DOCSLIB.ORG

Flatness of the Setting

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Flatness of the Setting Flatness of the setting Sun Z. N´eda and S. Volk´an Babe¸s-Bolyai University, Dept. of Physics, RO-3400, Cluj, Romania E-mail: [email protected] (Last revised May 28, 2018) Atmospheric refraction is responsible for the bending of light-rays in the atmosphere. It is a result of the continuous decrease in the refractive index of the air as a function of altitude. A well-known consequence of this phenomenon is the apparently elliptic shape of the setting or rising Sun (or full-Moon). In the present paper we systematically investigate this phenomenon in a standard atmosphere. Theoretical and numerical calculations are compared with experimental data. The asymmetric rim of the Sun is computed as a function of its inclination angle, observational height and meteorological conditions characterized by pressure, temperature and lapse-rate. We reveal and illustrate some extreme and highly unusual situations. I. ATMOSPHERIC REFRACTIONS conditions was recently published by Thomas and Joseph [4]. Here we plan a more complete analysis, considering Atmospheric refraction is between the first scientifi- three different theoretical methods, experiments, com- cally approached phenomenon. This effect is responsible puter simulations and illustration of the results with a for the apparent scintillation of stars, mirages, the puz- collection of pictures and movies. zling and spectacular green flash, difference between ap- The spectacular nature of sunset or sunrise makes the parent and real position of stars or the asymmetric rim of phenomenon attractive to students. After our experience the Sun near the horizon. The refractive index of dry air it can effectively be used to exemplify refraction phenom- is very close to 1. Its small dependence on temperature ena and exercising the principles of geometrical optics. and pressure leads to a refractive index gradient in the Our paper is structured as follows. First, we introduce atmosphere. Although this gradient is very small, due to the atmosphere model, and the refractive index profile the large distances travelled by the light-rays in the at- is given. Then, we present three different methods for mosphere, it can result observable bending or dispersion. computing the ray-path in this atmosphere. Results com- Atmospheric refraction is usually divided into three puted for different meteorological conditions and observa- categories: astronomical, terrestrial and geodesic. Ter- tion altitude will close the theoretical part. Experimen- restrial refraction appears when both the object and ob- tally, we analyze and compare with theory the measured server are within the Earth’s atmosphere. This refraction flatness for some sunsets photographed or video-filmed is responsible for ordinary mirages, and has been exten- by us. Finally, we discuss some extreme and unusual sively studied [1]. The first one reporting and account- conditions which are exemplified by pictures and movies ing for mirages was Aristotle in Meteorologica [2]. Cor- on a web-page supporting this study. From this web- rectly, he concluded that dense air layers can act as mir- page one can also freely download a computer-program rors, and considered this effect responsible for mirages. written by us, which visualizes the sunset for arbitrary (A complete historic and bibliographic study of mirages meteorological conditions and observation altitude. can be found on the splendid web-page of A.T.Young We emphasize here, that our study is restricted to stan- [3].) Geodesic refraction is a special case of terrestrial dard atmospheric conditions with smooth temperature refraction where both the object and observer are at low and pressure profile. Non-standard, but often encoun- altitudes. A well-known example for this is surveying. tered atmospheric profiles leads to non-standard distor- We speak about astronomical refraction when a terres- tions of the solar rim, and are not considered within this trial observer detects ray-bending effects for the light- study. rays coming from objects outside the Earth’s atmosphere. arXiv:physics/0204060v1 [physics.pop-ph] 19 Apr 2002 This refraction is responsible for the difference between the real and apparent position of stars near the horizon, II. THE OPTICAL ATMOSPHERE MODEL the green flash or the asymmetric rim of the setting (or (REFRACTIVE INDEX AS A FUNCTION OF rising) Sun. In the present paper we discuss in detail ALTITUDE) the flatness of the Sun or full-Moon near the horizon. Particularly, we are interested in the extreme values this The atmosphere of the Earth is composed mainly of N2 flatness can take for standard atmospheric profiles, and (79%) and O2 (20%), and extends up to a few hundreds the dependence of the flatness on the altitude of the ob- kilometer height. The refractive index of air is very close server and meteorological conditions (temperature and to 1, and depends slightly on its pressure and temper- pressure). A similar study, considering fixed atmospheric ature following Edlen’s semi-empirical law [5], valid for 1 dry air: is the U.S. Standard Atmosphere, established in 1953 and re-actualized in 1976 [6]. The U.S. Standard At- − − P n =1+10 6(776.2+4.36 × 10 8ν2) . (1) mosphere consists of single profiles, representing the ide- T alized steady-state atmosphere for moderate solar activ- ity. The listed parameters include temperature, pressure, In the above formula ν is the wave-number of the light in − density, gravitational acceleration, mean particle speed, cm 1, P is the pressure in kPa and T the temperature mean collision frequency, mean free path, etc. as a func- in K. Since the pressure and temperature varies within tion of altitude. In our study we consider an atmosphere the atmosphere, we get a refractive index gradient which model with a spherical symmetry, all relevant physical is responsible for atmospheric refractions. Although the quantities (temperature and pressure) varying only as a variations in n are quite small, the large distances trav- function of altitude. We then calculate the refraction in- elled by light-rays in the atmosphere makes refraction dex of air as a function of altitude as follows: effects observable and sometimes important. (i) The temperature profile in the troposphere is linearly decreasing with a λ =6.5K/km lapse-rate, as suggested by the U.S. Standard Atmosphere. Following again the Ionosphere U.S. Standard Atmosphere we consider the temperature 100 constant within the tropopause. Although the temper- 0.001 ature increases as a function of altitude in the strato- Height(km) 80 0.01 Mesosphere sphere, due to the rarefied air (small pressure) the re- 0.1 60 fractive index is close to 1, and for the sake of simplicity Pessure(hPa) we assume the temperature as constant in this region, 1 OzoneLayer Stratosphere 40 too. (We checked that this approximation is fully jus- 10 Tropopause tified.) Above zs = 50km height we assume that the 20 refractive index is 1, and do not calculate it anymore by 100 Troposphere Edlen’s formula. Up to the top of the stratosphere the 1000 -80 -60 -40 -20 Ocean 20 0 temperature profile is therefore presumed as Earth Temperature(C)o FIG. 1. Distinct layers of the atmosphere, and the standard T (z)= T0 − λz for z<zt (2) temperature and pressure profile. T (z)= T0 − λzt for zt ≤ z ≤ zs, (3) As a function of altitude several layers with different where z is the altitude from sea-level, and T0 the tem- physical properties are distinguishable. The lowest layer perature at sea-level. extending from sea-level to approximative zt = 14km (ii) For the pressure profile we use a barometric formula height is called the troposphere. This is the region where in which we take into account the variation of tempera- the wheatear takes place, i.e. the region of rising and ture with altitude. Considering a vertical slice of air with falling packets of air. In this layer the air pressure drops thickness dz, the variation of pressure within this slice is drastically, at the top of the troposphere being only 10% due to the hydrostatic pressure of the value measured at sea-level. In the troposphere the temperature decreases almost linearly with the altitude dP = −ρ(z) g(z) dz, (4) (Fig. 1). A thin buffer zone between the troposphere and the next layer (the stratosphere) is called the tropopause. where g(z) is the gravitational acceleration and ρ(z) the Within the tropopause the temperature is in good ap- density of air at height z: proximation constant. The stratosphere extends from the M Nm P (z)m altitude of approximately 18km up to zs = 50km (Fig. 1). ρ(z)= = = . (5) Within the stratosphere the air flow is mostly horizontal. V V kT (z) In the upper part of the stratosphere we have the ozone (We denoted by m the mass of one molecule, N the num- layer. Inside the stratosphere the pressure decreases fur- ber of molecules in volume V , T (z) the temperature at ther with the altitude, but surprisingly the temperature height z and k the Boltzmann constant.) Since we fo- increases with height. Above the stratosphere we find cus on the troposphere and the stratosphere only, the the mesosphere and the ionosphere. In these regions the z height is small in comparison with the radius of the air is very rare and the temperature profile is shown in Earth (R ≈ 6378km), thus the g gravitational acceler- Fig. 1. E ation can be considered constant. We can write thus From the viewpoint of atmospheric refractions only the first two layers, the troposphere and the stratosphere are P (z)mgdz dP = − , (6) important. In the upper layers of the atmosphere the air kT (z) is so rarefied, that the refractive index can be considered 1 within a good approximation.
Load more

Recommended publications
  • Light Color and Atmospheric Light, Color, and Atmospheric Optics
    Light, Color, and Atmospheric Optics Chapter 19 April 28 and 30, 2009 Colors • Sunlight contains all colors (visible spectrum) Wavelength Ranges in µm UV-C: 0.25 - 0.29 UV-B: 0.29 - 0.32 UV-A: 0.32 - 0.38 Visible: 0.38 - 0.75 Near IR: 0.75 - 4 Mid IR: 4 - 8 Longwave IR: 8 - 100 Colors • If object is white then all colors are reflected • If object is red then only red is reflected and all others are absorbed From Malm (1999). Introduction to Visibility Blue Skies and Hazy days • Selective scattering – Scattering depends on wavelength of light • Rayleigh scattering – Very small particles, gases • Mie scattering – Particles the size of wavelength of visible light • Blue haze • Some particles from plants: terpenes, α- pinene Blue Ridge Mountains • Blue haze caused by scattering of blue light by fine particles Creppyuscular Rays • Scattering of sunlight by dust and haze produces white bands Selective Scattering: Sunset • Notice the effects of scattering on color as sunlight penetrates into the atmosphere Twinkling, Twilight, and the Green Flash • Light that travels from a less dense to a more dense medium loses speed and bends toward the normal, while light that enters a less dense medium increase speed and bends away from the normal. • Apparent position, scintillation, and green flash all depend of density variations in the athtmosphere • Scintillation also indicates the amount of turbulence in the atmosphere Bending of Light Paths from Atmosphere Green Flash • Green flash at top may be seen under circumstances of very cold (dense) air near the surface rapidly changing to warmer (less dense) air aloft Mirages •Miraggyges are caused by refraction of light due to strong density differences in atmospheric layers usually caused by strong temperature differences.
    [Show full text]
  • Why Doesn't the Sky Turn Green?
    Why Doesn't The Sky Turn Green? Rushi Shah 09 November 2015 I was leafing through the US Army Corps of Engineers' Manual on Remote Sensing and learned about how Rayleigh scattering creates blue skies during the day and redish-orange sunsets. Well, everybody knows about blue skies and red sunsets, was the title just click-bait, you ask? No, but I'll get to that. 1 The Basics of Rayleigh Scattering Let's start with this whole Rayleigh scattering thing. Basically the idea is that particles in the atmosphere (like Oxygen and Nitrogen particles) scatter rays of light as they enter the atmosphere. How much the light is scattered is heavily dependent on the wavelength of the light. Remember how ROY-G-BIV represents the colors of the rainbow (and thus the spectrum of visible light)? Well that spectrum of light starts with long wavelength rays (reds, oranges, and yellows) and ends with short wavelength rays (blues, indigos, and violets). 1 The amount of light that is scattered (denoted with the variable I) is highly inversely proportional to the wavelength of the light (denoted with the greek letter ). Put simply, as the wavelength goes down, the light waves are scattered more quickly. 1 I / λ4 When sunlight hits the earth directly during mid-day, it travels through a small amount of atmosphere, and thus we see the wavelengths of light that are immediately scattered. Based on the equation above, the blues, indigos, and violets would be scattered first (and they blend together into the blue sky we see). As the sun sets, it goes through more and more particles to reach us.
    [Show full text]
  • The Gas Laws and the Weather
    IMPACT 1 ON ENVIRONMENTAL SCIENCE The gas laws and the weather The biggest sample of gas readily accessible to us is the atmos- 24 phere, a mixture of gases with the composition summarized in Table 1. The composition is maintained moderately constant by diffusion and convection (winds, particularly the local turbu- 18 lence called eddies) but the pressure and temperature vary with /km altitude and with the local conditions, particularly in the tropo- h sphere (the ‘sphere of change’), the layer extending up to about 11 km. 12 In the troposphere the average temperature is 15 °C at sea level, falling to −57 °C at the bottom of the tropopause at 11 km. This Altitude, variation is much less pronounced when expressed on the Kelvin 6 scale, ranging from 288 K to 216 K, an average of 268 K. If we suppose that the temperature has its average value all the way up to the tropopause, then the pressure varies with altitude, h, 0 according to the barometric formula: 0 0.5 1 Pressure, p/p0 −h/H p = p0e Fig. 1 The variation of atmospheric pressure with altitude, as predicted by where p0 is the pressure at sea level and H is a constant approxi- the barometric formula and as suggested by the ‘US Standard Atmosphere’, mately equal to 8 km. More specifically,H = RT/Mg, where M which takes into account the variation of temperature with altitude. is the average molar mass of air and T is the temperature. This formula represents the outcome of the competition between the can therefore be associated with rising air and clear skies are potential energy of the molecules in the gravitational field of the often associated with descending air.
    [Show full text]
  • ESSENTIALS of METEOROLOGY (7Th Ed.) GLOSSARY
    ESSENTIALS OF METEOROLOGY (7th ed.) GLOSSARY Chapter 1 Aerosols Tiny suspended solid particles (dust, smoke, etc.) or liquid droplets that enter the atmosphere from either natural or human (anthropogenic) sources, such as the burning of fossil fuels. Sulfur-containing fossil fuels, such as coal, produce sulfate aerosols. Air density The ratio of the mass of a substance to the volume occupied by it. Air density is usually expressed as g/cm3 or kg/m3. Also See Density. Air pressure The pressure exerted by the mass of air above a given point, usually expressed in millibars (mb), inches of (atmospheric mercury (Hg) or in hectopascals (hPa). pressure) Atmosphere The envelope of gases that surround a planet and are held to it by the planet's gravitational attraction. The earth's atmosphere is mainly nitrogen and oxygen. Carbon dioxide (CO2) A colorless, odorless gas whose concentration is about 0.039 percent (390 ppm) in a volume of air near sea level. It is a selective absorber of infrared radiation and, consequently, it is important in the earth's atmospheric greenhouse effect. Solid CO2 is called dry ice. Climate The accumulation of daily and seasonal weather events over a long period of time. Front The transition zone between two distinct air masses. Hurricane A tropical cyclone having winds in excess of 64 knots (74 mi/hr). Ionosphere An electrified region of the upper atmosphere where fairly large concentrations of ions and free electrons exist. Lapse rate The rate at which an atmospheric variable (usually temperature) decreases with height. (See Environmental lapse rate.) Mesosphere The atmospheric layer between the stratosphere and the thermosphere.
    [Show full text]
  • Atmospheric Chemistry and Dynamics
    Atmospheric Chemistry and Dynamics Condensed Course of the Universities of Cologne and Wuppertal in cooperation with the Institutes Stratosphere (IEK-7) und Troposphere (IEK-8) of the Forschungszentrums Jülich Prüfungsrelevanz Universität zu Köln - "Physik der Erde und der Atmosphäre" Für das Masterprogramm "Physik der Erde und der Atmosphäre" und dem "International Master of Environmental Sciences" der Universität zu Köln können 3 Kreditpunkte erworben werden. Der Leistungsnachweis erfolgt in einem Fachgespräch. Universität Wuppertal Der Kompaktkurs ist Bestandteil des "Schwerpunkts Atmosphärenphysik" im Rahmen des "Master-Studiengangs Physik" an der Bergischen Universität Wuppertal. Mit der Teilnahme können 5 Leistungspunkte erworben werden. Der Leistungsnachweis erfolgt in einem Fachgespräch. Monday, 07.10.2013 09:00am - 10:30am 1. Structure of the Atmosphere Wahner Layering (troposphere, stratosphere, ...) barometric formula, temperature gradient, potential temperature, isentropes water in the atmosphere ozone 11:00am - 12:30pm 2. Atmospheric Chemistry I (part 1) Benter, Kleffmann, Hofzumahaus atmospheric composition photochemically active radiation and its height dependence photochemistry, radicals, gas phase kinetics lifetime of molecules and molecule families 12:30am - 01:30pm lunch break (canteen) 01:30pm - 03:00pm 3. Dynamics of the Atmosphere I (part 1) Shao transport and mixing in the atmosphere diffusion, advection, and turbulence Navier-Stokes equations and Ekman spiral atmospheric scales in time and space global circulation 03:30pm - 04:45pm 4. Atmospheric Chemistry I (part 2) Benter, Kleffmann, Hofzumahaus 05:00pm - 06:00pm 5. Dynamics of the Atmosphere I (part 2) Shao from 06:00pm icebreaker und dinner Tuesday, 08.10.2013 09:00am - 10:30am 6. Tropospheric gas phase chemistry Benter, Kleffmann Loss of organic trace gases by OH, O3 und NO3 (reaction mechanisms) selected trace gas cycles anthropogenic impacts on tropospheric chemistry 11:00am - 12:30pm 7.
    [Show full text]
  • Atmospheric Refraction
    Z w o :::> l­ I­ ~ <x: '----1-'-1----- WAVE FR ON T Z = -rnX + Zal rn = tan e '----------------------X HORIZONTAL POSITION de = ~~ = (~~) tan8dz v FIG. 1. Origin of atmospheric refraction. DR. SIDNEY BERTRAM The Bunker-Ramo Corp. Canoga Park, Calif. Atmospheric Refraction INTRODUCTION it is believed that the treatment presented herein represents a new and interesting ap­ T IS WELL KNOWN that the geometry of I aerial photographs may be appreciably proach to the problem. distorted by refraction in the atmosphere at THEORETICAL DISCUSSION the time of exposure, and that to obtain maximum mapping accuracy it is necessary The origin of atmospheric refraction can to compensate this distortion as much as be seen by reference to Figure 1. A light ray knowledge permits. This paper presents a L is shown at an angle (J to the vertical in a solution of the refraction problem, including medium in which the velocity of light v varies a hand calculation for the ARDC Model 1 A. H. Faulds and Robert H. Brock, Jr., "Atmo­ Atmosphere, 1959. The effect of the curva­ spheric Refraction and its Distortion of Aerial ture of the earth on the refraction problem is Photography," PSOTOGRAMMETRIC ENGINEERING analyzed separately and shown to be negli­ Vol. XXX, No.2, March 1964. 2 H. H. Schmid, "A General Analytical Solution gible, except for rays approaching the hori­ to the Problem of Photogrammetry," Ballistic Re­ zontal. The problem of determining the re­ search Laboratories Report No. 1065, July 1959 fraction for a practical situation is also dis­ (ASTIA 230349). cussed. 3 D. C.
    [Show full text]
  • The Min Min Light and the Fata Morgana Pettigrew
    C L I N I C A L A N D E X P E R I M E N T A L OPTOMETRYThe Min Min light and the Fata Morgana Pettigrew COMMENTARY The Min Min light and the Fata Morgana An optical account of a mysterious Australian phenomenon Clin Exp Optom 2003; 86: 2: 109–120 John D Pettigrew BSc(Med) MSc MBBS Background: Despite intense interest in this mysterious Australian phenomenon, the FRS Min Min light has never been explained in a satisfactory way. Vision Touch and Hearing Research Methods and Results: An optical explanation of the Min Min light phenomenon is of- Centre, University of Queensland fered, based on a number of direct observations of the phenomenon, as well as a field demonstration, in the Channel Country of Western Queensland. This explanation is based on the inverted mirage or Fata Morgana, where light is refracted long distances over the horizon by the refractive index gradient that occurs in the layers of air during a temperature inversion. Both natural and man-made light sources can be involved, with the isolated light source making it difficult to recognise the features of the Fata Morgana that are obvious in daylight and with its unsuspected great distance contribut- ing to the mystery of its origins. Submitted: 11 September 2002 Conclusion: Many of the strange properties of the Min Min light are explicable in terms Revised: 2 December 2002 of the unusual optical conditions of the Fata Morgana, if account is also taken of the Accepted for publication: 3 December human factors that operate under these highly-reduced stimulus conditions involving a 2002 single isolated light source without reference landmarks.
    [Show full text]
  • Atmospheric Optics
    53 Atmospheric Optics Craig F. Bohren Pennsylvania State University, Department of Meteorology, University Park, Pennsylvania, USA Phone: (814) 466-6264; Fax: (814) 865-3663; e-mail: [email protected] Abstract Colors of the sky and colored displays in the sky are mostly a consequence of selective scattering by molecules or particles, absorption usually being irrelevant. Molecular scattering selective by wavelength – incident sunlight of some wavelengths being scattered more than others – but the same in any direction at all wavelengths gives rise to the blue of the sky and the red of sunsets and sunrises. Scattering by particles selective by direction – different in different directions at a given wavelength – gives rise to rainbows, coronas, iridescent clouds, the glory, sun dogs, halos, and other ice-crystal displays. The size distribution of these particles and their shapes determine what is observed, water droplets and ice crystals, for example, resulting in distinct displays. To understand the variation and color and brightness of the sky as well as the brightness of clouds requires coming to grips with multiple scattering: scatterers in an ensemble are illuminated by incident sunlight and by the scattered light from each other. The optical properties of an ensemble are not necessarily those of its individual members. Mirages are a consequence of the spatial variation of coherent scattering (refraction) by air molecules, whereas the green flash owes its existence to both coherent scattering by molecules and incoherent scattering
    [Show full text]
  • 1 Barometric Formula
    Mathematical Methods for Physicists, FK7048, fall 2019 Exercise sheet 1, due Tuesday september 10th, 15:00 Total amount of points: 12p, and 2 bonus points (2bp). 1 Barometric formula Hydrostatics is governed by the following equation: −! − r P + ρ ~g = ~0 (1) where ~g is the gravitational acceleration, assumed constant, P and ρ are the pressure and density fields. A barotropic fluid is a fluid whose density depends only on pressure viz. ρ = ρ(P ). (a) (1p) The earth's atmosphere can be considered in a first approximation as a barotropic fluid at equilibrium in the gravitational field ~g. Find an integral relation from which the evolution of the pressure as a function of altitude z for any given relation ρ(P ) can be obtained. Consider only the vertical direction and do not forget to set the initial condition. (b) (1p) Find the relation ρ(P ) for an ideal gas, starting from the usual equation of states (that is, the ideal gas las). Any parameter you may need to introduce will be considered constant so far. (c) (1p+1bp) Use the expression ρ(P ) for an ideal gas in your solution of question (a) to find P (z). − z You should obtain the so-called barometric formula P (z) = P0 e h . Give the analytical expression for h. Bonus: obtain a numerical value for h. Use your physical intuition to evaluate the parameters you have introduced in question (b). Is the answer you obtain resonable? (d) (1p) So far we have assumed that Earth's atmosphere is isothermal, however the temperature lapse rate is clearly non-negligible on the kilometer scale.
    [Show full text]
  • How to Format a SCCG Papaer
    Chasing the Green Flash: a Global Illumination Solution for Inhomogeneous Media D. Gutierrez F.J. Seron O. Anson A. Muñoz University of Zaragoza University of Zaragoza University of Zaragoza University of Zaragoza [email protected] [email protected] [email protected] [email protected] restrictions on the scenes and effects that can be Abstract reproduced, including some of the phenomena that occur in our atmosphere. Several natural phenomena, such as mirages or the Most of the media are in fact inhomogeneous to one green flash, are owed to inhomogeneous media in degree or another, with properties varying continuously which the index of refraction is not constant. This from point to point. The atmosphere, for instance, is in makes the light rays travel a curved path while going fact inhomogeneous since pressure, temperature and through those media. One way to simulate global other properties do vary from point to point, and illumination in inhomogeneous media is to use a therefore its optic characterization, given by the index curved ray tracing algorithm, but this approach of refraction, is not constant. presents some problems that still need to be solved. A light ray propagating in a straight line would then be This paper introduces a full solution to the global accurate only in two situations: either there is no media illumination problem, based on what we have called through which the light travels (as in outer space, for curved photon mapping, that can be used to simulate instance), or the media are homogeneous. But with several natural atmospheric phenomena. We also inhomogeneous media, new phenomena occur.
    [Show full text]
  • Evaluating the Effectiveness of Current Atmospheric Refraction Models in Predicting Sunrise and Sunset Times
    Michigan Technological University Digital Commons @ Michigan Tech Dissertations, Master's Theses and Master's Reports 2018 Evaluating the Effectiveness of Current Atmospheric Refraction Models in Predicting Sunrise and Sunset Times Teresa Wilson Michigan Technological University, [email protected] Copyright 2018 Teresa Wilson Recommended Citation Wilson, Teresa, "Evaluating the Effectiveness of Current Atmospheric Refraction Models in Predicting Sunrise and Sunset Times", Open Access Dissertation, Michigan Technological University, 2018. https://doi.org/10.37099/mtu.dc.etdr/697 Follow this and additional works at: https://digitalcommons.mtu.edu/etdr Part of the Atmospheric Sciences Commons, Other Astrophysics and Astronomy Commons, and the Other Physics Commons EVALUATING THE EFFECTIVENESS OF CURRENT ATMOSPHERIC REFRACTION MODELS IN PREDICTING SUNRISE AND SUNSET TIMES By Teresa A. Wilson A DISSERTATION Submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY In Physics MICHIGAN TECHNOLOGICAL UNIVERSITY 2018 © 2018 Teresa A. Wilson This dissertation has been approved in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY in Physics. Department of Physics Dissertation Co-advisor: Dr. Robert J. Nemiroff Dissertation Co-advisor: Dr. Jennifer L. Bartlett Committee Member: Dr. Brian E. Fick Committee Member: Dr. James L. Hilton Committee Member: Dr. Claudio Mazzoleni Department Chair: Dr. Ravindra Pandey Dedication To my fellow PhD students and the naive idealism with which we started this adventure. Like Frodo, we will never be the same. Contents List of Figures ................................. xi List of Tables .................................. xvii Acknowledgments ............................... xix List of Abbreviations ............................. xxi Abstract ..................................... xxv 1 Introduction ................................. 1 1.1 Introduction . 1 1.2 Effects of Refraction on Horizon .
    [Show full text]
  • Barometric Pressure Activity: Teacher Guide
    Barometric Pressure Activity: Teacher Guide Level: Intermediate Subject: Geography and Mathematics Duration: 1 hour Type: Guided classroom activity Learning Goals: • Use the scientific process to find a relationship between barometric pressure and altitude • Use data from the School2School.net website • Use statistics to verify the relationship between barometric pressure and altitude Materials: • Access to the School2School.net website • Barometric Pressure Powerpoint - https://docs.google.com/presentation/d/1G8R3GJ9aHg2me2-z3OdZV4ke- arQ_ualpZ_AgEE1ycE/edit?usp=sharing • Pressure and Elevation Spreadsheet - https://drive.google.com/file/d/0BxNcyc_sE4pPcnZya1FIb3BaRlE/view?usp=sharing Methods: As a class work though the Barometric Pressure Powerpoint using the scientific process 1. The first step of the scientific process is to ask a question. In this case, the question is: is barometric pressure different between stations? Start making observations by going to School2School.net, and clicking on the “Stations” tab. Navigate to your school’s station if you have your own TAHMO station, or else just choose a close station. Pick the Barometric Pressure icon (third from the left) to display the graph of the recorded pressures (See image below). Note the maximum, minimum, and average pressure values (using estimations is okay- just a rough guess by eye is appropriate). Choose another station and compare your results, do you see a difference in the range of pressures for different stations? [Answer: the maximum pressure recorded is different
    [Show full text]