Many topics in planetary studies demand an estimate of the collision probability of two objects moving on nearly Keplerian orbits. In the classic works of Opik and Wetherill, the collision probability was derived by linearizing the motion near the collision points, and there is now a vast amount of literature using their method. We present here a simpler and more physically motivated derivation for non-tangential collisions in Keplerian orbits, as well as for tangential collisions that were not previously considered. Our formulas have the added advantage of being manifestly symmetric in the parameters of the two colliding bodies. In common with the Opik-Wetherill treatments, we linearize the motion of the bodies in the vicinity of the point of orbit intersection (or near the points of minimum distance between the two orbits) and assume a uniform distribution of impact parameter within the collision radius. We point out that the linear approximation leads to singular results for the case of tangential encounters. We regularize this singularity by use of a parabolic approximation of the motion in the vicinity of a tangential encounter.

<p dir="ltr">Here we present two studies of different aspects of meteoritic impacts. The first study is about the behavior of ejecta plumes after a hypervelocity impact onto a body with an atmosphere. The second study looks at the effect vaporization has on meteoroids as they descend through Earth's atmosphere, specifically the effect permeability and meteor size have on the vaporization during their explosive fragmentation.</p><p dir="ltr">Atmospheres play an important role in ejecta deposition after an impact event. Many impact experiments and simulations neglect the effect of atmospheres. In the first study, we simulate ejecta plumes created by craters with transient diameters of 2 km and 20 km on Mars and Earth to show the difference atmospheric density and crater size have on the strength of the interaction. The interaction of ejecta with an atmosphere is explored in this study using a two-fluid hydrocode that simultaneously simulates ejecta and atmospheres as coupled, continuum fields to correctly capture the transfer of mass, energy, and momentum between the two. Here we study the effect of vaporization of plume material as well as the effect of the bow shock. We find that only the fastest ejecta is vaporized with a peak vaporized mass of 2.5x10⁵ kg, 3.5 s after the impact in our 2 km diameter Terrestrial crater. Terrestrial meteorites are preferentially formed from the fastest ejecta. However, that fastest ejecta is mostly vaporized in our simulations, so to form a Terrestrial meteorite there must be a sufficiently large impact for solid material to be ejected and not vaporize. Thus, we place a lower limit of 33 km on the size of crater needed to generate terrestrial meteorites, but the crater size needed could be substantially larger. The bow shocks in our simulations result in lofting of ejecta, especially vaporized material, in the wake of the impactor. We find that Mars' thin atmosphere slows the ejecta but does not significantly change the trajectory of the plume. Earth's atmosphere can stop and entrain ejecta particles to suspend heated material long after the majority of material has already been deposited, resulting in 4x10¹⁰ kg of material being suspended in the atmosphere 100 seconds after the impact for a 2 km diameter crater. For larger craters, we find that Earth's atmosphere has a more limited effect and ejecta more closely follows a ballistic trajectory.</p><p dir="ltr">The 1908 Tunguska bolide event and the 2013 Chelyabinsk bolide event underscore the potential damage posed by relatively small meteoroids as compared to the dinosaur-killing Chicxulub meteoroid. In this study, we model Tunguska- and Chelyabinsk-sized bolide events, extending the work of Tabetah and Melosh (2018) by exploring a larger parameter space and introducing the novel feature of material vaporization. Building upon their findings that the porosity and permeability of a meteoroid significantly influence fragmentation, we investigate additional factors such as meteoroid size, entry speed, and entry angle. Furthermore, we demonstrate that vaporization plays a crucial role, lowering the fragmentation height by extracting energy through latent heat. We find that a larger meteoroid size or higher entry speed increases the amount of vaporization that occurs while lowering the altitude of disruption of the meteoroid, and that a shallower entry angle decreases the amount of vaporization and increases the altitude of disruption. Our study not only refines the understanding of bolide events but also introduces a novel perspective with potential implications for planetary science and impact risk assessment.</p>

A meteor observed with the naked eye is colloquially called a shooting star. The streak of light is generated by an extra-terrestrial particle, a meteoroid, entering the Earth’s atmosphere. The term meteor includes both luminosity detectable by optical means and ionization detectable by radar. The radar targets of meteor head echoes have the same motion as the meteoroids on their atmospheric flight and are relatively independent of aspect angle. They appear to be compact regions of plasma created at around 100 km altitude and have no appreciable duration. This thesis reviews the meteor head echo observations carried out with the tristatic 930 MHz EISCAT UHF radar system during four 24h runs between 2002 and 2005, and a 6h run in 2003 with the monostatic 224 MHz EISCAT VHF radar. It contains the first strong observational evidence of a submillimeter-sized meteoroid breaking apart into two distinct fragments. This discovery promises to be useful in the further understanding of the interaction processes of meteoroids with the Earth’s atmosphere and thus also the properties of interplanetary/interstellar dust. The tristatic capability of the EISCAT UHF system makes it a unique tool for investigating the physical properties of meteoroids and the meteor head echo scattering process. The thesis presents a method for determining the position of a compact radar target in the common volume of the antenna beams and demonstrates its applicability for meteor studies. The inferred positions of the meteor targets are used to estimate their velocities, decelerations, directions of arrival and radar cross sections (RCS) with unprecedented accuracy. The head echoes are detected at virtually all possible aspect angles all the way out to 130° from the meteoroid trajectory, limited by the antenna pointing directions. The RCS of individual meteors simultaneously observed with the three receivers are equal within the accuracy of the measurements with a very slight trend suggesting that the RCS decreases with increasing aspect angle. A statistical evaluation of the measurement technique shows that the determined Doppler velocity agrees with the target range rate. This demonstrates that no contribution from slipping plasma is detected and that the Doppler velocities are unbiased within the measurement accuracy. The velocities of the detected meteoroids are in the range of 19-70 km/s, but with very few detections at velocities below 30 km/s. The thesis compares observations with a numerical single-body ablation model, which simulates the physical processes during meteoroid flight through the atmosphere. The estimated meteoroid masses are in the range of 10-9 - 10-5.5 kg. / Meteorer är ljusfenomen på natthimlen som i vardagligt tal kallas fallande stjärnor. Ljusstrimmorna alstras av meteoroider, små partiklar på banor genom solsystemet, som kolliderar med jordens atmosfär. Förutom ljus genererar meteoroider regioner av joniserat plasma, som är detekterbara med radar. Meteoriska huvudekon tycks komma från kompakta radarmål på ungefär 100 km höjd och rör sig genom atmosfären med de infallande meteoroidernas hastighet. Huvudekons signalstyrka förefaller oberoende av vinkeln mellan radarmålens rörelseriktning och riktningen från vilken radiovågorna infaller och sprids. Avhandlingen sammanfattar huvudekoobservationer från fyra 24-timmarsmätningar mellan 2002 och 2005 med det trestatiska 930 MHz EISCAT UHF-radarsystemet och en 6-timmarsmätning under 2003 med den monostatiska 224 MHz EISCAT VHF-radarn. Avhandlingen innehåller den första observationella bekräftelsen på att en meteoroid av sub-millimeterstorlek faller sönder i två distinkta fragment i atmosfären. Upptäckten är betydelsefull för studier av meteoroiders växelverkansprocesser med atmosfären och interplanetärt/interstellärt stofts materialegenskaper. EISCAT UHF-systemet består av tre vitt åtskilda mottagarstationer, vilket gör det till ett unikt mätinstrument för studier av meteoroiders egenskaper och hur radiovågor sprids från de radarmål som ger upphov till huvudekon. Avhandlingen presenterar en metod med vilken ett radarmåls position kan bestämmas om det detekteras simultant med de tre mottagarna. Metoden används till att med hög noggrannhet beräkna meteorers radartvärsnitt samt meteoroiders hastighet och atmosfärsinbromsning. De detekterade huvudekona genereras av meteoroider med i princip alla av mätgeometrin tillåtna rörelseriktningar i förhållande till radarstrålen, ända ut till 130° från radiovågornas spridningsriktning. Enskilda meteorers radartvärsnitt är likvärdiga inom mätnoggrannheten i de tre mottagarstationernas dataserier, men en svag trend antyder att radartvärsnittet minskar med ökande vinkel mellan meteoroidernas rörelseriktning och spridningsriktningen. En statistisk utvärdering av mättekniken visar att den uppmätta dopplerhastigheten stämmer överens med radarmålens flygtidshastighet. Detta innebär att dopplerhastigheterna är väntevärdesriktiga och opåverkade av bidrag från det spår av plasma som meteoroiderna lämnar efter sig. De uppmätta hastigheterna är 19-70 km/s, men bara ett fåtal detekterade meteoroider är långsammare än 30 km/s. Meteoroidmassorna är uppskattade till 10-9 – 10-5.5 kg genom jämförelser av observationerna med simuleringar av meteoroiders färd genom atmosfären i en numerisk ablationsmodell.

This thesis presents results based on data collected with the 930 MHz EISCAT UHF radar system and three SKiYMet specular meteor radars. It describes in detail a method for meteoroid orbit calculation. The EISCAT UHF system comprises three identical 32 m parabolic antennae: one high-power transmitter/receiver and two remote receivers. Precise meteoroid deceleration and radar cross section are determined from 410 meteor head echoes simultaneously observed with all three receivers between 2002 and 2005, during four 24h runs at the summer/winter solstice and the vernal/autumnal equinox. The observations are used to calculate meteoroid orbits and estimate meteor visual magnitudes. None of the observed meteors appear to be of extrasolar or asteroidal origin; comets, particularly short period (&lt;200 years) ones, may be the dominant source for the particles observed. About 40% of the radiants are associated with the north apex sporadic meteor source and 58% of the orbits are retrograde. The geocentric velocity distribution is bimodal with a prograde population centred around 38 km/s and a retrograde population peaking at 59 km/s. The absolute visual magnitudes of meteors are estimated to be in the range of +9 to +5 using a single-object numerical ablation model. They are thus observable using intensified CCD cameras with telephoto lenses. The thesis also investigates diurnal meteor rate differences and sporadic meteor radiant distributions at different latitudes using specular meteor trail radar measurements from 68°N, from 55°N and from 8°S. The largest difference in amplitude of the diurnal flux variation is at equatorial latitudes, the lowest variation is found at high latitudes. The largest seasonal variation of the diurnal flux is observed with the high-latitude meteor radar. The investigations show a variation in the sources with both latitude and time of day. The EISCAT UHF system and the high-latitude meteor radar are located close to the Arctic Circle. Such a geographical position means that zenith points towards the North Ecliptic Pole (NEP) once every day all year round. This particular geometry allows the meteoroid influx from the north ecliptic hemisphere to be compared throughout the year as the ecliptic plane coincides with the local horizon. Considering only the hour when NEP is closest to zenith, the EISCAT UHF head echo rate is about a factor of three higher at summer solstice than during the other seasons, a finding which is consistent with the high-latitude meteor radar measurements. / Avhandlingens resultat är baserade på mätningar med den trestatiska EISCAT UHF-radarn och tre SKiYMet meteorradarsystem. En metod för meteoroidbanberäkning presenteras i detalj. EISCAT UHF-systemet består av tre identiska, 32 m stora parabolantenner: en högeffektssändare/mottagare och två fjärrstyrda mottagare. Under fyra 24-timmarsmätningar vid vår-/höstdagjämning och sommar-/vintersolstånd mellan 2002 och 2005 detekterades 410 meteoriska huvudekon simultant med alla tre mottagare. Dessa trestatiska meteorers atmosfärsinbromsning och radartvärsnitt har fastställts mycket noggrant och använts till att beräkna meteoroidernas banor samt uppskatta meteorernas luminositeter. Ingen av de observerade meteoroiderna verkar vara av interstellärt eller asteroidursprung. Deras troligaste ursprung är kometer, framför allt kortperiodskometer (&lt;200 år). Ungefär 40% av meteorradianterna kan associeras till norra apex, ett källområde för sporadiska meteorer, och totalt är 58% av partiklarnas banor retrograda. Meteoroidernas geocentriska hastighetsfördelning har två lokala maxima: ett för den prograda populationen vid 38 km/s och ett för den retrograda vid 59 km/s. Genom att anpassa datat till en numerisk ablationsmodell som simulerar meteoroidernas färd genom atmosfären har de detekterade meteorernas absoluta visuella magnituder uppskattats till mellan +9 och +5. Detta innebär att de är observerbara med bildförstärkta, teleskopiska CCD-kameror. Avhandlingen diskuterar även hur sporadiska meteorers dygns- och säsongsinflöde beror på geografisk latitud och meteorradianternas distribution på himmelssfären. Detta utreds med hjälp av spårekon detekterade under perioden 1999-2004 med tre meteorradarsystem på latituderna 68°N, 55°N och 8°S. Dygnsinflödet varierar mest på låga latituder och minst på höga. Ju högre latitud, desto mer förändras däremot dygnsinflödet över året. Avhandlingen visar att de dominerande källområdena varierar med säsong, över dygnet och med latitud. Både EISCAT UHF-systemet och meteorradarn på 68°N är belägna nära polcirkeln. Detta innebär att norra ekliptiska polen (NEP) är i zenit en gång per dygn, året om. Vid just denna tidpunkt sammanfaller ekliptikan med den lokala horisonten, vilket möjliggör att det observerade meteorinflödet från norra ekliptiska hemisfären kan jämföras över året. Under timmen då NEP är närmast zenit har EISCAT UHF uppmätt ett ungefär tre gånger högre meteorinflöde vid sommarsolståndet än under de andra säsongerna, vilket överensstämmer med resultaten från meteorradarn på 68°N.

We use a model of aerosol microphysics to investigate the impact of high-altitude photochemical aerosols on the transmission spectra and atmospheric properties of close-in exoplanets, such as HD 209458 b and HD 189733 b. The results depend strongly on the temperature profiles in the middle and upper atmospheres, which are poorly understood. Nevertheless, our model of HD 189733 b, based on the most recently inferred temperature profiles, produces an aerosol distribution that matches the observed transmission spectrum. We argue that the hotter temperature of HD 209458 b inhibits the production of high-altitude aerosols and leads to the appearance of a clearer atmosphere than on HD 189733 b. The aerosol distribution also depends on the particle composition, photochemical production, and atmospheric mixing. Due to degeneracies among these inputs, current data cannot constrain the aerosol properties in detail. Instead, our work highlights the role of different factors in controlling the aerosol distribution that will prove useful in understanding different observations, including those from future missions. For the atmospheric mixing efficiency suggested by general circulation models, we find that the aerosol particles are small (similar to nm) and probably spherical. We further conclude that a composition based on complex hydrocarbons (soots) is the most likely candidate to survive the high temperatures in hot-Jupiter atmospheres. Such particles would have a significant impact on the energy balance of HD 189733 b's atmosphere and should be incorporated in future studies of atmospheric structure. We also evaluate the contribution of external sources to photochemical aerosol formation and find that their spectral signature is not consistent with observations.