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Squashing and Spaghettification in Newtonian Gravitation
Revista Brasileira de Ensino de F´ısica, vol. 42, e20200278 (2020) Artigos Gerais www.scielo.br/rbef c b DOI: https://doi.org/10.1590/1806-9126-RBEF-2020-0278 Licenc¸aCreative Commons Squashing and spaghettification in Newtonian gravitation R. R. Machado*1 , A. C. Tort2 , C. A. D. Zarro2 1Centro Federal de Educa¸c˜aoTecnol´ogicaCelso Suckow da Fonseca, Rio de Janeiro, RJ, Brasil 2Universidade Federal do Rio de Janeiro, Instituto de F´ısica,Rio de Janeiro, RJ, Brasil Received on July 06, 2020. Revised on September 07, 2020. Accepted on October 08, 2020. Action films and sci-fi novels should be common resources in classrooms since they serve as examples and references involving physical situations. This is due to the abstract nature of many physical concepts, and the lack of references in students’ daily lives makes them more difficult to be visualized or imagined. In this work we bring a discussion of how we can resort to films and literary works in order to elucidate the concepts regarding tidal forces. To this effect, we have used the action film Total Recall (2012) to present the squashing effect and the classic of juvenile literature From Earth to the Moon (1865) to discuss the effect of spaghettification in the context of Newtonian mechanics. Keywords: Newtonian gravitation, non-inertial frames, tidal forces. 1. Introduction Earth to the Moon [3], see Figure 2. On Verne’s chap- ter XXIII, he describes the Projectile-Vehicle, to which Action movies and sci-fi novels can always be resorted to we will refer as Verne’s projectile, designed to trans- whenever we look for situations, or examples, capable of port adventurous people through space; more precisely motivating our students. -
BLACK HOLES: the OTHER SIDE of INFINITY General Information
BLACK HOLES: THE OTHER SIDE OF INFINITY General Information Deep in the middle of our Milky Way galaxy lies an object made famous by science fiction—a supermassive black hole. Scientists have long speculated about the existence of black holes. German astronomer Karl Schwarzschild theorized that black holes form when massive stars collapse. The resulting gravity from this collapse would be so strong that the matter would become more and more dense. The gravity would eventually become so strong that nothing, not even radiation moving at the speed of light, could escape. Schwarzschild’s theories were predicted by Einstein and then borne out mathematically in 1939 by American astrophysicists Robert Oppenheimer and Hartland Snyder. WHAT EXACTLY IS A BLACK HOLE? First, it’s not really a hole! A black hole is an extremely massive concentration of matter, created when the largest stars collapse at the end of their lives. Astronomers theorize that a point with infinite density—called a singularity—lies at the center of black holes. SO WHY IS IT CALLED A HOLE? Albert Einstein’s 1915 General Theory of Relativity deals largely with the effects of gravity, and in essence predicts the existence of black holes and singularities. Einstein hypothesized that gravity is a direct result of mass distorting space. He argued that space behaves like an invisible fabric with an elastic quality. Celestial bodies interact with this “fabric” of space-time, appearing to create depressions termed “gravity wells” and drawing nearby objects into orbit around them. Based on this principle, the more massive a body is in space, the deeper the gravity well it will create. -
Spacetime Warps and the Quantum World: Speculations About the Future∗
Spacetime Warps and the Quantum World: Speculations about the Future∗ Kip S. Thorne I’ve just been through an overwhelming birthday celebration. There are two dangers in such celebrations, my friend Jim Hartle tells me. The first is that your friends will embarrass you by exaggerating your achieve- ments. The second is that they won’t exaggerate. Fortunately, my friends exaggerated. To the extent that there are kernels of truth in their exaggerations, many of those kernels were planted by John Wheeler. John was my mentor in writing, mentoring, and research. He began as my Ph.D. thesis advisor at Princeton University nearly forty years ago and then became a close friend, a collaborator in writing two books, and a lifelong inspiration. My sixtieth birthday celebration reminds me so much of our celebration of Johnnie’s sixtieth, thirty years ago. As I look back on my four decades of life in physics, I’m struck by the enormous changes in our under- standing of the Universe. What further discoveries will the next four decades bring? Today I will speculate on some of the big discoveries in those fields of physics in which I’ve been working. My predictions may look silly in hindsight, 40 years hence. But I’ve never minded looking silly, and predictions can stimulate research. Imagine hordes of youths setting out to prove me wrong! I’ll begin by reminding you about the foundations for the fields in which I have been working. I work, in part, on the theory of general relativity. Relativity was the first twentieth-century revolution in our understanding of the laws that govern the universe, the laws of physics. -
Pos(NLS1)058 Ce of Broad Emission Lines in Their Ds Reveals Strong Similarities in the Ant Differences (E.G
BL Lac objects with optical jets: PKS 2201+044, 3C 371 and PKS 0521-365. PoS(NLS1)058 E∗. Liuzzo Istituto di Radioastronomia-INAF-Bologna (Italy) E-mail: [email protected] R. Falomo Osservatorio Astronomico di Padova-INAF (Italy) A. Treves Università dell’Insubria (Como-Italy), associated to INAF and INFN We investigate the properties of the three BL Lac objects, PKS 2201+044, 3C 371 and PKS 0521- 365, that exhibit prominent optical jets. We present high resolution near-IR images of the jet of the first two, obtained with an innovative adaptive-optics system (MAD) at ESO VLT telescope. Comparison of the jet in the optical, radio, NIR and X-ray bands reveals strong similarities in the morphology. A common property of these sources is the presence of broad emission lines in their optical spectra at variance with the typical featureless spectrum of the nearby BL Lac objects. Despite some resemblances (e.g. in the radio type), significant differences (e.g. in the central black hole masses and radio structures) with radio-loud NLS1s are found. Narrow-Line Seyfert 1 Galaxies and their place in the Universe - NLS1, April 04-06, 2011 Milan Italy ∗Speaker. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ BL Lac objects with optical jets. E 1. Introduction Radio loud (RL) Active Galactic Nuclei (AGN), in the contrary to their radio quiet (RQ) counterparts, show prominent jets mainly observable in the radio band. Blazars, including BL Lac objects and flat-spectrum radio quasars (FSRQs), are an important class of RL AGNs in which jets are relativistic and beamed in the observing direction. -
Extragalactic Radio Jets
Annual Reviews www.annualreviews.org/aronline Ann. Rev. Astron.Astrophys. 1984. 22 : 319-58 Copyright© 1984 by AnnualReviews Inc. All rights reserved EXTRAGALACTIC RADIO JETS Alan H. Bridle National Radio AstronomyObservatory, 1 Charlottesville, Virginia 22901 Richard A. Perley National Radio Astronomy Observatory, Socorro, New Mexico 87801 1. INTRODUCTION Powerful extended extragalactic radio sources pose two vexing astro- physical problems [reviewed in (147) and (157)]. First, from what energy reservoir do they draw their large radio luminosities (as muchas 10a8 W between 10 MHzand 100 GHz)?Second, how does the active center in the parent galaxy or QSOsupply as muchas 10~4 J in relativistic particles and fields to radio "lobes" up to several hundredkiloparsecs outside the optical object? Newaperture synthesis arrays (68, 250) and new image-processing algorithms (66, 101, 202, 231) have recently allowed radio imaging subarcsecond resolution with high sensitivity and high dynamicrange; as a result, the complexityof the brighter sources has been revealed clearly for the first time. Manycontain radio jets, i.e. narrow radio features between compact central "cores" and more extended "lobe" emission. This review examinesthe systematic properties of such jets and the dues they give to the by PURDUE UNIVERSITY LIBRARY on 01/16/07. For personal use only. physics of energy transfer in extragalactic sources. Wedo not directly consider the jet production mechanism,which is intimately related to the Annu. Rev. Astro. Astrophys. 1984.22:319-358. Downloaded from arjournals.annualreviews.org first problemnoted above--for reviews, see (207) and (251). 1. i Why "’Jets"? Baade & Minkowski(3) first used the term jet in an extragalactic context, describing the train of optical knots extending ,-~ 20" from the nucleus of M87; the knots resemble a fluid jet breaking into droplets. -
Structure in Radio Galaxies
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7.5 X 11.5.Threelines.P65
Cambridge University Press 978-0-521-19267-5 - Observing and Cataloguing Nebulae and Star Clusters: From Herschel to Dreyer’s New General Catalogue Wolfgang Steinicke Index More information Name index The dates of birth and death, if available, for all 545 people (astronomers, telescope makers etc.) listed here are given. The data are mainly taken from the standard work Biographischer Index der Astronomie (Dick, Brüggenthies 2005). Some information has been added by the author (this especially concerns living twentieth-century astronomers). Members of the families of Dreyer, Lord Rosse and other astronomers (as mentioned in the text) are not listed. For obituaries see the references; compare also the compilations presented by Newcomb–Engelmann (Kempf 1911), Mädler (1873), Bode (1813) and Rudolf Wolf (1890). Markings: bold = portrait; underline = short biography. Abbe, Cleveland (1838–1916), 222–23, As-Sufi, Abd-al-Rahman (903–986), 164, 183, 229, 256, 271, 295, 338–42, 466 15–16, 167, 441–42, 446, 449–50, 455, 344, 346, 348, 360, 364, 367, 369, 393, Abell, George Ogden (1927–1983), 47, 475, 516 395, 395, 396–404, 406, 410, 415, 248 Austin, Edward P. (1843–1906), 6, 82, 423–24, 436, 441, 446, 448, 450, 455, Abbott, Francis Preserved (1799–1883), 335, 337, 446, 450 458–59, 461–63, 470, 477, 481, 483, 517–19 Auwers, Georg Friedrich Julius Arthur v. 505–11, 513–14, 517, 520, 526, 533, Abney, William (1843–1920), 360 (1838–1915), 7, 10, 12, 14–15, 26–27, 540–42, 548–61 Adams, John Couch (1819–1892), 122, 47, 50–51, 61, 65, 68–69, 88, 92–93, -
Lecture 19 Black Holes and Gamma-Ray Bursts
Black holes in nature – end points of stellar evolution • In our galaxy alone, theory suggests 50 million black holes (2 SN per century for 1010 years ¼ of which make black holes • Most massive galaxies have massive black holes Lecture 19 at their centers (109 galaxies) • Dozens of black hole binary x-ray sources per Black Holes and galaxy – at least Gamma-Ray Bursts • One gravitational radiation detection so far http://apod.nasa.gov/apod/astropix.html They are out there… Some Properties of Black Holes Kinds of black holes: • Entirely defined by their mass, rotation rate, and charge. All memory of how the hole was made Mass Size is lost. Almost like an elementary particle. “Black holes Class have no hair” (Wheeler, Israel, Hawking, etc.) (solar masses) • Believed that all the mass is concentrated at the AGN Supermassive ~105 - 1010 0.001 - 10 AU center in a small quantum-mechanical singularity Intermediate ~1000 ~ R • The effective density of stellar mass black holes, as ? earth defined by their event horizons is very high, but there are supermassive black hole in active galactic nuclei Stellar ~10 ~30 km with average densities no greater than water. they are just XRBin very big (this ignores the central concentration in a singularity though.) The average density matters to tidal forces. ? Primordial Up to ~Moon Up to ~0.1 mm • The gravitational field of a black hole close to the event horizon is complicated, but by the time you are ⎛ 2GM ⎞ ⎛ M ⎞ RS = 2 = 2.96 km ⎜ ⎟ several Schwarzschild radii away, it is indistinguishable ⎜ c ⎟ M ⎝ ⎠ ⎝ ⎠ from that of an ordinary star. -
Cycle 12 Abstract Catalog
Cycle 12 Abstract Catalog Generated April 04, 2003 ================================================================================ Proposal Category: GO Scientific Category: ISM AND CIRCUMSTELLAR MATTER ID: 9718 Title: SMC Extinction Curve Towards a Quiescent Molecular Cloud PI: Francois Boulanger PI Institution: Institut d'Astrophysique Spatiale The lack of 2175 A bump in the SMC extinction curve is interpreted as an absence of small carbon grains. ISO Mid-IR observations support this interpretation by showing that PAH features are absent in the spectra of SMC and LMC massive star forming regions. However, the only ISO observation of an SMC quiescent molecular cloud shows all PAH features, indicating a PAH abundance relative to large dust grains similar to that of Milky Way clouds. We identified a reddened B2III star associated with this cloud. We propose to observe it with STIS. This observation will provide the first measure of the extinction properties of SMC dust away from star forming regions. It will allow us to disentangle the effects of metallicity and massive stars on the SMC extinction curve and dust composition and to assess the relevance of the SMC bump-free extinction curve to low metallicity and/or starburst galaxies in general. ================================================================================ Proposal Category: GO Scientific Category: STELLAR POPULATIONS ID: 9719 Title: Search For Metallicity Spreads in M31 Globular Clusters PI: Terry Bridges PI Institution: Anglo-Australian Observatory Our recent deep HST photometry of the M31 halo globular cluster (GC) Mayall~II, also called G1, has revealed a red-giant branch with a clear spread that we attribute to an intrinsic metallicity dispersion of at least 0.4 dex in [Fe/H]. -
Introduction to Black Hole Astrophysics, 2010 Gustavo E
Lecture Notes Introduction to Black Hole Astrophysics, 2010 Gustavo E. Romero Introduction to black hole astrophysics Gustavo E. Romero Instituto Argentino de Radioastronomía, C.C. 5, Villa Elisa (1894), and Facultad de Cs. Astronómicas y Geofísicas, UNLP, Paseo del Bosque S/N, (1900) La Plata, Argentina, [email protected] Es cosa averiguada que no se sabe nada, y que todos son ignorantes; y aun esto no se sabe de cierto, que, a saberse, ya se supiera algo: sospéchase. Quevedo Abstract. Black holes are perhaps the most strange and fascinating objects in the universe. Our understanding of space and time is pushed to its limits by the extreme conditions found in these objects. They can be used as natural laboratories to test the behavior of matter in very strong gravitational fields. Black holes seem to play a key role in the universe, powering a wide variety of phenomena, from X-ray binaries to active galactic nuclei. In these lecture notes the basics of black hole physics and astrophysics are reviewed. 1. Introduction Strictly speaking, black holes do not exist. Moreover, holes, of any kind, do not exist. You can talk about holes of course. For instance you can say: “there is a hole in the wall”. You can give many details of the hole: it is big, it is round shaped, light comes in through it. Even, perhaps, the hole could be such that you can go through to the outside. But I am sure that you do not think that there is a thing made out of nothingness in the wall. -