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Design and performance of 4 x 5120-element visible and 2 x 2560-element shortwave infrared multispectral focal planes

Two solid-state sensors for use in remote sensing instruments operating in the pushbroom mode are examined. The design and characteristics of the visible/near-infrared (VIS/NIR) device and the short-wavelength infrared (SWIR) device are described. The VIS/NIR is a CCD imager with four parallel sensor lines, each 1024 pixel long; the chip design and filter system of the VIS/NIR are studied. The performance of the VIS/NIR sensor with mask and its system performance are measured. The SWIR is a dual-band line imager consisting of palladium silicide Schottky-barrier detectors coupled to CCD multiplexers; the performance of the device is analyzed. The substrate materials and layout designs used to assemble the 4 x 5120-element VIS/NIR array and the 2 x 2560-element SWIR array are discussed, and the planarity of the butted arrays are verified using a profilometer. The optical and electrical characteristics, and the placement and butting accuracy of the arrays are evaluated. It is noted that the arrays met or exceed their expected performance.

Tower, J. R.↗

Non-destructive trace element microanalysis of as-received cometary nucleus samples using synchrotron x ray fluorescence

The Synchrotron X ray Fluorescence (SXRF) microprobe at the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory, will be an excellent instrument for non-destructive trace element analyses of cometary nucleus samples. Trace element analyses of as-received cometary nucleus material will also be possible with this technique. Bulk analysis of relatively volatile elements will be important in establishing comet formation conditions. However, as demonstrated for meteorites, microanalyses of individual phases in their petrographic context are crucial in defining the histories of particular components in unequilibrated specimens. Perhaps most informative in comparing cometary material with meteorites will be the halogens and trace metals. In-situ, high spatial resolution microanalyses will be essential in establishing host phases for these elements and identifying terrestrial (collection/processing) overprints. The present SXRF microprobe is a simple, yet powerful, instrument in which specimens are excited with filtered, continuum synchrotron radiation from a bending magnet on a 2.5 GeV electron storage ring. A refrigerated cell will be constructed to permit analyses at low temperatures. The cell will consist essentially of an air tight housing with a cold stage. Kapton windows will be used to allow the incident synchrotron beam to enter the cell and fluorescent x rays to exit it. The cell will be either under vacuum or continuous purge by ultrapure helium during analyses. Several other improvements of the NSLS microprobe will be made prior to the cometary nucleus sample return mission that will greatly enhance the sensitivity of the technique.

Sutton, S. R.↗

Steady-state and dynamic characteristics of a 20-kHz spacecraft power system - Control of harmonic resonance

A detailed computer simulation was used to illustrate the steady-state and dynamic operating characteristics of a 20-kHz resonant spacecraft power system. The simulated system consists of a parallel-connected set of DC-inductor resonant inverters (drivers), a 440-V cable, a node transformer, a 220-V cable, and a transformer-rectifier-filter (TRF) AC-to-DC receiver load. Also included in the system are a 1-kW 0.8-pf RL load and a double-LC filter connected at the receiving end of the 20-kHz AC system. The detailed computer simulation was used to illustrate the normal steady-state operating characteristics and the dynamic system performance following, for example, TRF startup. It is shown that without any filtering the given system exhibits harmonic resonances due to an interaction between the switching of the source and/or load converters and the AC system. However, the double-LC filter at the receiving-end of the AC system and harmonic traps connected in series with each of the drivers significantly reduce the harmonic distortion of the 20-kHz bus voltage. Significant additional improvement in the waveform quality can be achieved by including a double-LC filter with each driver.

Wasynczuk, O.↗

TDRSS-user orbit determination using batch least-squares and sequential methods

The Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) commissioned Applied Technology Associates, Incorporated, to develop the Real-Time Orbit Determination/Enhanced (RTOD/E) system on a Disk Operating System (DOS)-based personal computer (PC) as a prototype system for sequential orbit determination of spacecraft. This paper presents the results of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite System (TDRSS) user spacecraft, Landsat-4, obtained using RTOD/E, operating on a PC, with the accuracy of an established batch least-squares system, the Goddard Trajectory Determination System (GTDS), and operating on a mainframe computer. The results of Landsat-4 orbit determination will provide useful experience for the Earth Observing System (EOS) series of satellites. The Landsat-4 ephemerides were estimated for the January 17-23, 1991, timeframe, during which intensive TDRSS tracking data for Landsat-4 were available. Independent assessments were made of the consistencies (overlap comparisons for the batch case and covariances and the first measurement residuals for the sequential case) of solutions produced by the batch and sequential methods. The forward-filtered RTOD/E orbit solutions were compared with the definitive GTDS orbit solutions for Landsat-4; the solution differences were less than 40 meters after the filter had reached steady state.

Oza, D. H.↗

Hubble Space Telescope far-ultraviolet imaging of M31, M32, and NGC 205

Hubble Space Telescope (HST) Faint Object Camera (FOC) f/48 images of M31, M32, and NGC 205 (field of view 23 sec x 23 sec with 0.45 sec pixel size) are analyzed as observed through the combined UV filters F150W and F130LP. The absolute calibration of the data and the internal disagreement between observed and expected count rates in the UV region lead us to suggest that the filter combination F150W+F130LP suffers from a 5 times degraded UV sensitivity. A corrected efficiency curve is construced using the UV/optical spectral energy distributions of these three galaxies, which is consistent with all of the data analyzed here. Eighty-one individual stars are detected in M31, 10 stars in M32, and 78 stars in NGC 205. Comparisons with other UV images and optical images indicates that these stars are hot, UV-bright stars, even though our corrected efficiency curve suggests that flux from 1200-2450 A contributes only 7% of the counts in M32, 19% in M31, and 60% in NGC 205. The complex nucleus of M31 as seen by Lauer et al. (1993) is confirmed; M32 has a generally smooth appearance and NGC 205 is dominated by a UV-bright, somewhat resolved nucleus. Analysis of these data is done through the new, extensive stellar isochrones of Bertelli et al. (1994) and the population synthesis models of Bressan, Chiosi, and Fagotto (1994). This analysis shows that high-metal stars (Z greater than 0.05) evolve into UV-bright stars (P-EAGB, H-HB, and AGB-manque stars) that are less luminous and cooler but are significantly longer lived than the P-AGB stars produced by stars with Z less than 0.05. Moreover, the proportion of P-EAGB, H-HB, and AGB-manque stars is also a function of age, with older stars of fixed mean metallicity having a higher proportion than younger stars. Hence, with either metallicity or age differences as an interpretation of the line-strength luminosity correlation for ellipticals, the high-metallicity 'tail' of the stellar content of a galaxy can produce far-UV flux in much greater proportion than its actual proportion of galaxy mass. The resulting model of the sources of far-UV flux is inherently composite, with the total UV flux from a stellar population both rapidly increasing and changing its mean spectrum with increasing mean metallicity (or mean age). This model is consistent with several pieces of observational evidence.

Bertola, F.↗

Evaluation of Landsat-4 orbit determination accuracy using batch least-squares and sequential methods

The Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) commissioned Applied Technology Associates, Incorporated, to develop the Real-Time Orbit Determination/Enhanced (RTOD/E) system on a Disk Operating System (DOS)-based personal computer (PC) as a prototype system for sequential orbit determination of spacecraft. This paper presents the results of a study to compare the orbit determination accuracy for a Tracking and Data Relay Satellite (TDRS) System (TDRSS) user spacecraft, Landsat-4, obtained using RTOD/E, operating on a PC, with the accuracy of an established batch least-squares system, the Goddard Trajectory Determination System (GTDS), operating on a mainframe computer. The results of Landsat-4 orbit determination will provide useful experience for the Earth Observing System (EOS) series of satellites. The Landsat-4 ephemerides were estimated for the May 18-24, 1992, timeframe, during which intensive TDRSS tracking data for Landsat-4 were available. During this period, there were two separate orbit-adjust maneuvers on one of the TDRSS spacecraft (TDRS-East) and one small orbit-adjust maneuver for Landsat-4. Independent assessments were made of the consistencies (overlap comparisons for the batch case and covariances and the first measurement residuals for the sequential case) of solutions produced by the batch and sequential methods. The forward-filtered RTOD/E orbit solutions were compared with the definitive GTDS orbit solutions for Landsat-4; the solution differences were generally less than 30 meters after the filter had reached steady state.

Oza, D. H.↗

Externally Illuminated Proto-Planetary Disks

We used the Hubble Space Telescope (HST) to obtain high angular resolution images and the first UV spectra of young stars and their circumstellar environments embedded within the Orion Nebula. The observations consists of: Direct imaging of young stars, their disks, and the surrounding environments with the Planetary Camera (PC) portion of Wide Field and Planetary Camera (WFPC2) using narrow band interference filters; The first UV imaging of these objects with the Faint Object Camera (FOC); and The first UV spectroscopy of these objects using the Faint Object Spectrograph (FOS).

Bally, John↗

Development of a Test Protocol for Spacecraft Post-Fire Atmospheric Cleanup and Monitoring

Detecting and extinguishing fires, along with post-fire atmospheric cleaning and monitoring, are vital components of a spacecraft fire response system. Preliminary efforts focused on the technology evaluation of these systems under realistic conditions are described in this paper. While the primary objective of testing is to determine a smoke mitigation filter s performance, supplemental evaluations measuring the smoke-filled chamber handheld commercial off-the-shelf (COTS) atmospheric monitoring devices (combustion product monitors) are also conducted. The test chamber consists of a 1.4 cubic meter (50 cu. ft.) volume containing a smoke generator. The fuel used to generate the smoke is a mixture of polymers in quantities representative of materials involved in a circuit board fire as a typical spacecraft fire. Two fire conditions were examined: no flame and flame. No flame events are produced by pyrolyzing the fuel mixture in a quartz tube furnace with forced ventilation to produce a white, lingering-type smoke. Flame events ignite the smoke at the outlet of the tube furnace producing combustion characterized by a less opaque smoke with black soot. Electrochemical sensor measurements showed carbon monoxide is a major indicator of each fire. Acid gas measurements were recorded, but cross interferents are currently uncharacterized. Electrochemical sensor measurements and sample acquisition techniques from photoacoustic sensors are being improved. Overall, this research shows fire characterization using traditional analytical chemistry techniques is required to verify measurements recorded using COTS atmospheric monitoring devices.

Zuniga, David↗

TOWARD A METHOD FOR SCALING HUMAN BODY MODELS IN AN IMU-BASED WORKFLOW

BACKGROUND Scaled biomechanical models can more accurately inform crew health decisions when tailored to the wide range of astronaut sizes. One component to improve scaling of existing models to better represent each unique astronaut’s size is the individual length scaling of limbs. Traditionally, these lengths are determined by motion capture or manual measurement. A new method is herein proposed for length scaling which can be done by measuring linear and angular accelerations at a desired point during isolated motion around a point of rotation, then calculating the distance between the desired point and point of rotation. When an Inertial Measurement Unit (IMU) device is placed at the distal point of a limb, the isolated motion is about that limb’s proximal joint. For example, to measure forearm length, an IMU is placed at the wrist, the point of rotation is at the elbow, and the isolated motion is forearm flexion and extension. These calculated lengths are then used to scale models to each unique astronaut’s size, thereby improving the applicability of the model. This method of scaling limb segments can be used for any limb that has an easily defined proximal joint for the limb to rotate around including hands, arms, legs, feet. Utilizing IMUs for data collection also provides the synergistic ability to record data without a dedicated space in a room with many cameras, therefore reducing the data collection footprint, or record data where optical motion capture is not possible, such as inside a spacesuit. METHODS AND RESULTS To test this method, upper body data collection was performed with 5 Xsens DOT IMUs on a single subject. IMUs consist of an accelerometer, a gyroscope, and a magnetometer which collect linear acceleration, angular velocity, and magnetic fluctuations, respectively. Before any ground-based laboratory collection, the magnetic fluctuations are used to correct the heading of the IMU in space relative to the Earth’s magnetic field. The direct measurement of angular velocity is integrated to calculate angular acceleration. Then the linear acceleration ( a ) and angular acceleration (α) are solved using r = at/α to calculate the radius, which in this case is the distance between the IMU and the point of rotation (i.e., segment length). The IMU must be placed at the most distal point of the limb being measured (i.e., ankle if measuring lower leg length) and the test plan must consist of an isolated motion about that limb’s proximal joint (i.e., knee flexion and extension if measuring lower leg length). The distances (radii) calculated at every time interval were filtered (bandpass filter keeping 5th-90th percentile data) to eliminate outliers and spurious data that occur when the isolated motion was stopped or nearly stopped. The remaining distances were averaged, resulting in the calculated limb length. Scaling factors were then computed by dividing the calculated limb length by the unscaled model’s length. These scale factors are plugged into the Scale Tool in OpenSim [1,2] to apply the scaling to the OpenSim Full Body Rajagopal Model [3,4]. Manual measurements of limb lengths were taken before data collection started and used for comparing against the calculated lengths. The Anthropometric Survey of US Army Personnel (ANSUR II) [5] was also used as a third source of reference for limb length measurements. The following measurements were retrieved from the subject before data collection: 34.5 cm from L1 to C7 (thorax), 25.7 cm from C7 Joint Center (JC) to head vertex (neck and head), 36.3 cm from shoulder JC to elbow JC (humerus), 29.5 cm from elbow JC to wrist JC (forearm), and 16.2 cm from clavicle to acromion (clavicle). Of those five, forearm and humerus lengths were calculated using this proposed method to obtain preliminary results. The forearm length after filtering and averaging was calculated to be 37.6 cm. This is a 28% overestimation from the measured forearm length (29.5 cm). The humerus length after filtering and averaging was calculated to be 47.8 cm. This is a 31% difference from the measured subject length (36.3 cm). Sources of error include imperfect isolated motion (method currently expects that motion should be perfectly circular in a 2D plane, include no rotation of the IMU, and be relatively smooth; a more secure IMU attachment method will help), unrefined filter techniques (removed highest and lowest values with 20% high and low pass filters and no smoothing filters), arbitrary removal of stopped or near stopped data (kept data for only a short range before and after the angular velocity peaking), and a more representative method for removing gravitational acceleration is needed (current method is to zero all accelerations against a baseline taken just before the isolated motion which does not account for the gravitational acceleration changed due to IMU rotation during movement). Addressing these error sources will improve the accuracy of the limb length calculation. Next steps include creating a method for whole-body scaling estimation using individual limb scale factors. Continued pursuit of these techniques is expected to enable acquiring anthropometric information using only IMUs in real-time.

E. K. Marecki↗

Zonal and Regional Jupiter Brightness Trends from the Hubble Outer Planet Atmospheres Legacy Program

The Hubble Outer Planet Atmospheres Legacy (OPAL) program began in 2014 and has observed Jupiter yearly from 2015 to 2024. Using high spatial resolution imaging from the Hubble Wide Field Camera 3, brightness trends were investigated focusing on the unique UV capability and absolute calibration consistency of the Hubble Space Telescope. From these data, a 4- to 5- year period is observed at 24° N, particularly in the blue (F395N) and methane gas absorption (FQ889N) filters. Additionally, several wavelengths show a potential seasonal periodicity, especially at the equator, but more years of data are needed to confirm this trend over multiple Jupiter years. Variability in Oval BA and the Great Red Spot brightness is not cyclical, but these two anticyclonic features show changes on a yearly timescale.

Amy A Simon↗

A knock-on deuteron imager for measurements of fuel and hotspot asymmetry in direct-drive inertial confinement fusion implosions (invited)

A knock-on deuteron imager (KoDI) has been implemented to measure the fuel and hotspot asymmetry of cryogenic inertial confinement fusion implosions on OMEGA. Energetic neutrons produced by D–T fusion elastically scatter (“knock on”) deuterons from the fuel layer with a probability that depends on ρR. Deuterons above 10 MeV are produced by near-forward scattering, and imaging them is equivalent to time-integrated neutron imaging of the hotspot. Deuterons below 6 MeV are produced by a combination of side scattering and ranging in the fuel, and encode information about the spatial distribution of the dense fuel. Here, the KoDI instrument consists of a multi-penumbral aperture positioned 10–20 cm from the implosion using a ten-inch manipulator and a detector pack at 350 cm from the implosion to record penumbral images with magnification of up to 35×. Range filters and the intrinsic properties of CR-39 are used to distinguish different charged-particle images by energy along the same line of sight. Image plates fielded behind the CR-39 record a 10 keV x-ray image using the same aperture. A maximum-likelihood reconstruction algorithm has been implemented to infer the source from the projected penumbral images. The effects of scattering and aperture charging on the instrument point-spread function are assessed. Synthetic data are used to validate the reconstruction algorithm and assess an appropriate termination criterion. Significant aperture charging has been observed in the initial experimental dataset, and increases with aperture distance from the implosion, consistent with a simple model of charging by laser-driven EMP.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Comparison of TOPEX/Poseidon orbit determination solutions obtained by the Goddard Space Flight Center Flight Dynamics Division and Precision Orbit Determination Teams

Orbit determination results are obtained by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) using the Goddard Trajectory Determination System (GTDS) and a real-time extended Kalman filter estimation system to process Tracking Data and Relay Satellite (TDRS) System (TDRSS) measurements in support of the Ocean Topography Experiment (TOPEX)/Poseidon spacecraft navigation and health and safety operations. GTDS is the operational orbit determination system used by the FDD, and the extended Kalman fliter was implemented in an analysis prototype system, the Real-Time Orbit Determination System/Enhanced (RTOD/E). The Precision Orbit Determination (POD) team within the GSFC Space Geodesy Branch generates an independent set of high-accuracy trajectories to support the TOPEX/Poseidon scientific data. These latter solutions use the Geodynamics (GEODYN) orbit determination system with laser ranging tracking data. The TOPEX/Poseidon trajectories were estimated for the October 22 - November 1, 1992, timeframe, for which the latest preliminary POD results were available. Independent assessments were made of the consistencies of solutions produced by the batch and sequential methods. The batch cases were assessed using overlap comparisons, while the sequential cases were assessed with covariances and the first measurement residuals. The batch least-squares and forward-filtered RTOD/E orbit solutions were compared with the definitive POD orbit solutions. The solution differences were generally less than 10 meters (m) for the batch least squares and less than 18 m for the sequential estimation solutions. The differences among the POD, GTDS, and RTOD/E solutions can be traced to differences in modeling and tracking data types, which are being analyzed in detail.

Doll, C.↗

Decentralized Data-Driven Estimation of Generator Rotor Speed and Inertia Constant Based on Adaptive Unscented Kalman Filter

This paper proposes an online decentralized and data-driven method for synchronous generator rotor speed and inertia estimation. First, an analytical relationship between the generator terminal voltage/current phasors and its internal rotor speed is derived using the Thevenin equivalent. The parameters of the latter are obtained via a recursive estimator, which allows us to estimate the generator's internal rotor speed from voltage/current phasors without the need for any generator information. Second, we reformulate the equivalent swing equation into the Kalman filter form, which enables us to use a priori-estimated internal rotor speed along with measured real and reactive power injections to obtain an estimate of the inertia for each online synchronous generator. This is achieved through an adaptive unscented Kalman filter. We demonstrate that the use of terminal bus frequency to approximate the rotor speed for inertia estimation by existing methods leads to large estimation biases/errors. Numerical simulations carried out on the IEEE 39-bus and Texas 2000-bus systems reveal that our proposed method is consistently more accurate than existing methods. Moreover, our proposed method is insensitive to both the type and location of system disturbances, and it is robust to different levels of measurement noise.

bus frequency↗

Time transfer using geostationary satellites: Implementation of a Kalman filter

Since 1988, various experiments have shown that the TV signals transmitted by direct TV satellites may easily be used to perform time transfers at the level of a few tens of nanoseconds, the main source of error being the uncertainty on the satellite position. We first present the two methods used in our experiment to reduce the effects of the satellite residual motion: the first one consists in estimating the longitude variations of the satellite and then using this information to improve other measurements. This allows reducing the uncertainty to values between 9 and 50 nanoseconds according to the position of the involved stations. In the second method we determine the satellite position by using the data collected by three calibrated stations. Time transfer between each of these stations and a fourth one has been shown to be achievable at the precision level of ten nanoseconds. A new approach based on the use of a Kalman filter is proposed in order to take into account the dynamics of the geostationary satellite. The precisions on orbital elements and clock differences and rates determination given by the first simulated applications of the Kalman filter are presented and compared to those obtained by the other methods.

Meyer, F.↗

Integrating State Data Assimilation and Innovative Model Parameterization Reduces Simulated Carbon Uptake in the Arctic and Boreal Region

Model representation of carbon uptake and storage is essential for accurate projection of the response of the arctic-boreal zone to a rapidly changing climate. Land model estimates of LAI and aboveground biomass that can have a marked influence on model projections of carbon uptake and storage vary substantially in the arctic and boreal zone, making it challenging to correctly evaluate model estimates of Gross Primary Productivity (GPP). To understand and correct bias of LAI and aboveground biomass in the Community Land Model (CLM), we assimilated the 8-day Moderate Resolution Imaging Spectroradiometer (MODIS) LAI observation and a machine learning product of annual aboveground biomass into CLM using an Ensemble Adjustment Kalman Filter (EAKF) in an experimental region including Alaska and Western Canada. Assimilating LAI and aboveground biomass reduced these model estimates by 58% and 72%, respectively. The change of aboveground biomass was consistent with independent estimates of canopy top height at both regional and site levels. The International Land Model Benchmarking system assessment showed that data assimilation significantly improved CLM's performance in simulating the carbon and hydrological cycles, as well as in representing the functional relationships between LAI and other variables. Here, to further reduce the remaining bias in GPP after LAI bias correction, we re-parameterized CLM to account for low temperature suppression of photosynthesis. The LAI bias corrected model that included the new parameterization showed the best agreement with model benchmarks. Combining data assimilation with model parameterization provides a useful framework to assess photosynthetic processes in LSMs.

58 GEOSCIENCES↗

A tangentially viewing fast ion D-alpha diagnostic for NSTX

A second fast ion D-alpha (FIDA) installation is planned at NSTX to complement the present perpendicular viewing FIDA diagnostics. Following the present diagnostic scheme, the new diagnostic will consist of two instruments: a spectroscopic diagnostic that measures fast ion spectra and profiles at 16 radial points with 5-10 ms resolution and a system that uses a band pass filter and photomultiplier to measure changes in FIDA light with 50 kHz sampling rate. The new pair of FIDA instruments will view the heating beams tangentially. The viewing geometry minimizes spectral contamination by beam emission or edge sources of background emission. The improved velocity-space resolution will provide detailed information about neutral-beam current drive and about fast ion acceleration and transport by injected radio frequency waves and plasma instabilities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Note: On-line weak signal detection via adaptive stochastic resonance

We design an instrument with a novel embedded adaptive stochastic resonance (SR) algorithm that consists of a SR module and a digital zero crossing detection module for on-line weak signal detection in digital signal processing applications. The two modules are responsible for noise filtering and adaptive parameter configuration, respectively. The on-line weak signal detection can be stably achieved in seconds. The prototype instrument exhibits an advance of 20 dB averaged signal-to-noise ratio and 5 times averaged adjust R-square as compared to the input noisy signal, in considering different driving frequencies and noise levels.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A STUDY OF DIFFERENTIAL ROTATION ON II PEGASI VIA PHOTOMETRIC STARSPOT IMAGING

We present the results of a study of differential rotation on the K2 IV primary of the RS CVn binary II Pegasi (HD 224085) performed by inverting light curves to produce images of the dark starspots on its surface. The data were obtained in the standard Johnson B and V filter passbands via the Tennessee State University T3 0.4 m Automated Photometric Telescope from JD 2447115.8086-2455222.6238 (1987 November 16-2010 January 26). The observations were subdivided into 79 data sets consisting of pairs of B and V light curves, which were then inverted using a constrained nonlinear inversion algorithm that makes no a priori assumptions regarding the number of spots or their shapes. The resulting surface images were then assigned to 24 groups corresponding to time intervals over which we could observe the evolution of a given group of spots (except for three groups consisting of single data sets). Of these 24 groups, six showed convincing evidence of differential rotation over time intervals of several months. For the others, the spot configuration was such that differential rotation was neither exhibited nor contraindicated. The differential rotation we infer is in the same sense as that on the Sun: lower latitudes have shorter rotation periods. From plots of the range in longitude spanned by the spotted regions versus time, we obtain estimates of the differential rotation coefficient k defined as in earlier work by Henry et al. and show that our results for its value are consistent with the value obtained therein.

79 ASTRONOMY AND ASTROPHYSICS↗