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Saturn's rings act as a system of innumerable test particles that are remarkably sensitive to periodic disturbances in the planet's gravitational field. We identify 15 additional density and bending waves in Saturn's C ring driven by the planet's internal normal mode oscillations. Taking advantage of a highly accurate absolute radius scale for the rings, we are able to detect weak, high-wavenumber (up to m=14) waves with km-scale radial wavelengths. From a systematic scan of the entire C ring, we report the discovery and identification of 11 new Outer Lindblad Resonances (OLRs), two counterpart inner Lindblad resonances (ILRs), and two new Outer Vertical Resonances (OVRs). The close agreement of the observed resonance locations and wave rotation rates with the predictions of models of Saturn's interior suggests that all of the new waves are driven by Saturnian f-mode oscillations. As classified by their spherical harmonic shapes, the modes in question range in azimuthal wavenumber from m=8 to 14, with associated resonance orders l-m ranging from 0 to 8, where l is the overall angular wavenumber of the mode. Our suite of detections for l-m=4 is now complete from m=8 to m=14. Curiously, detections with l-m=2 are less common. These newly-identified non-sectoral waves sample latitudinal as well as radial structure within the planet and may thus provide valuable constraints on Saturn's differential rotation. Allowing for the fact that the two ILR-type waves appear to be due to the same normal modes as two of the OLR-type waves, the 13 additional modes identified here bring to 34 the number of distinct f-modes suitable for constraining interior models., Comment: Accepted for publication in Icarus

We now know that the outer solar system is host to at least six diverse planetary ring systems, each of which is a scientifically compelling target with the potential to inform us about the evolution, history and even the internal structure of the body it adorns. These diverse ring systems represent a set of distinct local laboratories for understanding the physics and dynamics of planetary disks, with applications reaching beyond our Solar System. We highlight the current status of planetary rings science and the open questions before the community to promote continued Earth-based and spacecraft-based investigations into planetary rings. As future spacecraft missions are launched and more powerful telescopes come online in the decades to come, we urge NASA for continued support of investigations that advance our understanding of planetary rings, through research and analysis of data from existing facilities, more laboratory work and specific attention to strong rings science goals during future mission selections.

Context. Pluto's tenuous nitrogen (N2) atmosphere undergoes strong seasonal effects due to high obliquity and orbital eccentricity, and has been recently (July 2015) observed by the New Horizons spacecraft. Goals are (i) construct a well calibrated record of the seasonal evolution of surface pressure on Pluto and (ii) constrain the structure of the lower atmosphere using a central flash observed in 2015. Method: eleven stellar occultations by Pluto observed between 2002 and 2016 are used to retrieve atmospheric profiles (density, pressure, temperature) between $\sim$5 km and $\sim$380 km altitude levels (i.e. pressures from about 10 microbar to 10 nanobar). Results: (i) Pressure has suffered a monotonic increase from 1988 to 2016, that is compared to a seasonal volatile transport model, from which tight constraints on a combination of albedo and emissivity of N2 ice are derived; (ii) A central flash observed on 2015 June 29 is consistent with New Horizons REX profiles, provided that (a) large diurnal temperature variations (not expected by current models) occur over Sputnik Planitia and/or (b) hazes with tangential optical depth of about 0.3 are present at 4-7 km altitude levels and/or (c) the nominal REX density values are overestimated by an implausibly large factor of about 20% and/or (d) higher terrains block part of the flash in the Charon facing hemisphere., Comment: 21 pages, 11 figures

Recent studies of stellar occultations observed by the Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft have demonstrated that multiple spiral wave structures in Saturn's rings are probably generated by normal-mode oscillations inside the planet. Wavelet-based analyses have been able to unambiguously determine both the number of spiral arms and the rotation rate of many of these patterns. However, there are many more planetary normal modes that should have resonances in the rings, implying that many normal modes do not have sufficiently large amplitudes to generate obvious ring waves. Fortunately, recent advances in wavelet analysis allow weaker wave signals to be uncovered by combining data from multiple occultations. These new analytical tools reveal that a pattern previously identified as a single spiral wave actually consists of two superimposed waves, one with 5 spiral arms rotating at 1593.6 degrees/day and one with 11 spiral arms rotating at 1450.5 degrees/day. Furthermore, a broad search for new waves revealed four previously unknown wave patterns with 6, 7, 8 and 9 spiral arms rotating around the planet at 1538.2 degrees/day, 1492.5 degrees/day, 1454.2 degrees/day and 1421.8 degrees/day, respectively. These six patterns provide precise frequencies for another six fundamental normal modes inside Saturn, yielding what is now a complete sequence of fundamental sectoral normal modes with azimuthal wavenumbers from 2 to 10. These frequencies should place strong constraints on Saturn's interior structure and rotation rate, while the relative amplitudes of these waves should help clarify how the corresponding normal modes are excited inside the planet., Comment: 18 pages, 24 figures, updated to fix some typographical errors identified in proofs

In this paper we investigate the opportunities provided by the James Webb Space Telescope (JWST) for significant scientific advances in the study of solar system bodies and rings using stellar occultations. The strengths and weaknesses of the stellar occultation technique are evaluated in light of JWST's unique capabilities. We identify several possible JWST occultation events by minor bodies and rings, and evaluate their potential scientific value. These predictions depend critically on accurate a priori knowledge of the orbit of JWST near the Sun-Earth Lagrange-point 2 (L2). We also explore the possibility of serendipitous stellar occultations by very small minor bodies as a by-product of other JWST observing programs. Finally, to optimize the potential scientific return of stellar occultation observations, we identify several characteristics of JWST's orbit and instrumentation that should be taken into account during JWST's development., Comment: This paper is one of a series for a special issue on Solar System observations with JWST in PASP. Accepted 2-Oct-2015. Preprint 30 pages, 5 tables, 8 figures

Combining stellar occultation observations probing Pluto's atmosphere from 1988 to 2013 and models of energy balance between Pluto's surface and atmosphere, we conclude that Pluto's atmosphere does not collapse at any point in its 248-year orbit. The occultation results show an increasing atmospheric pressure with time in the current epoch, a trend present only in models with a high thermal inertia and a permanent N2 ice cap at Pluto's north rotational pole., Comment: 12 pages, 3 figures

The PHOT (Portable High-Speed Occultation Telescope) systems were developed for the specific purpose of observing stellar occultations by solar system objects. Stellar occultations have unique observing constraints: they may only be observable from certain parts of the globe; they often require a rapid observing cadence; and they require accurate timestamp information for each exposure. The PHOT systems consist of 14" telescopes, CCD cameras, camera mounting plates, GPS-based time standards, and data acquisition computers. The PHOT systems are similar in principle to the POETS systems (Portable Occultation, Eclipse and Transit Systems, described by Souza et al. 2006 and reported on by Gulbis et al. 2008), with the main differences being (a) different CCD/Cameras with slightly different specifications and (b) a stand-alone custom-built time standard used by PHOT, whereas POETS uses a commercial time-standard that is controlled from a computer. Since 2005, PHOT systems have been deployed on over two dozen occasions to sites in the US, Mexico, Chile, Namibia, South Africa, France, Austria, Switzerland, Australia and New Zealand, mounted on portable 14" telescopes or on larger stationary telescopes. Occultation light curves acquired from the 3.9-m AAT (Anglo-Australian Telescope) have produced photometric signal-to-noise ratios (SNR) of 333 per scale height for a stellar occultation by Pluto (Young et al. 2008). In this paper we describe the seven PHOT subsystems in detail (telescopes, cameras, timers and data stations) and present SNR estimates for actual and predicted occultations as functions of star brightness, telescope aperture and frame rate.

Cassini radio science experiments have provided multiple occultation optical depth profiles of Saturn's rings that can be used in combination to analyze density waves. This paper establishes an accurate procedure of inversion of the wave profiles to reconstruct the wave kinematic parameters as a function of semi-major axis, in the nonlinear regime. This procedure is achieved from simulated data in the presence of realistic noise perturbations, to control the reconstruction error. By way of illustration we have applied our procedure to the Mimas 5:3 density wave. We were able to recover precisely the kinematic parameters from the radio experiment occultation data in most of the propagation region; a preliminary analysis of the pressure-corrected dispersion allowed us to determine new but still uncertain values for the opacity ($K\simeq 0.02$ cm$^2$/g) and velocity dispersion of ($c_o\simeq 0.6$ cm/s) in the wave region. Our procedure constitutes the first step in our planned analysis of the density waves of Saturn's rings. It is very accurate and efficient in the far-wave region. However, improvements are required within the first wavelength. The ways in which this method can be used to establish diagnostics of ring physics are outlined., Comment: 50 pages,13 figures, 2 tables. Published in Icarus.

The Cassini Division in Saturn's rings contains a series of eight named gaps, three of which contain dense ringlets. Observations of stellar occultations by the Visual and Infrared Mapping Spectrometer onboard the Cassini spacecraft have yielded ~40 accurate and precise measurements of the radial position of the edges of all of these gaps and ringlets. These data reveal suggestive patterns in the shapes of many of the gap edges: the outer edges of the 5 gaps without ringlets are circular to within 1 km, while the inner edges of 6 of the gaps are eccentric, with apsidal precession rates consistent with those expected for eccentric orbits near each edge. Intriguingly, the pattern speeds of these eccentric inner gap edges, together with that of the eccentric Huygens ringlet,form a series with a characteristic spacing of 0.06 degrees/day. The two gaps with non-eccentric inner edges lie near first-order Inner Lindblad Resonances (ILRs) with moons. One such edge is close to the 5:4 ILR with Prometheus. The other resonantly confined edge is the outer edge of the B ring, which lies near the 2:1 Mimas ILR. Detailed investigation of the B-ring-edge data confirm the presence of an m=2 perturbation on the B-ring edge, but also suggest that this pattern moves or librates relative to Mimas. The B-ring edge also has an m=1 component that rotates around the planet at a rate close to the expected apsidal precession rate. The pattern speeds of the eccentric edges in the Cassini Division can potentially be generated from various combinations of the pattern speeds of structures observed on the edge of the B ring. We therefore suggest that the locations of most of the gaps in the Cassini Division may be determined by resonances involving a combination of perturbations from Mimas and the massive edge of the B ring., Comment: 47 pages, 12 figures, accepted for publication in the Astronomical Journal, Some small typographical and wording errors fixed

In this paper, we investigate the opportunities provided by the James Webb Space Telescope (JWST) for significant scientific advances in the study of Solar System bodies and rings using stellar occultations. The strengths and weaknesses of the stellar occultation technique are evaluated in light of JWST's unique capabilities. We identify several possible JWST occultation events by minor bodies and rings and evaluate their potential scientific value. These predictions depend critically on accurate a priori knowledge of the orbit of JWST near the Sun–Earth Lagrange point 2 (L2). We also explore the possibility of serendipitous stellar occultations by very small minor bodies as a byproduct of other JWST observing programs. Finally, to optimize the potential scientific return of stellar occultation observations, we identify several characteristics of JWST's orbit and instrumentation that should be taken into account during JWST's development.

This paper discusses our determination of the Saturn's pole orientation and precession using a combination of Earthbased and spacecraft based observational data. From our model of the polar motion and the observed precession rate we obtain a value for Saturn's polar moment of inertia

A series of near-equatorial radio occultations of Cassini by Saturn occurred in 2005 and again in 2009-2010. Comparison of the temperature-pressure profiles obtained from the two sets of occultations shows evidence of a descending pattern in the stratosphere that is similar to those associated with equatorial oscillations in Earth's middle atmosphere. This is the first time that this descent has been observed in another planetary atmosphere. If absorption of upwardly propagating waves drives the descent, the implied absorbed flux is 0.05 square meters per square second at least as large if not greater than on Earth.

Ground-based and Cassini CIRS thermal-infrared data have characterized the spatial and temporal characteristics of an equatorial oscillation in Saturn's middle atmosphere above the 100-mbar level. The CIRS data indicate a vertical pattern of alternating warm and cold anomalies at the equator. From the thermal wind equation this implies a concomitant reversal of zonal winds with attitude, relative to the cloud-top winds, with peak-to-peak amplitude approximately 200 meters per second. The ground-based observations do not having the altitude range or vertical resolution of the CIRS observations, but they cover several years and indicate an oscillation cycle of 1 years, roughly half of Saturn's year. Equatorial oscillations in Earth's middle atmosphere have primarily exhibited either quasi-biennial or semi-annual "periodicities," and both types have been extensively observed and modeled. They exhibit a vertical pattern of alternating warmer and cooler zonal-mean temperatures and zonal winds analogous to that described above for Saturn. Moreover, the pattern of winds and temperatures descends with time. Momentum deposition by damped vertically propagating easterly and westerly waves is thought to play a key role in forcing both types of oscillation, and it can plausibly account for the descent. Here we report the direct observation of this descent in Saturn's equatorial atmosphere from Cassini radio occultation soundings in 2005 and 2009. The retrieved temperatures are consistent with a descent of 0.6 x the pressure scale height over this time period. The descent rate is related to the magnitude of the wave forcing, radiative damping, and induced meridional circulations. A simple calculation implies that vertical wave fluxes of zonal momentum approximately 0.05 square meters per square second could account for the observed vertical descent on Saturn, which is comparable to the magnitude of the wave fluxes associated with the terrestrial quasi-biennial oscillation.

The intensity of the received signal at Earth in the radio occultations of Titan is attenuated both by refractive defocusing and pressure-induced absorption from N2-N2 and CH4-N2 pairs. Because the absorption strength is different for the two sets of pairs, matching the retrieved absorptivity profile can in principle yield the vertical variation in gaseous methane in the troposphere. There are two factors that make this difficult. The first is the propagation of noise in the phase and amplitude of the received signal in the absorption retrieval. The phase data is first inverted to retrieve vertical profiles of refractivity, from which the refractive defocusing is calculated. This is then subtracted from the observed. intensity attenuation of the received signal to generate a profile of atmospheric absorption. The second problem is the uncertainty in the pressure-induced absorption coefficients. Laboratory data at radio wavelengths is only available near room temperature (see, e.g., [1] for N2-N2), and the extrapolation to the low temperatures in Titan's troposphere is not well established. Ab initio calculations by Borysow et al. [2, 3] provide absorption coefficients at low temperatures and long wavelengths, but their accuracy has come into question. We present examples from Cassini radio occultations of Titan to illustrate the difficulties. For methane mole fractions in the lower troposphere comparable to that inferred from the Huygens probe (approximately 0.05), it will be difficult to separate the contributions of N2-N2 collisions from those of N2-CH4, collisions to the retrieved absorption. However, higher concentrations of CH4 and/or a higher signal-to-noise ratio from a future uplink experiment could result in a successful separation of the two components. However, key to this are highly accurate estimates of the absorption from a combination of laboratory measurements at love temperatures and long wavelengths, and possibly improved theoretical calculations.

The radiative response of Titan's atmosphere varies by several orders of magnitude with altitude. This presents an interesting situation in which most of the stratosphere---at least that part above 100km is characterized by radiative relaxation times that are short compared to the length of a Titan season, and the troposphere and tropopause region by times that are larger than seasonal timescales. Consistent with this, Cassini CIRS spectra indicate stratospheric temperatures at 100-170 kin that are 20-30 K cooler at high northern latitudes in winter than those at equatorial and southern latitudes. Given the expectation that the situation will largely reverse in southern winter, the observed large meridional contrast is likely indicative of the expected seasonal variation at polar latitudes in both hemispheres. CIRS spectra do not as easily yield temperatures below 100 km in the lower stratosphere and tropopause region, because of the contribution of heterogeneously distributed aerosols and condensates to the infrared opacity. However, Cassini radio occultations probe both the stratosphere and troposphere, and below 80 km they show the thermal contrast with latitude to be muted, e.g, approx.5 K near the tropopause at 40-50 km and approx.3 K just above the surface. This is consistent with the large radiative relaxation times at these altitudes and with efficient meridional heat transport. What is curious is the manner in which temperatures in the north winter polar atmosphere make the transition between the troposphere and lower stratosphere, where seasonal variations are relatively small, and higher altitudes, where they are large. Temperatures at all latitudes sounded by the radio occultations exhibit similar behavior in the lower stratosphere, increasing with altitude. Between 80 and 100 kin, however, the temperatures at high northern latitudes exhibit a sudden drop with increasing altitude, producing the meridional contrast in the upper stratosphere described above. While the radiative relaxation time associated with infrared gaseous coolants decreases with altitude in the stratosphere, it is not likely to account for the abrupt transition observed. Possible mechanisms for this transition are discussed, including the presence of an optically thick. cloud at thermal-infrared wavelengths.

Photometric observations of the five medium-sized satellites of Saturn were obtained with the 60-inch telescope at Palomar Mountain Observatory during the Ring Plane Crossing in August 1995.

Recent research efforts were directed towards sharpening the understanding of kinematical and dynamical properties of the Uranian rings, with the combination of Earth-based and Voyager observations, and in obtaining and interpreting new observations of the Saturn system from the remarkable stellar occultation of 3 Jul. 1989. Some of the highlights studied include: (1) a detailed comparison of structure and dynamics of the Uranus rings from joint analysis of high quality Earth-based data and the complete set of Voyager occultation measurements; (2) a comprehensive search for weak normal modes excited in the Uranian rings, analogous to the m = 2 and m = 0 normal modes previously identified for the delta and gamma rings; (3) an ongoing search for faint rings and ring arcs of Uranus, using both Voyager images of the rings and Earth-based and spacecraft stellar occultation data; (4) a comparison of upper stratospheric temperatures of Uranus inferred from Voyager ultraviolet occultations with results of ground-based occultation observations; and (5) observations of the 3 Jul. 1989 Saturn occultation of 28 Sgr.

K-filter/InSb observations of the March 25, 1983 occultation of KME 17 by Uranus and its rings yielded nonchopping-mode recordings of the immersion of the nine main rings and the emersion of rings 5, 4, alpha, and beta; a diffracted square-well model has been fitted to these data in order to derive the midtime, width, and equivalent depth for each profile, in view of a profile model encompassing the diameter of the occulted star as a free parameter. Assuming a fully darkened disk, the angular diameter of KME 17 is 0.096 + or - 0.005 milliarcsec. Attention is also given to JHKL-band photometry for both KME 17 and other Uranian-ring-occulted stars.

A comparison between Voyager 2 UV spectrometer data for stellar occultations of the Uranian ring system obtained at 0.11 microns and 2.2-micron earth-based occultation data reveals the anticipated factor-of-two reduction in observed optical depths relative to those observed from earth. This is due to Voyager's proximity to the rings, which allows light diffracted out of the direct beam by ring particles to be replaced by light diffracted into the direct beam light from other particles, and further permits the placing of firm lower limits on typical particle sizes of 0.3 and 1 cm for the epsilon and delta rings, respectively. As a function of true anomaly, the epsilon ring profile is noted to remain very similar in shape and essentially constant in equivalent depth, even very near periapse.

Data were obtained on stellar occultations by Neptune on June 7 and 25, 1985 in an attempt to validate previous data which supported the presence of a ring-like 'arc' near the planet. The data were taken with an IR photometer at the South African Astronomical Observatory using continuous measurements at 2.2 microns. One dip was observed in the light curve of an occulted binary star. The dip was similar to a previously observed dip and, because no dip was seen for the companion star, indicated a discontinuous structure. Two estimates, around 62,600 and 63,760 km, are made for the equatorial radius of the potential arc structure, which may be discontinuous on a scale of a few thousand kilometers.

A square-well model was used to calculate the midtimes, widths and optical depths at visible and IR wavelengths of the nine Uranian rings based on 13 occultation measurements from 1977-1983. Many of the measurement campaigns contained data from repeated crossings. An improved kinematical model is developed for the ring system, noting that the gamma and delta rings were confirmed to depart from Keplerian ellipses. Upper limits are calculated for the sizes of shepherd satellites of various potential densities. The ring width determinations demonstrate the existence of significant width perturbations in the rings, which all displayed particle shadowing.

Observations on 15 June 1983 of an occultation of a star by Neptune from Mauna Kea, Mount Stromlo, Siding Spring, and the Kuiper Airborne Observatory show no evidence for equatorial rings between 25,300 and 200,000 km (R/N/ = 25,269 km). Within most of this region, the upper limit on the optical depth along the line of sight, for rings broader than 6 km , is 0.04, which corresponds to a normal optical depth of 0.016. These results rule out a Neptunian ring system similar to that of Saturn or Uranus, but not a system of low optical depth similar to the Jovian rings. The data show no features that appear likely to have been caused by material in the equatorial plane of Neptune near the Roche limit.

The oblateness and radius of Neptune were determined from an analysis of photoelectric observations of the June 15, 1983 occultation by Neptune at six stations, combined with the results of the Apr. 7, 1968 Neptune occultation of BD - 17 deg 4388. The oblateness is 0.0191 + or - 0.0017 and the equatorial radius is 25,268 + or - 12 km at the level probed by the occultation. The results are consistent with recent determinations of Neptune's rotation period and J2 (the second-order gravitational harmonic coefficient) and suggest that Neptune is far less centrally condensed than Uranus. Temperature profiles for Neptune's upper atmosphere were also derived from these data.

Since the discovery of the Uranian rings in 1977, it has been possible to determine the orbits of the rings with remarkable precision. It has been found that seven of the nine known rings follow well-behaved Keplerian ellipses. However, two adjacent rings, gamma and delta, deviate significantly from simple ellipses, with residuals of up to 10 km. The present report is concerned with a test of two possible causes of the observed perturbations in the case of the gamma and delta rings, taking into account shepherd satellites which are presumed to confine the sharp-edged narrow rings, and low-order Lindblad resonances.

A least squares fitting is added to the diffraction model for the Uranian rings and the model is then used to determine the relative optical depths of the rings at visible and near-IR wavelengths. Light transmission is assumed constant on a scale of a few radial km in the rings. The amount of starlight passing through the rings is calculated from occultations with account taken of a monolayer ring, diffraction effects, and multiple ring layers. A diffracted occultation profile is generated with consideration given to the angular diameter of the star, the impulse response of the detector, and atmospheric aberrations. Calculation procedures which remove noise are outlined and results are compared with the observational data base. The wavelength dependence of optical depth is formulated. It is shown that occultation data do not support the presence of a large fraction of submicron particles. No optical depth variations are projected for 0.88-2.2 microns wavelengths. Unchopped data are needed to verify the model predictions.

The oblateness of a planet is closely related to its rotation rate and internal mass distribution, and is therefore an important indicator of gross planetary structure. Analysis of Stratoscope II images of Uranus yields epsilon = 0.022 + or - 0.001, and stellar occultation observations yield epsilon = 0.024 + or - 0.003. Because of the current pole on aspect of Uranus, it is unlikely that a significantly more accurate value can be determined by stellar occultations before Voyager 2 encounters Uranus in January, 1986. Neptune's oblateness has been determined from stellar occultation observations made in 1968 and 1983. The 1968 observations yield an oblateness of 0.021 + or - 0.004. A recent determination of Neptune's oblateness using both the 1968 and 1983 observations is consistent with this value. Space Telescope observations of several stellar occultations by Neptune could provide a significantly more accurate determination of the oblateness before the Voyager 2 encounter in 1990.

Occultation profiles for the nine confirmed Uranian rings obtained from Las Campanas, the European Southern Observatory, and Cerro Tololo on 15-16 August 1980 are compared. The alpha ring shows a 'double-dip' structure; the eta ring shows a broad and narrow component (similar to Saturn's F ring); and the epsilon ring shows six features that appear in the data from all three observatories. Diffraction fringes appear at the edges of several of the occultation profiles.

General techniques for producing model lightcurves for a variety of realistic atmospheric irregularities, including turbulence and inertia-gravity waves, are presented and applied. The restrictions of weak scintillation theory are relaxed and model lightcurves are constructed using wave optics for atmospheres with strong, anisotropic turbulence. This is accomplished by numerical simulations which model the propagation of a wave through a phase-changing screen while maintaining complete amplitude and phase information from the wave. The results are compared with available weak scintillation theory and with recent occultation data. The effects of large scale atmospheric waves with realistic horizontal structure are examined, and the reliability of the numerical inversion method in retrieving the true atmospheric vertical structure under conditions of strong ray crossing and horizontal inhomogeneities is assessed. The nature of model lightcurve spikes generated using geometric optics and wave optics are compared.

Observations of the 24 May 1981 occulation of an uncatalogued star by Neptune made at the Cerro Tololo Inter-American Observatory have been analyzed to yield temperature profiles of Neptune's upper atmosphere for number densities near 5 x 10 to the 13th per cu cm. The mean temperatures at immersion (latitude - 56 deg) and emersion (latitude - 16 deg) obtained by numerical inversion were 140 + or - 10 K and 154 + or - 10 K, respectively. The immersion and emersion profiles are remarkably similar in overall shape, suggestive of global atmospheric layering. From the astrometry of the event, precise relative positions of Neptune and the occulted star were obtained.