Glossary 2010 Ablation Erosion of an Object (Generally a Meteorite) by The
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Appendix: Derivations
Paleomagnetism: Chapter 11 224 APPENDIX: DERIVATIONS This appendix provides details of derivations referred to throughout the text. The derivations are devel- oped here so that the main topics within the chapters are not interrupted by the sometimes lengthy math- ematical developments. DERIVATION OF MAGNETIC DIPOLE EQUATIONS In this section, a derivation is provided of the basic equations describing the magnetic field produced by a magnetic dipole. The geometry is shown in Figure A.1 and is identical to the geometry of Figure 1.3 for a geocentric axial dipole. The derivation is developed by using spherical coordinates: r, θ, and φ. An addi- tional polar angle, p, is the colatitude and is defined as π – θ. After each quantity is derived in spherical coordinates, the resulting equation is altered to provide the results in the convenient forms (e.g., horizontal component, Hh) that are usually encountered in paleomagnetism. H ^r H H h I = H p r = –Hr H v M Figure A.1 Geocentric axial dipole. The large arrow is the magnetic dipole moment, M ; θ is the polar angle from the positive pole of the magnetic dipole; p is the magnetic colatitude; λ is the geo- graphic latitude; r is the radial distance from the magnetic dipole; H is the magnetic field produced by the magnetic dipole; rˆ is the unit vector in the direction of r. The inset figure in the upper right corner is a magnified version of the stippled region. Inclination, I, is the vertical angle (dip) between the horizontal and H. The magnetic field vector H can be broken into (1) vertical compo- nent, Hv =–Hr, and (2) horizontal component, Hh = Hθ . -
Rotational Motion of Electric Machines
Rotational Motion of Electric Machines • An electric machine rotates about a fixed axis, called the shaft, so its rotation is restricted to one angular dimension. • Relative to a given end of the machine’s shaft, the direction of counterclockwise (CCW) rotation is often assumed to be positive. • Therefore, for rotation about a fixed shaft, all the concepts are scalars. 17 Angular Position, Velocity and Acceleration • Angular position – The angle at which an object is oriented, measured from some arbitrary reference point – Unit: rad or deg – Analogy of the linear concept • Angular acceleration =d/dt of distance along a line. – The rate of change in angular • Angular velocity =d/dt velocity with respect to time – The rate of change in angular – Unit: rad/s2 position with respect to time • and >0 if the rotation is CCW – Unit: rad/s or r/min (revolutions • >0 if the absolute angular per minute or rpm for short) velocity is increasing in the CCW – Analogy of the concept of direction or decreasing in the velocity on a straight line. CW direction 18 Moment of Inertia (or Inertia) • Inertia depends on the mass and shape of the object (unit: kgm2) • A complex shape can be broken up into 2 or more of simple shapes Definition Two useful formulas mL2 m J J() RRRR22 12 3 1212 m 22 JRR()12 2 19 Torque and Change in Speed • Torque is equal to the product of the force and the perpendicular distance between the axis of rotation and the point of application of the force. T=Fr (Nm) T=0 T T=Fr • Newton’s Law of Rotation: Describes the relationship between the total torque applied to an object and its resulting angular acceleration. -
Instrumental Methods for Professional and Amateur
Instrumental Methods for Professional and Amateur Collaborations in Planetary Astronomy Olivier Mousis, Ricardo Hueso, Jean-Philippe Beaulieu, Sylvain Bouley, Benoît Carry, Francois Colas, Alain Klotz, Christophe Pellier, Jean-Marc Petit, Philippe Rousselot, et al. To cite this version: Olivier Mousis, Ricardo Hueso, Jean-Philippe Beaulieu, Sylvain Bouley, Benoît Carry, et al.. Instru- mental Methods for Professional and Amateur Collaborations in Planetary Astronomy. Experimental Astronomy, Springer Link, 2014, 38 (1-2), pp.91-191. 10.1007/s10686-014-9379-0. hal-00833466 HAL Id: hal-00833466 https://hal.archives-ouvertes.fr/hal-00833466 Submitted on 3 Jun 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Instrumental Methods for Professional and Amateur Collaborations in Planetary Astronomy O. Mousis, R. Hueso, J.-P. Beaulieu, S. Bouley, B. Carry, F. Colas, A. Klotz, C. Pellier, J.-M. Petit, P. Rousselot, M. Ali-Dib, W. Beisker, M. Birlan, C. Buil, A. Delsanti, E. Frappa, H. B. Hammel, A.-C. Levasseur-Regourd, G. S. Orton, A. Sanchez-Lavega,´ A. Santerne, P. Tanga, J. Vaubaillon, B. Zanda, D. Baratoux, T. Bohm,¨ V. Boudon, A. Bouquet, L. Buzzi, J.-L. Dauvergne, A. -
Appulses of Jupiter and Saturn
IN ORIGINAL FORM PUBLISHED IN: arXiv:(side label) [physics.pop-ph] Sternzeit 46, No. 1+2 / 2021 (ISSN: 0721-8168) Date: 6th May 2021 Appulses of Jupiter and Saturn Joachim Gripp, Emil Khalisi Sternzeit e.V., Kiel and Heidelberg, Germany e-mail: gripp or khalisi ...[at]sternzeit-online[dot]de Abstract. The latest conjunction of Jupiter and Saturn occurred at an optical distance of 6 arc minutes on 21 December 2020. We re-analysed all encounters of these two planets between -1000 and +3000 CE, as the extraordinary ones (< 10′) take place near the line of nodes every 400 years. An occultation of their discs did not and will not happen within the historical time span of ±5,000 years around now. When viewed from Neptune though, there will be an occultation in 2046. Keywords: Jupiter-Saturn conjunction, Appulse, Trigon, Occultation. Introduction reason is due to Earth’s orbit: while Jupiter and Saturn are locked in a 5:2-mean motion resonance, the Earth does not The slowest naked-eye planets Jupiter and Saturn made an join in. For very long periods there could be some period- impressive encounter in December 2020. Their approaches icity, however, secular effects destroy a cycle, e.g. rotation have been termed “Great Conjunctions” in former times of the apsides and changes in eccentricity such that we are and they happen regularly every ≈20 years. Before the left with some kind of “semi-periodicity”. discovery of the outer ice giants these classical planets rendered the longest known cycle. The separation at the instant of conjunction varies up to 1 degree of arc, but the Close Encounters latest meeting was particularly tight since the planets stood Most pass-bys of Jupiter and Saturn are not very spectac- closer than at any other occasion for as long as 400 years. -
Astronomical Calendar 2021 1
© 2020 by Guy Ottewell ASTRONOMICAL CALENDAR 2021 1 www.universalworkshop.com The left column gives Julian Dates For meteor showers: ZHR (zenithal (number of days from 4713 B.C. Jan. 1 hourly rate) is an estimate of the noon), useful for finding time spans number to be seen under ideal condi- between events by subtraction. The tions at the peak time if the radiant first 3 digits of the Julian date were overhead. Actual rates may be (245) are omitted, to save space. very different. Peak times (predicted Hours and minutes, where given, from where the center of the stream are in Universal Time. (Sometimes seems to cross nearest to Earth’s the hour appears as “24” or the orbit) are uncertain; best to start minute as “60,” because the instant watching the night before. Meteor was shortly before the end of the day are usually most abundant in the or hour.) morning hours. Occasions such as “Moon 1.25° NNE Tell me of errors you notice. of Venus” are appulses: closest appar- It’s hard to check the accuracy of ent approaches. They are slightly every detail, but errors are more different from conjunctions, when one easily corrected here than in the passes north of the other as measured former printed Astronomical Calendars! in right ascension or in ecliptic universalworkshop.com/contact longitude. A quasi-conjunction is an This calendar may be subject to appulse without a conjunction, and improvement. Come back to it! typically happens when a planet is near its stationary moment. Explanation of terms can be found in Occasions when three bodies are our glossary book Albedo to Zodiac. -
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. -
The Prediction and Observation of the 1997 July 18 Stellar Occultation by Triton: More Evidence for Distortion and Increasing Pressure in Triton’S Atmosphere
Icarus 148, 347–369 (2000) doi:10.1006/icar.2000.6508, available online at http://www.idealibrary.com on The Prediction and Observation of the 1997 July 18 Stellar Occultation by Triton: More Evidence for Distortion and Increasing Pressure in Triton’s Atmosphere J. L. Elliot,1,2 M. J. Person, and S. W. McDonald Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307 E-mail: [email protected] M. W. Buie, E. W. Dunham, R. L. Millis, R. A. Nye, C. B. Olkin, and L. H. Wasserman Lowell Observatory, 1400 West Mars Hill Road, Flagstaff, Arizona 86001-4499 L. A. Young3 Center for Space Physics, Boston University, Boston, Massachusetts 02215 W. B. Hubbard and R. Hill Lunar and Planetary Laboratory, University of Arizona, Tucson, Arizona 85721 H. J. Reitsema Ball Aerospace, P.O. Box 1062, Boulder, Colorado 80306-1062 J. M. Pasachoff and T. H. McConnochie4 Astronomy Department, Williams College, Williamstown, Massachusetts 01267-2565 B. A. Babcock Physics Department, Williams College, Williamstown, Massachusetts 01267-2565 R. C. Stone U.S. Naval Observatory, Flagstaff Station, P.O. Box 1149, Flagstaff, Arizona 86002-1149 and P. Francis Mt. Stromlo Observatory, Private Bag, Weston Creek Post Office, Weston, ACT 2611, Australia Received December 21, 1999; revised June 20, 2000 1 Also at Lowell Observatory, 1400 West Mars Hill Road, Flagstaff, AZ 86001-4499. 2 A variety of CCD astrometric data was used to predict the lo- Also at Department of Physics, MIT, and guest observer, Cerro Tololo Inter- cation of the path for the occultation of the star we have denoted American Observatory, National Optical Astronomy Observatories, operated by “Tr176” by Triton, which occurred on 1997 July 18, and was visible the Association of Universities for Research in Astronomy, Inc., under cooper- ative agreement with the National Science Foundation. -
Fluid Mechanics 2 Course Code MPEG222 Second Semester Fall 2019/2020 by Dr
South valley University Faculty of Engineering Mechanical Power Engineering Dep. Fluid Mechanics 2 Course Code MPEG222 Second Semester Fall 2019/2020 By Dr. Eng./Ahmed Abdelhady Mobile: 01118501269 Email: [email protected] Review of Rotational Motion and Angular Momentum The motion of a rigid body can be considered to be the combination of the: ➢ Translational motion of its center of mass and, The translational motion can be analyzed using the linear momentum equation. ➢ Rotational motion about its center of mass. all points in the body move in circles about the axis of rotation. The amount of rotation of a point in a body is expressed in terms of the angle θ swept by a line of length r that connects the point to the axis of rotation and is perpendicular to the axis. The physical distance traveled by a point along its circular path is l = θr, where r is the normal distance of the point from the axis of rotation and θ is the angular distance in rad. Note that 1 rad corresponds to 360/(2π) = 57.3°. V is the linear velocity and at is the linear acceleration in the tangential direction for a point located at a distance r from the axis of rotation. Newton’s second law requires that there must be a force acting in the tangential direction to cause angular acceleration. The strength of the rotating effect, called the moment or torque, is proportional to the magnitude of the force and its distance from the axis of rotation. ➢ I is the moment of inertia of the body about the axis of rotation Note that: ➢ The linear momentum of a body of mass m having a velocity V is mV, and the direction of linear momentum is identical to the direction of velocity. -
Glossary: Only Some Selected Terms Are Defined Here; for a Full Glossary
Glossary: Only some selected terms are defined here; for a full glossary consult an astronomical dictionary or google the word you need defined. Aphelion/Perihelion: Earth’s orbit is elliptical so the planet is farthest from the Sun at aphelion (first week of July) and closest at perihelion (first week of Jan). Apogee/Perigee: Since orbits around the Sun or Earth are usually ellipses, the farthest and nearest distances use “apo” (far) and “peri” (near) to describe the maximum and minimum values. For Earth and its satellites, apogee is the farthest point and perigee is the nearest (“geo” = Earth). The same prefixes are applied to orbits around the Moon -”luna” (apolune and perilune) Sun -”helios” (aphelion/perihelion), etc. Appulse: A close approach of two astronomical objects. i.e. minimum separation expressed in degrees, minutes and seconds of arc where 1 degree = 60 minutes and 1 minute = 60 seconds of arc. Note: the Moon and Sun are about 0.5 degrees or 30 minutes of arc across. Bolides or Fireballs: A very bright meteor (shooting star) that often can light up the ground and produce meteorites. See Meteor Shower below for more. Conjunction: The point in time when two stellar objects have the same Right Ascension. This is usually close to the minimum separation of the two objects but may not necessarily be minimum. (See also appulse above). When a planet is at Inferior Conjunction with the Sun it is between Earth and Sun and in Superior Conjunction, it is on the opposite side of the sun. At neither time are they easy (but not impossible) to see since they are near the Sun. -
Astronomy I – Vocabulary You Need to Know
Astronomy I – Vocabulary you need to know: Altitude – Angular distance above or below the horizon, measured along a vertical circle, to the celestial object. Angular measure – Measurement in terms of angles or degrees of arc. An entire circle is divided into 360 º, each degree in 60 ´ (minutes), and each minute into 60 ´´ (seconds). This scale is used to denote, among other things, the apparent size of celestial bodies, their separation on the celestial sphere, etc. One example is the diameter of the Moon’s disc, which measures approximately 0.5 º= 30 ´. Azimuth – The angle along the celestial horizon, measured eastward from the north point, to the intersection of the horizon with the vertical circle passing through an object. Big Bang Theory – States that the universe began as a tiny but powerful explosion of space-time roughly 13.7 billion years ago. Cardinal points – The four principal points of the compass: North, South, East, West. Celestial equator – Is the great circle on the celestial sphere defined by the projection of the plane of the Earth’s equator. It divides the celestial sphere into the northern and southern hemisphere. The celestial equator has a declination of 0 º. Celestial poles – Points above which the celestial sphere appears to rotate. Celestial sphere – An imaginary sphere of infinite radius, in the centre of which the observer is located, and against which all celestial bodies appear to be projected. Constellation – A Precisely defined part of the celestial sphere. In the older, narrower meaning of the term, it is a group of fixed stars forming a characteristic pattern. -
Observer's Handbook 1974
the OBSERVER’S HANDBOOK 1974 sixty- sixth year of publication the ROYAL ASTRONOMICAL SOCIETY of CANADA THE ROYAL ASTRONOMICAL SOCIETY OF CANADA Incorporated 1890 Federally Incorporated 1968 The National Office of the Society is located at 252 College Street, Toronto 130, Ontario; the business office, reading room and astronomical library are housed here. Membership is open to anyone interested in astronomy and applicants may affiliate with one of the eighteen Centres across Canada established in St. John’s, Halifax, Quebec, Montreal, Ottawa, Kingston, Hamilton, Niagara Falls, London, Windsor, Winnipeg, Saskatoon, Edmonton, Calgary, Vancouver, Victoria and Toronto, or join the National Society direct. Publications of the Society are free to members, and include the Jo u r n a l (6 issues per year) and the O bserver’s H a n d b o o k (published annually in November). Annual fees of $12.50 ($7.50 for full-time students) are payable October 1 and include the publications for the following calendar year. VISITING HOURS AT SOME CANADIAN OBSERVATORIES Burke-Gaffney Observatory, Saint Mary’s University, Halifax, Nova Scotia. October-April: Saturday evenings 7:00 p.m. May-September: Saturday evenings 9:00 p.m. David Dunlap Observatory, Richmond Hill, Ontario. Wednesday mornings throughout the year, 10:00 a.m. Saturday evenings, April through October (by reservations, tel. 884-2112). Dominion Astrophysical Observatory, Victoria, B.C. May-August: Daily, 9:15 a.m.-4:30 p.m. (Guide, Monday to Friday). Sept.-April: Monday to Friday, 9:15 a.m.-4:30 p.m. Public observing, Saturday evenings, April-October, inclusive. -
Lunar Distances Final
A (NOT SO) BRIEF HISTORY OF LUNAR DISTANCES: LUNAR LONGITUDE DETERMINATION AT SEA BEFORE THE CHRONOMETER Richard de Grijs Department of Physics and Astronomy, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia Email: [email protected] Abstract: Longitude determination at sea gained increasing commercial importance in the late Middle Ages, spawned by a commensurate increase in long-distance merchant shipping activity. Prior to the successful development of an accurate marine timepiece in the late-eighteenth century, marine navigators relied predominantly on the Moon for their time and longitude determinations. Lunar eclipses had been used for relative position determinations since Antiquity, but their rare occurrences precludes their routine use as reliable way markers. Measuring lunar distances, using the projected positions on the sky of the Moon and bright reference objects—the Sun or one or more bright stars—became the method of choice. It gained in profile and importance through the British Board of Longitude’s endorsement in 1765 of the establishment of a Nautical Almanac. Numerous ‘projectors’ jumped onto the bandwagon, leading to a proliferation of lunar ephemeris tables. Chronometers became both more affordable and more commonplace by the mid-nineteenth century, signaling the beginning of the end for the lunar distance method as a means to determine one’s longitude at sea. Keywords: lunar eclipses, lunar distance method, longitude determination, almanacs, ephemeris tables 1 THE MOON AS A RELIABLE GUIDE FOR NAVIGATION As European nations increasingly ventured beyond their home waters from the late Middle Ages onwards, developing the means to determine one’s position at sea, out of view of familiar shorelines, became an increasingly pressing problem.