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Although the risk posed to spacecraft due to meteoroid impacts is dominated by sporadic meteoroids, meteor showers can raise this risk for short periods of time. NASA's Meteoroid Environment Office issues meteor shower forecasts that describe these periods of elevated risk, primarily for the purpose of helping plan extravehicular activities. These forecasts are constructed using a list of meteor shower parameters that has evolved over time to include newly discovered showers and incorporate improved measurements of their characteristics. However, at this point in time, more than a thousand meteor showers have been reported by researchers, many of which are extremely minor, are unconfirmed, or lack measurements of critical parameters. Thus, a comprehensive approach is no longer feasible. In this report we present a quantitative criterion for a potentially hazardous meteor shower and apply this criterion to the list of established meteor showers in order to determine which showers should be included in our annual forecasts., Comment: Accepted for publication in Advances in Space Research

The rate at which meteors pass through Earth's atmosphere has been measured or estimated many times over; existing flux measurements span at least 12 astronomical magnitudes, or roughly five decades in mass. Unfortunately, the common practice of scaling flux to a universal reference magnitude of +6.5 tends to collapse the magnitude or mass dimension. Furthermore, results from different observation networks can appear discrepant due solely to the use of different assumed population indices, and readers cannot resolve this discrepancy without access to magnitude data. We present an alternate choice of reference magnitude that is representative of the observed meteors and minimizes the dependence of flux on population index. We apply this choice to measurements of recent Orionid meteor shower fluxes to illustrate its usefulness for synthesizing independent flux measurements., Comment: Accepted for publication in the Astronomical Journal

18 mm-sized Orionid meteoroids were captured in 2019 and 2020 by the Canadian Automated Observatory's mirror tracking system. Meteor position measurements were made to an accuracy of $\sim1$ m and the meteors were tracked to a limiting magnitude of about $+7.5$ at the faintest point. The trajectory estimation shows the intrinsic physical dispersion of the Orionid radiant is $0.400^{\circ} \pm 0.062^{\circ}$. An erosion-based entry model was fit to the observations to reproduce ablation and fragmentation for each meteor, simultaneously reproducing the light curve, the dynamics, and the wake. Wake observations were found to directly inform the grain mass distribution released in the modelled erosion. A new luminous efficiency model was derived from simultaneous radar and optical observations and applied in the modelling to improve its accuracy. The results show that the apparent strength of Orionids varies with radiant location and time of appearance during the period of shower activity. The average differential grain mass distribution index was 2.15, higher than found from in-situ estimates, possibly due to the evolution of the physical properties of meteoroids since ejection. All Orionids showed leading fragment morphology which was best explained by stopping the erosion at the peak of the light curve, leaving a non-fragmenting meteoroid with $\sim10\%$ of the original mass. The inverted Orionid meteoroid average bulk density of $\sim300$ kg m$^{-3}$, corresponding to porosities of $\sim90\%$, is consistent with in-situ measurements of larger dust particles by Vega-2 at 1P/Halley and Rosetta at 67P., Comment: Accepted for publication in Icarus

The Daytime Sextantids meteor shower, part of the Phaethon-Geminid Stream Complex (PGC), is closely related to the Geminids, currently the strongest meteor shower visible at the Earth. The DSX share a similar orbit to asteroid 2005 UD, but the nature of the association remains unclear. From optical data we find that DSX meteors ablate similarly to Geminids, suggesting that they are also high density and consistent with a common origin. From radar data we have isolated 19,007 DSX orbits through application of a novel convex hull approach to determine stream membership. We find at the peak the mean semi-major axis is near 1 AU, eccentricity is 0.86 and that both decrease as a function of solar longitude. The inclination averages 25 degrees at the peak but increases over time. Noticeable DSX activity extends from solar longitude 173-196$^{\circ}$ with a flux plateau between 186 - 189$^{\circ}$. The peak flux is $2 \pm 0.05 \times 10^{-3}$ km$^{-2}$ hr$^{-1}$, equivalent to a ZHR of 20. We estimate a true differential mass index for the shower of $s = 1.64 \pm 0.06$ at the time of peak and an average of $1.70 \pm 0.07$ for days surrounding the peak. The mass of the DSX stream is estimated to be $10^{16}$ g, the same order as 2005 UD, suggesting the stream is too massive to have been created by recent meteoroid production from 2005 UD. We propose that the DSX and 2005 UD were created in the same break-up event that created 3200 Phaethon., Comment: Accepted for publication at Monthly Notices of the Royal Astronomical Society (MNRAS)

Meteor showers and their outbursts are the dominant source of meteoroid impact risk to spacecraft on short time scales. Meteor shower prediction models depend on historical observations to produce accurate forecasts. However, the current lack of quality and persistent world-wide monitoring at optical meteoroid sizes has left some recent major outbursts poorly observed. A novel method of computing meteor shower flux is developed and applied to Global Meteor Network data. The method is verified against previously published observations of the Perseids and the Geminids. The complete mathematical and algorithmic details of computing meteor shower fluxes from video observations are described. As an example application of our approach, the flux measurements of the 2021 Perseid outburst, the 2020-2022 Quadrantids, and 2020-2021 Geminids are presented. The flux of the 2021 Perseids reached similar levels to the 1991-1994 and 2016 outbursts (ZHR $\sim$ 280). The flux of the Quadrantids shows high year-to-year variability in the core of the stream while the longer lasting background activity is less variable, consistent with an age difference between the two components. The Geminids show a double peak in flux near the time of peak., Comment: Accepted for publication in MNRAS, 18 pages, 15 figures

Context. The mirror tracking system of the Canadian Automated Meteor Observatory (CAMO) can track meteors in real time, providing an effective angular resolution of 1 arc second and a temporal resolution of 100 frames per second. Aims. We describe the upgraded hardware and give details of the data calibration and reduction pipeline. We investigate the influence of meteor morphology on radiant and velocity measurement precision, and use direct observations of meteoroid fragmentation to constrain their compressive strengths. Methods. On July 21, 2017, CAMO observed a ~4 second meteor on a JFC orbit. It had a shallow entry angle ~8 deg and 12 fragments were visible in the narrow-field video. The event was manually reduced and the exact moment of fragmentation was determined. The aerodynamic ram pressure at the moment of fragmentation was used as a proxy for compressive strength, and strengths of an additional 19 fragmenting meteoroids were measured in the same way. The uncertainty in the atmosphere mass density was estimated to be +/-25% using NAVGEM-HA data. Results. We find that meteor trajectory accuracy significantly depends on meteor morphology. The CAMO radiant and initial velocity precision for non-fragmenting meteors with short wakes is ~0.5' and 1 m/s, while that for meteors with fragments or long wakes is similar to non-tracking, moderate field of view optical systems (5', ~50 m/s). Measured compressive strengths of 20 fragmenting meteoroids (with less precise radiants due to their morphology) was in the range of 1-4 kPa, which is in excellent accord with Rosetta in-situ measurements of 67P. Fragmentation type and strength do not appear to be dependent on orbit. The mass index of the 12 fragments in the July 21 meteoroid was very high (s = 2.8), indicating possible progressive fragmentation., Comment: Accepted for publication in Icarus

We present a new numerical model of the eta-Aquariid and Orionid meteor showers. The model investigates the origin, variability and age of the eta-Aquariid and Orionid apparitions from 1985 to the present day, in order to forecast their activity over the next several decades. Through the numerical integration of millions of simulated meteoroids and a custom-made particle weighting scheme, we model the characteristics of every eta-Aquariid and Orionid apparition between 1985 and 2050. The modeled showers are calibrated using 35 years of meteor observations including the showers activity profiles and interannual variability. Our model reproduces the general characteristics of the present-day eta-Aquariids, and part of the Orionid activity. Simulations suggest that the age of the eta-Aquariids somewhat exceeds 5000 years, while a greater fraction of the Orionids are composed of older material. The 1:6 mean-motion resonance with Jupiter plays a major role in generating some (but not all) Halleyid stream outbursts. We find consistent evidence for a periodicity of 11.8 years in both the observations and modeled maximum meteor rates for the Orionids. A weaker evidence of a 10.7 year period in the peak activity for the eta-Aquariids needs to be investigated with future meteor observations. The extension of our model to future years predicts no significant Orionid outburst through 2050 and four significant eta-Aquariid outbursts in 2023, 2024, 2045 and 2046., Comment: This paper has been accepted for publication in Astronomy & Astrophysics on August 1, 2020

We consider dispersing billiard tables whose boundary is piecewise smooth and the free flight function is unbounded. We also assume there are no cusps. Such billiard tables are called type D in the monograph of Chernov and Markarian. For a class of non-degenerate type D dispersing billiards, we prove exponential decay of correlation and several other statistical properties.

Context. Several authors predicted an outburst of the Draconid meteor shower in 2018, but with an uncertain level of activity. Aims. Optical meteor observations were used to derive the population and mass indices, flux, and radiant positions of Draconid meteors. Methods. 90 minutes of multi-station observations after the predicted peak of activity were performed using highly sensitive Electron Multiplying Charge Coupled Device (EMCCD) cameras. The data calibration is discussed in detail. A novel maximum likelihood estimation method of computing the population and mass index with robust error estimation was developed. We apply the method to observed Draconids and use the values to derive the flux. Meteor trajectories are computed and compared to predicted radiant positions from meteoroid ejection models. Results. We found that the mass index was $1.74 \pm 0.18$ in the 30 minute bin after the predicted peak, and $2.32 \pm 0.27$ in the next 60 minutes. The location and the dispersion of the radiant matches well to modeled values, but there is an offset of $0.4^{\circ}$ in solar longitude., Comment: Accepted for publication in A&A

In the first paper of this series we examined existing methods of optical meteor trajectory estimation and developed a novel method which simultaneously uses both the geometry and the dynamics of meteors to constrain their trajectories. We also developed a simulator which uses an ablation model to generate realistic synthetic meteor trajectories which we use to test meteor trajectory solvers. In this second paper, we perform simulation validation to estimate radiant and velocity accuracy which may be achieved by various meteor observation systems as applied to several meteor showers. For low-resolution all-sky systems, where the meteor deceleration is generally not measurable, the multi-parameter fit method assuming a constant velocity better reproduces the radiant and speed of synthetic meteors. For moderate field of view systems, our novel method performs the best at all convergence angles, while multi-parameter fit methods generally produce larger speed errors. For high-resolution, narrow field of view systems, we find our new method of trajectory estimation reproduces radiant and speed more accurately than all other methods tested. The ablation properties of meteoroids are commonly found to be the limiting factor in velocity accuracy. We show that the true radiant dispersion of meteor showers can be reliably measured with moderate field of view (or more precise) systems provided appropriate methods of meteor trajectory estimation are employed. Finally, we compare estimated and real angular radiant uncertainty and show that for the solvers tested the real radiant error is on average underestimated by a factor of two., Comment: Accepted for publication in MNRAS, 16 pages

It has recently been shown by Egal et al. (2017) that some types of existing meteor in-atmosphere trajectory estimation methods may be less accurate than others, particularly when applied to high precision optical measurements. The comparative performance of trajectory solution methods has previously only been examined for a small number of cases. Besides the radiant, orbital accuracy depends on the estimation of pre-atmosphere velocities, which have both random and systematic biases. Thus it is critical to understand the uncertainty in velocity measurement inherent to each trajectory estimation method. In this first of a series of two papers, we introduce a novel meteor trajectory estimation method which uses the observed dynamics of meteors across stations as a global optimization function and which does not require either a theoretical or empirical flight model to solve for velocity. We also develop a 3D observational meteor trajectory simulator that uses a meteor ablation model to replicate the dynamics of meteoroid flight, as a means to validate different trajectory solvers. We both test this new method and compare it to other methods, using synthetic meteors from three major showers spanning a wide range of velocities and geometries (Draconids, Geminids, Perseids). We determine which meteor trajectory solving algorithm performs better for: all-sky, moderate field of view, and high-precision narrow-field optical meteor detection systems. The results are presented in the second paper in this series. Finally, we give detailed equations for estimating meteor trajectories and analytically computing meteoroid orbits, and provide the Python code of the methodology as open source software., Comment: Accepted for publication in MNRAS

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which focuses on the problems faced by low attaining Key Stage three students in developing their maths understanding, and the effectiveness of teaching approaches in overcoming these difficulties. This project, "Low attainment in mathematics: An investigation focusing on Year 9 pupils" includes a systematic review of the evidence relating to teaching of low-attaining secondary students, which the current report builds upon in the wider context of teaching maths in Key Stages two and three. The purpose of the review is to synthesise the best available international evidence regarding teaching mathematics to children between the ages of 9 and 14 and to address the question: what is the evidence regarding the effectiveness of different strategies for teaching mathematics? Additionally, a set of more detailed topics developed by a group of teachers and related to aspects of pupil learning, pedagogy, the use of resources, the teaching of specific mathematical content, and pupil attitudes and motivation are addressed. Using these topics, the authors derived the 24 research questions that they address in this review. Using a systematic literature search strategy, 66 relevant meta-analyses were identified, which synthesise the findings of more than 3000 original studies. This review begins with an executive summary with the study's headline findings. Then, the authors' theoretical understanding of how children learn and develop mathematically is provided in Section 3: The development of mathematics competency. In this section, they summarise a range of background literature that they used to inform their analysis and synthesis of literature. Sections 4 and 5 provide a guide for the reader and describe the method used in the study. In the subsequent sections, findings are presented relating to the 24 detailed questions. [For the related guidance report, see ED612294.]