Methods of Measuring Astronomical Distances
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Quantity Symbol Value One Astronomical Unit 1 AU 1.50 × 10
Quantity Symbol Value One Astronomical Unit 1 AU 1:50 × 1011 m Speed of Light c 3:0 × 108 m=s One parsec 1 pc 3.26 Light Years One year 1 y ' π × 107 s One Light Year 1 ly 9:5 × 1015 m 6 Radius of Earth RE 6:4 × 10 m Radius of Sun R 6:95 × 108 m Gravitational Constant G 6:67 × 10−11m3=(kg s3) Part I. 1. Describe qualitatively the funny way that the planets move in the sky relative to the stars. Give a qualitative explanation as to why they move this way. 2. Draw a set of pictures approximately to scale showing the sun, the earth, the moon, α-centauri, and the milky way and the spacing between these objects. Give an ap- proximate size for all the objects you draw (for example example next to the moon put Rmoon ∼ 1700 km) and the distances between the objects that you draw. Indicate many times is one picture magnified relative to another. Important: More important than the size of these objects is the relative distance between these objects. Thus for instance you may wish to show the sun and the earth on the same graph, with the circles for the sun and the earth having the correct ratios relative to to the spacing between the sun and the earth. 3. A common unit of distance in Astronomy is a parsec. 1 pc ' 3:1 × 1016m ' 3:3 ly (a) Explain how such a curious unit of measure came to be defined. Why is it called parsec? (b) What is the distance to the nearest stars and how was this distance measured? 4. -
Could a Nearby Supernova Explosion Have Caused a Mass Extinction? JOHN ELLIS* and DAVID N
Proc. Natl. Acad. Sci. USA Vol. 92, pp. 235-238, January 1995 Astronomy Could a nearby supernova explosion have caused a mass extinction? JOHN ELLIS* AND DAVID N. SCHRAMMtt *Theoretical Physics Division, European Organization for Nuclear Research, CH-1211, Geneva 23, Switzerland; tDepartment of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637; and *National Aeronautics and Space Administration/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, IL 60510 Contributed by David N. Schramm, September 6, 1994 ABSTRACT We examine the possibility that a nearby the solar constant, supernova explosions, and meteorite or supernova explosion could have caused one or more of the comet impacts that could be due to perturbations of the Oort mass extinctions identified by paleontologists. We discuss the cloud. The first of these has little experimental support. possible rate of such events in the light of the recent suggested Nemesis (4), a conjectured binary companion of the Sun, identification of Geminga as a supernova remnant less than seems to have been excluded as a mechanism for the third,§ 100 parsec (pc) away and the discovery ofa millisecond pulsar although other possibilities such as passage of the solar system about 150 pc away and observations of SN 1987A. The fluxes through the galactic plane may still be tenable. The supernova of y-radiation and charged cosmic rays on the Earth are mechanism (6, 7) has attracted less research interest than some estimated, and their effects on the Earth's ozone layer are of the others, perhaps because there has not been a recent discussed. -
Distances and Magnitudes Distance Measurements the Cosmic Distance
Distances and Magnitudes Prof Andy Lawrence Astronomy 1G 2011-12 Distance Measurements Astronomy 1G 2011-12 The cosmic distance ladder • Distance measurements in astronomy are a chain, with each type of measurement relative to the one before • The bottom rung is the Astronomical Unit (AU), the (mean) distance between the Earth and the Sun • Many distance estimates rely on the idea of a "standard candle" or "standard yardstick" Astronomy 1G 2011-12 Distances in the solar system • relative distances to planets given by periods + Keplers law (see Lecture-2) • distance to Venus measured by radar • Sun-Earth = 1 A.U. (average) • Sun-Jupiter = 5 A.U. (average) • Sun-Neptune = 30 A.U. (average) • Sun- Oort cloud (comets) ~ 50,000 A.U. • 1 A.U. = 1.496 x 1011 m Astronomy 1G 2011-12 Distances to nearest stars • parallax against more distant non- moving stars • 1 parsec (pc) is defined as distance where parallax = 1 second of arc in standard units D = a/✓ (radians, metres) in AU and arcsec D(AU) = 1/✓rad = 206, 265/✓00 in parsec and arcsec D(pc) = 1/✓00 nearest star Proxima Centauri 1.30pc Very hard to measure less than 0.1" 1pc = 206,265 AU = 3.086 x 1016m so only good for stars a few parsecs away... until launch of GAIA mission in 2014..... Astronomy 1G 2011-12 More distant stars : standard candle technique If a star has luminosity L (total energy emitted per sec) then at L distance D we will observe flux density F (i.e. energy per second F = 2 per sq.m. -
Aspects of Spatially Homogeneous and Isotropic Cosmology
Faculty of Technology and Science Department of Physics and Electrical Engineering Mikael Isaksson Aspects of Spatially Homogeneous and Isotropic Cosmology Degree Project of 15 credit points Physics Program Date/Term: 02-04-11 Supervisor: Prof. Claes Uggla Examiner: Prof. Jürgen Fuchs Karlstads universitet 651 88 Karlstad Tfn 054-700 10 00 Fax 054-700 14 60 [email protected] www.kau.se Abstract In this thesis, after a general introduction, we first review some differential geom- etry to provide the mathematical background needed to derive the key equations in cosmology. Then we consider the Robertson-Walker geometry and its relation- ship to cosmography, i.e., how one makes measurements in cosmology. We finally connect the Robertson-Walker geometry to Einstein's field equation to obtain so- called cosmological Friedmann-Lema^ıtre models. These models are subsequently studied by means of potential diagrams. 1 CONTENTS CONTENTS Contents 1 Introduction 3 2 Differential geometry prerequisites 8 3 Cosmography 13 3.1 Robertson-Walker geometry . 13 3.2 Concepts and measurements in cosmography . 18 4 Friedmann-Lema^ıtre dynamics 30 5 Bibliography 42 2 1 INTRODUCTION 1 Introduction Cosmology comes from the Greek word kosmos, `universe' and logia, `study', and is the study of the large-scale structure, origin, and evolution of the universe, that is, of the universe taken as a whole [1]. Even though the word cosmology is relatively recent (first used in 1730 in Christian Wolff's Cosmologia Generalis), the study of the universe has a long history involving science, philosophy, eso- tericism, and religion. Cosmologies in their earliest form were concerned with, what is now known as celestial mechanics (the study of the heavens). -