dust production rate (A(0)fp(RC)) also reached the peak of 5110±25 cm on January 26, 2020, when the comet was at 2.08 au from the Sun (-100 days pre-perihelion). At the time of writing, we still monitoring the activity of the comet with TN at heliocentric distance of 1.70 au. Our observations show that C/2017 T2 is a normal LPC.
C/2018 Y1 (Iwamoto) is a nearly parabolic comet with a retrograde orbit discovered on December 18, 2018 by Japanese amateur astronomer Masayuki Iwamoto. We monitored the activity and composition of Iwamoto with both TN and TS telescopes from January to March 2019. The comet reached its maximum activity on January 29, 2019 when it was at 1.29 au from the Sun (-8 days pre-perihelion) with Q(H2O)=(1,68±0,05)1028 molecules/s and A(0)fp(RC)= 92±5 cm. These measurements show that it was a dust-poor comet compared to the typical LPCs.
C/2018 W2 (Africano) was discovered on November 27, 2018 at Mount Lemmon Survey with a visual magnitude of 20. The comet reached its perihelion on September 6, 2019 when it was at 1.45 au from the Sun. We monitored the comet from July 2019 (rh=1.71 au) to January 2020 (rh=2.18 au) with both TN and TS telescopes. The comet reached its maximum activity on September 21, 15 days post-perihelion (rh=1.47 au) with Q(H2O)=(0,40±0,03)1028 molecules/s.
C/2019 Y4 (ATLAS) is a comet with a nearly parabolic orbit discovered on December 18, 2019 by the ATLAS survey. We started to follow its activity and composition with broad- and narrow-band filters with the TN telescope on February 22, 2019 when it was at 1.32 au from the Sun until May 3, 2020 when the comet was at a heliocentric distance of 0.90 au inbound. The comet activity reached a maximum on March 22 (rh=1.65 au) 70 days before perihelion. At that time, the water-production rate reached (1,53±0,04)1028 molecules/s and the A(0)fp reached (1096±14) cm in the red filter. After that, the comet began to fade and disintegrated into several fragments.
How to cite:
Moulane, Y., Jehin, E., Pozuelos, F. J., Manfroid, J., Benkhaldoun, Z., and Yang, B.: Narrow-band photometry of Long Period Comets with TRAPPIST telescopes in 2019-2020, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-419, https://doi.org/10.5194/epsc2020-419, 2020.
Boris Pestoni, Kathrin Altwegg, Hans Balsiger, Nora Hänni, Martin Rubin, Isaac Schroeder I, Markus Schuhmann, and Susanne Wampfler
The coma of active comets contains two essential components resulting from cometary activity: gas and dust. To investigate the latter, the Rosetta spacecraft was equipped with several instruments fully dedicated to the analysis of dust in the coma of comet 67P/Churyumov-Gerasimenko (67P).
We show that, although not designed to observe dust, another instrument onboard Rosetta can obtain information about dust particles from 67P: the ROSINA-COPS ram gauge (RG, ) shown in Figure 1. In particular, it was possible to measure the sublimation of the volatile part of dust agglomerates entering the instrument. From these measurements, we find three different families of volatiles and dimensions, calculated as a diameter of an equivalent sphere of water, of hundreds of nanometres. This value is in accordance with the smallest (refractory) dust structures found so far at 67P.
The main scientific goal of the RG was to measure the ram pressure in the coma of 67P to derive the velocity of the gas. At times, the mostly smooth cometary signal showed sudden increases in measured density (Figure 2). This indicates the presence of a momentary additional source of gas and this is compatible with the sublimation of the volatile component of a dust particle within the RG . We therefore search in the data recorded by the RG for features similar to those in Figure 2, paying attention to exclude those attributable to spacecraft background effects such as offset measurements, slews and thruster firings .
COPS had two operating procedures, the so-called monitoring mode and the scientific mode; we studied the measurement datasets of both of them taking into account the strengths and weaknesses of the approaches. The scientific mode provided many measurements of a single feature and allowed monitoring of dust particles that sublimate too fast to be observed by the monitoring mode. However, the science mode has only been used scarcely. On the other hand, the monitoring mode was more frequently active, but operating at lower time-resolution (one minute). Therefore, in most cases, it is not possible to extrapolate information beyond the indication that at that moment there was an agglomerate containing volatiles within the RG.
Among all the features, the ones composed of at least five consecutive measurements are investigated (5+ minutes in monitoring mode and 10+ seconds in science mode). Through their distinct decay constants, we analyzed the amount of different groups of volatiles and for the total volume of the volatile part by integrating the obtained signal with time.
First, we model the tail of the feature, that is the part that follows immediately after the abrupt increase in density (cf. Figure 2). After subtracting the nominal coma signal, the measurements that make up the tail are fitted by either a single exponential decay function, thus indicating that there is only one volatile component, or by the sum of two different exponentials, thus contemplating the possibility that there are two distinct groups of volatiles.
As for the volume of the volatiles, we set a differential equation that describes the variation in the number of volatile particles within the RG as the difference between the sublimating molecules from the agglomerate and the particles escaping from the instrument. Thanks to this differential equation and the previously calculated fit of the tail, we determine the number of molecules of the agglomerate and calculate the diameter of an equivalent sphere based on the assumption that there is only water ice. We opted for this simplistic choice because water is the dominating volatile component in comets .
We identify the sublimation of 73 agglomerates, 25 of which allow a detailed analysis. Depending on their exponential decay constants, the latter can be divided into three separate families, meaning that there are either three groups of volatiles, or multiple arrangements of the volatiles inside the agglomerates. The volatile sublimation process lasts at most a few tens of minutes, thus explaining why COSIMA  detected only refractories: as already pointed out by , the interval between collection and analysis by COSIMA is too broad.
Moreover, we calculated their size as a diameter of an equivalent sphere of water. We obtain dimensions in the order of hundreds of nanometers, in accordance with the smallest (refractory) dust structures found so far at 67P .
3. Summary and conclusions
The RG has proven to be a very versatile tool, since it was able to obtain indications on dust particles, an element for which it was not developed. The data obtained provide redundancy to other instruments of the Rosetta mission, but also add new pieces to the complicated puzzle of cometary activity of 67P and the suggested approach may be an additional tool to better categorize dust agglomerates.
 Balsiger H. et al., Space Science Reviews 128, 745-801, 2007
 Altwegg K. et al., MNRAS 469, S130-S141, 2017
 Schläppi B. et al., Journal of Geophysical Research 115, A12, 2010
 Le Roy L. et al., Astronomy & Astrophysics 583, A1, 2015
 Fray, N. et al., Nature 538, 72-74, 2016
 Altwegg K. et al., Nature Astronomy 4, 533-540, 2020
 Mannel T. et al., Astronomy & Astrophysics 630, A26, 2019
How to cite:
Pestoni, B., Altwegg, K., Balsiger, H., Hänni, N., Rubin, M., Schroeder I, I., Schuhmann, M., and Wampfler, S.: Dust categorization starting from ROSINA-COPS ram gauge data, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-635, https://doi.org/10.5194/epsc2020-635, 2020.
David Heather, Diego Fraga, Patrick Martin, and Matthew Taylor
This presentation will outline the current status of the Rosetta archive, as well as highlighting some of the ‘enhanced archiving’ activities that have been completed in 2019.
On 30 September 2016, Rosetta completed its incredible mission by landing on the surface of comet 67P/Churyumov-Gerasimenko. Although this marked an end to the spacecraft’s active operations, intensive work is still ongoing, with the instrument teams updating their science data in response to recent scientific reviews and delivering them for ingestion into ESA’s Planetary Science Archive (PSA) . In addition to this, ESA is working with a number of instrument teams to produce new and enhanced data products and to improve documentation in an effort to provide the best long-term archive possible for the Rosetta mission.
2. Rosetta Science Archive Status
All science data from the Rosetta mission are hosted jointly by the Planetary Science Archive (PSA) at ESA (http://psa.esa.int) , and by NASA’s PDS Small Bodies Node (SBN).
The long duration of the Rosetta mission, along with its diverse suite of instrumentation and the range of targets observed throughout its lifetime combine to make this an extremely challenging mission to archive . A number of independent data reviews have taken place over the course of the mission in an attempt to track the evolution of the data pipelines from each instrument and ensure that the science data are documented and formatted in the best possible way to allow end-users to exploit them. The last of these took place in May 2019, and focused on final deliveries to close the archive content. The outcome of the review was very positive; the Rosetta archive is clearly in good scientific shape. There were nevertheless several issues raised, and the instrument teams and the PSA are working to implement the fixes requested this year.
It should be noted that teams have been asked to re-run all of their older data through the new pipelines to ensure we have consistently the best and most up to date data available in the final archive.
3. Rosetta Enhanced Archiving
Once the resources from the operational mission came to an end, ESA established a number of joint activities with the Rosetta instrument teams to allow them to continue to work on enhancing their archive content. The updates planned were focused on key aspects of an instrument’s calibration or the production of higher-level data / information, and are therefore very specific to each instrument’s needs.
Almost all instrument teams have now provided a Science User Guide for their data, which have been highly appreciated by the scientists in the recent reviews. Many teams have also updated their calibrations to deliver higher level and/or derived products.
For example, OSIRIS has delivered data with improved calibrations, as well as straylight corrected, I/F corrected, and three-dimensional georeferenced products. These are all already available in the archive. They now also provide data in FITS format, and have added quicklook versions of their products to allow an end-user to more easily identify the images they may be interested in. Internal straylight data and boresight corrected / full frame data were also added to the archive early this year. A full re-delivery of all pre-comet data using the latest pipelines has also been made and is currently being prepared for ingestion.
Similarly, the VIRTIS team will update both their spectral and geometrical calibrations, and deliver mapping products to the final archive.
The Rosetta Plasma Consortium (RPC) instrument suite has worked on cross-calibrations that will greatly improve the final data to be delivered from each experiment, as well as a number of activities individual to each instrument. The RPC team has also produced an illumination map of the comet to help with their cross-calibration work.
The MIDAS team has similarly been working on instrument cross-calibrations and has produced a dust particle catalog from the comet coma.
The GIADA team has delivered higher-level products in the form of dust environment maps, with omnidirectional plus time.
The COSIMA team recently delivered a ground-based catalog of spectra for comparison to help calibrate and understand their in-flight data.
A separate activity has also been established to produce and deliver data set(s) containing supporting ground-based observations of the comet. These data were taken simultaneously with Rosetta operations and could provide some important contextual information. Samples of these products were included in the recent scientific review, and it is clear that the development is on the right track. This activity will be closed out this autumn.
In addition, the Rosetta ESA archiving team is producing calibrated data sets for the NAVCAM instrument, will archive the radiation monitor data produced by the SREM instrument on Rosetta and will be working to include the latest shape models from the comet into the final Rosetta archive. The last of the Philae lander science data will also soon be added to the archive. Finally, a spacecraft housekeeping volume is being developed with key parameters from the operations.
4. Final Archive Reviews
The last big ‘mission archive review’ was held with independent reviewers in May 2019 to assess the final deliverables from the archive enhancement phase. A number of additional small reviews will be needed for upcoming deliveries such as the Spacecraft Housekeeping and SREM data. Together, these reviews will ensure that the ultimate Rosetta archive within the PSA will allow for scientists to fully exploit the data holdings for decades to come.
With the support of the instrument teams and the completion of the archive enhancement, the Rosetta archive can become an immensely valuable resource for scientists in years to come, and the full scientific potential of the mission can be realized.
 Besse, S. et al., (2018) Planetary and Space Science v150, 131-140.
 Barthelemy, M. et al., (2018) Planetary and Space Science v150, 91-103.
How to cite:
Heather, D., Fraga, D., Martin, P., and Taylor, M.: The Rosetta Science Archive: Enhancing the Scientific Content, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-679, https://doi.org/10.5194/epsc2020-679, 2020.
Here we report the possibility to identify the existence of satellites by finding anomalies when we compare thermal effective diameters with occultation-derived effective diameters. The comparison has to be done very carefully, taking into account many different aspects often not considered. Our sample of objects includes only those that have multichord stellar occultations with more than 3 chords. We find that the effective diameters from thermal models are, overall, in good agreement with the occultation-derived effective diameters, although they slightly underestimate the real sizes. In the case of 2002 TC302 we found a clear excess in the thermal data, indicating that a satellite might be responsible for it, and this scenario seems compatible with time series photometry and astrometry of 2002 TC302 taken along several years.
Satellites around TNOs have mostly been discovered through high-spatial-resolution imaging, mainly using the HST. Unfortunately, this causes a bias against finding satellites close to their primaries. To avoid this bias one can try to look for satellites from periodic residuals in rotational lightcurves , and one can also try to identify satellites by the astrometric wobble caused in the system . Also, contact binaries can be inferred through high-amplitude rotational lightcurves .
Binary TNOs and TNOs with satellites carry valuable information on the processes and the physics governing the formation of the TNOs from the initial protoplanetary disc. Therefore, efforts to search for satellites in close orbits are important. A potential new tool to address the topic is the comparison of occultation-derived effective diameters with thermal diameters. For non-spherical bodies (like most of TNOs except those that rotate slowly), the concept of diameter makes no sense. For non-spherical bodies we can use the concept “effective diameter” to mean the diameter of a spherical object with the same volume as the body. Then we talk about effective diameters “in equivalent volume sense”. We can use the term effective diameter to mean the diameter of a sphere with the same projected area as that of the TNO, but if the TNO is a triaxial body and is rotating, we have to specify also the rotation phase or correct to the mean projected area.
There are many tricky aspects and details that must be addressed before comparing the results from thermal observations with occultation observations. First of all, we have to compare the effective diameter in the projected area sense, not in volume. Also, one has to account for the presence of known satellites, which in some of the Herschel "`TNOs are cool"' papers was unknown or not shown in the tables, so the reported diameters are often for the combination of the primary plus the satellite, whereas the occultations only recorded the primaries. Also, the rotational phase at the occultation time has to be considered in the case of triaxial bodies. In addition, the different aspect angle at the time of the Herschel-Spitzer observations compared to the occultation has to be considered (this is often very small, only a few degrees, but should be computed if possible). On the other hand, we have to compare occultation observations with thermal observations analyzed the same way with the same kind of thermal models (not with thermophysical models). So, careful analysis has to be done.
Observations from the literature
From a sample of ~10 TNOs for which we have accurate occultation diameters and were observed within the “TNOs are cool” Herschel Key project, we have taken into account all the aspects mentioned in the introduction and have generated a table with all the relevant parameters.
We found that thermal models tend to slightly underestimate the true diameters. This is because all the analyzed TNOs are elongated, and as expected from the theoretical work by , highly elongated asteroids get their diameters underestimated when using thermal models, which are built for spherical bodies. We had already noticed this in the case of the occultation by Haumea , but we can now confirm the conclusion for other TNOs. Nevertheless, the general difference of the thermal diameters in comparison with the occultation ones is small, not as large as in the Haumea case. One notable exception to this is 2002 TC302 whose thermal diameter is considerably larger than that from the occultation. We have reassessed the thermal fluxes to double check that this is the case. Our preliminary results indicate that the Herschel PACS fluxes used in  came from the combination of observations at two epochs, but a close look at the Herschel PACS images of the second epoch revealed contamination from a bright source. If only the uncontaminated epoch is used to derive the fluxes, the effective diameter is even larger than that reported in  and the fit improves considerably. On the other hand, time series photometry and astrometry of this body tend to support the existence of a large satellite orbiting at a distance of the order for 2000 km . The approximate diameter of the satellite would be around 300 km.
 Fernández-Valenzuela et al. (2019) Astrophys. J. Lett. 883 L21 7 pp.  Ortiz et al. (2011) Astron. Astrophys 525, id.A31, 12 pp.  Thirouin et al. 2018 Astron. J. 155, id. 248, 16 pp.  Brown, R. H. 1985, Icarus, 64, 53  Ortiz et al. 2017, Nature, 550, 219-222,  Fornasier, et al. (2013), Astron Astrophys, 555, A15  Ortiz et al. (2020) Astron. Astrophys. In Press. arXiv e-prints,arXiv:2005.08881
How to cite:
Ortiz, J. L. and the 20-coauthor team: Thermal diameters versus occultation diameters of TNOs: a new tool to search for satellites?, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-686, https://doi.org/10.5194/epsc2020-686, 2020.
Pablo Santos-Sanz, Nicolás Morales, Estela Fernández-Valenzuela, José Luis Ortiz, Bruno Sicardy, Gustavo Benedetti-Rossi, Mónica Vara-Lubiano, Marcelo Assafin, Flavia Luane Rommel, Chrystian Luciano Pereira, Felipe Braga-Ribas, Damya Souami, René Duffard, Roberto Vieira Martins, Faustino Organero, Leonor Ana Hernández, Fernando Fonseca, Ramón Iglesias Marzoa, José Luis Lamadrid, and Sergio Alonso and the 'Lucky Star' and Bienor stellar occultation teams
1 Introduction Centaurs are objects that orbit the Sun with semi-major axis between those of Jupiter and Neptune, according to the JPL Horizons definition https://ssd.jpl.nasa.gov/sbdb_help.cgi?class=CEN. These objects are thought to come from the trans-Neptunian region being injected into inner parts of the solar system due to planetary encounters, mostly with Neptune . Therefore, centaurs present an excellent opportunity to study smaller trans-Neptunian objects much closer to the Earth, providing a better characterization of their physical properties. During the last years, there has been a growing momentum in the interest about the centaur population due to the discovery of ring systems around two of them, Chariklo  and Chiron [3,4], which has opened a new branch of research in order to understand how such rings are formed and how they can survive around these small bodies.
(54598) Bienor is one of the largest centaurs known to date, with a diameter of ∼ 200 km estimated from Herschel Space Observatory, Spitzer Space Telescope and ALMA thermal measurements [5,6], similar to that of Chiron and Chariklo. Bienor also has ellipsoidal shape and water ice spectral features analogous to Chariklo and Chiron [7,8,9], although its rotation period of ∼ 9.14 h, without being very slow, is slightly over the average of the TNO/centaur population . From the similarities with Chariklo and Chiron and from other reasons it has been proposed that Bienor could possess a ring system, similar to what has been found in the above mentioned centaurs .
2 Observations Within our program of physical characterization of TNOs and centaurs, a stellar occultation by the centaur Bienor was predicted to occur on January 11, 2019, with good observability potential. High accuracy astrometry runs were carried out to refine the prediction, and as a result, a shadow path favorable for the south of Europe was derived. This encouraged us to carry out an occultation observation campaign that resulted in 5 positive detections from 4 observing sites located in Spain and Portugal (see Figure 1 and Figure 2). Apart from occultations by the centaurs Chiron [3,4], Chariklo [2,11,12] and 2002 GZ32 , no other multichord occultations by centaurs had ever been obtained.