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Astrodynamics
Politecnico di Torino SEEDS SpacE Exploration and Development Systems Astrodynamics II Edition 2006 - 07 - Ver. 2.0.1 Author: Guido Colasurdo Dipartimento di Energetica Teacher: Giulio Avanzini Dipartimento di Ingegneria Aeronautica e Spaziale e-mail: [email protected] Contents 1 Two–Body Orbital Mechanics 1 1.1 BirthofAstrodynamics: Kepler’sLaws. ......... 1 1.2 Newton’sLawsofMotion ............................ ... 2 1.3 Newton’s Law of Universal Gravitation . ......... 3 1.4 The n–BodyProblem ................................. 4 1.5 Equation of Motion in the Two-Body Problem . ....... 5 1.6 PotentialEnergy ................................. ... 6 1.7 ConstantsoftheMotion . .. .. .. .. .. .. .. .. .... 7 1.8 TrajectoryEquation .............................. .... 8 1.9 ConicSections ................................... 8 1.10 Relating Energy and Semi-major Axis . ........ 9 2 Two-Dimensional Analysis of Motion 11 2.1 ReferenceFrames................................. 11 2.2 Velocity and acceleration components . ......... 12 2.3 First-Order Scalar Equations of Motion . ......... 12 2.4 PerifocalReferenceFrame . ...... 13 2.5 FlightPathAngle ................................. 14 2.6 EllipticalOrbits................................ ..... 15 2.6.1 Geometry of an Elliptical Orbit . ..... 15 2.6.2 Period of an Elliptical Orbit . ..... 16 2.7 Time–of–Flight on the Elliptical Orbit . .......... 16 2.8 Extensiontohyperbolaandparabola. ........ 18 2.9 Circular and Escape Velocity, Hyperbolic Excess Speed . .............. 18 2.10 CosmicVelocities -
Chapter 19 the Almanacs
CHAPTER 19 THE ALMANACS PURPOSE OF ALMANACS 1900. Introduction The Air Almanac was originally intended for air navigators, but is used today mostly by a segment of the Celestial navigation requires accurate predictions of the maritime community. In general, the information is similar to geographic positions of the celestial bodies observed. These the Nautical Almanac, but is given to a precision of 1' of arc predictions are available from three almanacs published and 1 second of time, at intervals of 10 minutes (values for annually by the United States Naval Observatory and H. M. the Sun and Aries are given to a precision of 0.1'). This Nautical Almanac Office, Royal Greenwich Observatory. publication is suitable for ordinary navigation at sea, but The Astronomical Almanac precisely tabulates celestial lacks the precision of the Nautical Almanac, and provides data for the exacting requirements found in several scientific GHA and declination for only the 57 commonly used fields. Its precision is far greater than that required by navigation stars. celestial navigation. Even if the Astronomical Almanac is The Multi-Year Interactive Computer Almanac used for celestial navigation, it will not necessarily result in (MICA) is a computerized almanac produced by the U.S. more accurate fixes due to the limitations of other aspects of Naval Observatory. This and other web-based calculators are the celestial navigation process. available from: http://aa.usno.navy.mil. The Navy’s The Nautical Almanac contains the astronomical STELLA program, found aboard all seagoing naval vessels, information specifically needed by marine navigators. contains an interactive almanac as well. -
Geodetic Position Computations
GEODETIC POSITION COMPUTATIONS E. J. KRAKIWSKY D. B. THOMSON February 1974 TECHNICALLECTURE NOTES REPORT NO.NO. 21739 PREFACE In order to make our extensive series of lecture notes more readily available, we have scanned the old master copies and produced electronic versions in Portable Document Format. The quality of the images varies depending on the quality of the originals. The images have not been converted to searchable text. GEODETIC POSITION COMPUTATIONS E.J. Krakiwsky D.B. Thomson Department of Geodesy and Geomatics Engineering University of New Brunswick P.O. Box 4400 Fredericton. N .B. Canada E3B5A3 February 197 4 Latest Reprinting December 1995 PREFACE The purpose of these notes is to give the theory and use of some methods of computing the geodetic positions of points on a reference ellipsoid and on the terrain. Justification for the first three sections o{ these lecture notes, which are concerned with the classical problem of "cCDputation of geodetic positions on the surface of an ellipsoid" is not easy to come by. It can onl.y be stated that the attempt has been to produce a self contained package , cont8.i.ning the complete development of same representative methods that exist in the literature. The last section is an introduction to three dimensional computation methods , and is offered as an alternative to the classical approach. Several problems, and their respective solutions, are presented. The approach t~en herein is to perform complete derivations, thus stqing awrq f'rcm the practice of giving a list of for11111lae to use in the solution of' a problem. -
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. -
The Golden Hour Refers to the Hour Before Sunset and After Sunrise
TheThe GoldenGolden HourHour The Golden Hour refers to the hour before sunset and after sunrise. Photographers agree that some of the very best times of day to take photos are during these hours. During the Golden Hours, the atmosphere is often permeated with breathtaking light that adds ambiance and interest to any scene. There can be spectacular variations of colors and hues ranging from subtle to dramatic. Even simple subjects take on an added glow. During the Golden Hours, take photos when the opportunity presents itself because light changes quickly and then fades away. 07:14:09 a.m. 07:15:48 a.m. Photographed about 60 seconds after previous photo. The look of a scene can vary greatly when taken at different times of the day. Scene photographed midday Scene photographed early morning SampleSample GoldenGolden HourHour photosphotos Top Tips for taking photos during the Golden Hours Arrive on the scene early to take test shots and adjust camera settings. Set camera to matrix or center-weighted metering. Use small apertures for maximizing depth-of-field. Select the lowest possible ISO. Set white balance to daylight or sunny day. When lighting is low, use a tripod with either a timed shutter release (self-timer) or a shutter release cable or remote. Taking photos during the Golden Hours When photographing the sun Don't stare into the sun, or hold the camera lens towards it for a very long time. Meter for the sky but don't include the sun itself. Composition tips: The horizon line should be above or below the center of the scene. -
Exploring Solar Cycle Influences on Polar Plasma Convection
Comparison of Terrestrial and Martian TEC at Dawn and Dusk during Solstices Angeline G. Burrell1 Beatriz Sanchez-Cano2, Mark Lester2, Russell Stoneback1, Olivier Witasse3, Marco Cartacci4 1Center for Space Sciences, University of Texas at Dallas 2Radio and Space Plasma Physics, University of Leicester 3European Space Agency, ESTEC – Scientific Support Office 4Istituto Nazionale di Astrofisica, Istituto di Astrofisica e Planetologia Spaziali 52nd ESLAB Symposium Outline • Motivation • Data and analysis – TEC sources – Data selection – Linear fitting • Results – Martian variations – Terrestrial variations – Similarities and differences • Conclusions Motivation • The Earth and Mars are arguably the most similar of the solar planets - They are both inner, rocky planets - They have similar axial tilts - They both have ionospheres that are formed primarily through EUV and X- ray radiation • Planetary differences can provide physical insights Total Electron Content (TEC) • The Global Positioning System • The Mars Advanced Radar for (GPS) measures TEC globally Subsurface and Ionosphere using a network of satellites and Sounding (MARSIS) measures ground receivers the TEC between the Martian • MIT Haystack provides calibrated surface and Mars Express TEC measurements • Mars Express has an inclination - Available from 1999 onward of 86.9˚ and a period of 7h, - Includes all open ground and allowing observations of all space-based sources locations and times - Specified with a 1˚ latitude by 1˚ • TEC is available for solar zenith longitude resolution with error estimates angles (SZA) greater than 75˚ Picardi and Sorge (2000), In: Proc. SPIE. Eighth International Rideout and Coster (2006) doi:10.1007/s10291-006-0029-5, 2006. Conference on Ground Penetrating Radar, vol. 4084, pp. 624–629. -
Celestial Coordinate Systems
Celestial Coordinate Systems Craig Lage Department of Physics, New York University, [email protected] January 6, 2014 1 Introduction This document reviews briefly some of the key ideas that you will need to understand in order to identify and locate objects in the sky. It is intended to serve as a reference document. 2 Angular Basics When we view objects in the sky, distance is difficult to determine, and generally we can only indicate their direction. For this reason, angles are critical in astronomy, and we use angular measures to locate objects and define the distance between objects. Angles are measured in a number of different ways in astronomy, and you need to become familiar with the different notations and comfortable converting between them. A basic angle is shown in Figure 1. θ Figure 1: A basic angle, θ. We review some angle basics. We normally use two primary measures of angles, degrees and radians. In astronomy, we also sometimes use time as a measure of angles, as we will discuss later. A radian is a dimensionless measure equal to the length of the circular arc enclosed by the angle divided by the radius of the circle. A full circle is thus equal to 2π radians. A degree is an arbitrary measure, where a full circle is defined to be equal to 360◦. When using degrees, we also have two different conventions, to divide one degree into decimal degrees, or alternatively to divide it into 60 minutes, each of which is divided into 60 seconds. These are also referred to as minutes of arc or seconds of arc so as not to confuse them with minutes of time and seconds of time. -
Planit! User Guide
ALL-IN-ONE PLANNING APP FOR LANDSCAPE PHOTOGRAPHERS QUICK USER GUIDES The Sun and the Moon Rise and Set The Rise and Set page shows the 1 time of the sunrise, sunset, moonrise, and moonset on a day as A sunrise always happens before a The azimuth of the Sun or the well as their azimuth. Moon is shown as thick color sunset on the same day. However, on lines on the map . some days, the moonset could take place before the moonrise within the Confused about which line same day. On those days, we might 3 means what? Just look at the show either the next day’s moonset or colors of the icons and lines. the previous day’s moonrise Within the app, everything depending on the current time. In any related to the Sun is in orange. case, the left one is always moonrise Everything related to the Moon and the right one is always moonset. is in blue. Sunrise: a lighter orange Sunset: a darker orange Moonrise: a lighter blue 2 Moonset: a darker blue 4 You may see a little superscript “+1” or “1-” to some of the moonrise or moonset times. The “+1” or “1-” sign means the event happens on the next day or the previous day, respectively. Perpetual Day and Perpetual Night This is a very short day ( If further north, there is no Sometimes there is no sunrise only 2 hours) in Iceland. sunrise or sunset. or sunset for a given day. It is called the perpetual day when the Sun never sets, or perpetual night when the Sun never rises. -
Here's Some Ideas
On that “Perfect Moment.” “Sometimes there’s that perfect moment when the crowd, the music, the energy of the room come together in a way that brings me to tears” John Legend. Covid-19 Safety Concerns The LCC executive advises against heading out right now. By staying home, you are protecting your life as well as the lives of others. If you are out and about though, remember to keep 2 meters apart, watch what you touch and wash your hands often (yeah, I know- I sound like your mom…). May 2020 Theme- Blue Hour. Definition: The blue hour is the period of twilight in the morning or evening, when the Sun is at a significant depth below the horizon and residual, indirect sunlight takes on a predominantly blue shade that is different from the blue shade visible during most of the day, which is caused by Rayleigh scattering. The requirement to have taken the picture at the Blue Hour has been suspended. Feel free to use post-production techniques in your editing software to add in the “Cool Blues.” Take out some of your old, Blue Hour images and work at enhancing them to best suit this theme. Here’s some ideas: Tim Shields critiques a number of pictures to describe what makes a great Blue Hour shot. Tim does a good job describing what works and what doesn’t. The video is about 15 minutes long but only the first 7 minutes is on the Blue Hour. Tim also touches on how some of the contributed photos could have been enhanced through simple steps in post production. -
Notes on Azimuth Reckoned from the South* a Hasty Examination of .The Early Rec.Orda of the Coast Survey, Hassler's Work 1N 1817
• \ , Notes on Azimuth reckoned from the South* A hasty examination of .the early rec.orda of the Coast Survey, Hassler's work 1n 1817 and work from 1830 on, suggests that there was no great uniformity of practice 1n the reckoning of azimuth. In working up astronomical observations it was sometimes reckoned from the north, apparently 1n either direction, without specially mentioning whether east or west, that point being determined by the attendant circumstances. However, 1n computing geodetic positions a form was used not unlike our present logarithmic form for the com putation of geodetic positions. This form was at first made out by hand but afterwards printed. In this form azimuth was counted from south through west up to 360°. A group of exceptions was noted, apparently a mere oversight. All this refers to the period around 1840. The formulas on which the form for position computa tion was based apparently came from Puissant. The proofs given in the earlier editions of Special Publication No. 8 , " resemble those in Puissant's Tra1te de Geodesle. The Library has the second edition dated 1819. Another source ( poggendorff) gives the date of the first edition as 1805. *See also 2nd paragraph on p. 94 of Special Pub. 8 2. ,The following passages are notes on or free translations from the second edit1on: Puissant Vol. I, p. 297 The formulas for position computation IIBlt 1 t 1s agreed in practice to reckon azimuths and longitudes from south to west and from zero to 400 grades" (360°). Puissant Vol. 1. p. 305 The formulas for position computation "The method just set forth for determining the geographic positions of the vertices of oblique triangles was proposed as early as 1787 by Legendre in a memoir on geodetic operations published by the Royal Academy of Sciences and 1s the one chiefly used by Delambre in the rec�nt measurement of a meridional arc. -
Ozone: Twilit Skies, and (Exo-)Planet Transits
Astronomical Science Ozone: Twilit Skies, and (Exo-)planet Transits Robert Fosbury1 the atmosphere, can be rich and varied. This article is about the effect of ozone George Koch 2 The processes that result in this palette on the colour of the twilit sky and, in the Johannes Koch 2 are geometrically complex, but comprise same vein, its appearance as the strong- a limited number of now well-understood est telluric absorption feature in the visi- physical effects. This understanding was ble spectrum of the Earth as it would be 1 ESO not gained easily. From the time when seen by a distant observer watching it 2 Lycée Français Jean Renoir, München, early humans first consciously posed the transit in front of the Sun. We present and Germany question: “What makes the sky blue?”, to analyse spectrophotometric observations the time when the processes of scatter- of sunset and also discuss observations ing by molecules and molecular density of the eclipsed Moon reported by Pallé et Although only a trace constituent gas fluctuations were elucidated, thousands al. (2009). in the Earth’s atmosphere, ozone plays of years passed, during which increas- a critical role in protecting the Earth’s ingly intensive experiments and theories surface from receiving a damaging flux were developed and carried out (Pesic, Ozone of solar ultraviolet radiation. What is not 2005). generally appreciated, however, is that Ozone (O3 or trioxygen) is an unstable the intrinsically weak, visible Chappuis Most physicists, if asked why the sky is allotrope of oxygen that most people can absorption band becomes an important blue, would answer with little hesitation: detect by smell at concentrations as influence on the colour of the entire sky “Because of Rayleigh scattering by mole low as 0.01 parts per million (ppm). -
The Celestial Sphere
The Celestial Sphere Useful References: • Smart, “Text-Book on Spherical Astronomy” (or similar) • “Astronomical Almanac” and “Astronomical Almanac’s Explanatory Supplement” (always definitive) • Lang, “Astrophysical Formulae” (for quick reference) • Allen “Astrophysical Quantities” (for quick reference) • Karttunen, “Fundamental Astronomy” (e-book version accessible from Penn State at http://www.springerlink.com/content/j5658r/ Numbers to Keep in Mind • 4 π (180 / π)2 = 41,253 deg2 on the sky • ~ 23.5° = obliquity of the ecliptic • 17h 45m, -29° = coordinates of Galactic Center • 12h 51m, +27° = coordinates of North Galactic Pole • 18h, +66°33’ = coordinates of North Ecliptic Pole Spherical Astronomy Geocentrically speaking, the Earth sits inside a celestial sphere containing fixed stars. We are therefore driven towards equations based on spherical coordinates. Rules for Spherical Astronomy • The shortest distance between two points on a sphere is a great circle. • The length of a (great circle) arc is proportional to the angle created by the two radial vectors defining the points. • The great-circle arc length between two points on a sphere is given by cos a = (cos b cos c) + (sin b sin c cos A) where the small letters are angles, and the capital letters are the arcs. (This is the fundamental equation of spherical trigonometry.) • Two other spherical triangle relations which can be derived from the fundamental equation are sin A sinB = and sin a cos B = cos b sin c – sin b cos c cos A sina sinb € Proof of Fundamental Equation • O is