Lecture 22 Giant Planets Rings
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Breaking Down the “Cosine Fourth Power Law”
Breaking Down The “Cosine Fourth Power Law” By Ronian Siew, inopticalsolutions.com Why are the corners of the field of view in the image captured by a camera lens usually darker than the center? For one thing, camera lenses by design often introduce “vignetting” into the image, which is the deliberate clipping of rays at the corners of the field of view in order to cut away excessive lens aberrations. But, it is also known that corner areas in an image can get dark even without vignetting, due in part to the so-called “cosine fourth power law.” 1 According to this “law,” when a lens projects the image of a uniform source onto a screen, in the absence of vignetting, the illumination flux density (i.e., the optical power per unit area) across the screen from the center to the edge varies according to the fourth power of the cosine of the angle between the optic axis and the oblique ray striking the screen. Actually, optical designers know this “law” does not apply generally to all lens conditions.2 – 10 Fundamental principles of optical radiative flux transfer in lens systems allow one to tune the illumination distribution across the image by varying lens design characteristics. In this article, we take a tour into the fascinating physics governing the illumination of images in lens systems. Relative Illumination In Lens Systems In lens design, one characterizes the illumination distribution across the screen where the image resides in terms of a quantity known as the lens’ relative illumination — the ratio of the irradiance (i.e., the power per unit area) at any off-axis position of the image to the irradiance at the center of the image. -
7 Planetary Rings Matthew S
7 Planetary Rings Matthew S. Tiscareno Center for Radiophysics and Space Research, Cornell University, Ithaca, NY, USA 1Introduction..................................................... 311 1.1 Orbital Elements ..................................................... 312 1.2 Roche Limits, Roche Lobes, and Roche Critical Densities .................... 313 1.3 Optical Depth ....................................................... 316 2 Rings by Planetary System .......................................... 317 2.1 The Rings of Jupiter ................................................... 317 2.2 The Rings of Saturn ................................................... 319 2.3 The Rings of Uranus .................................................. 320 2.4 The Rings of Neptune ................................................. 323 2.5 Unconfirmed Ring Systems ............................................. 324 2.5.1 Mars ............................................................... 324 2.5.2 Pluto ............................................................... 325 2.5.3 Rhea and Other Moons ................................................ 325 2.5.4 Exoplanets ........................................................... 327 3RingsbyType.................................................... 328 3.1 Dense Broad Disks ................................................... 328 3.1.1 Spiral Waves ......................................................... 329 3.1.2 Gap Edges and Moonlet Wakes .......................................... 333 3.1.3 Radial Structure ..................................................... -
Lesson 3: Moons, Rings Relationships
GETTING TO KNOW SATURN LESSON Moons, Rings, and Relationships 3 3–4 hrs Students design their own experiments to explore the fundamental force of gravity, and then extend their thinking to how gravity acts to keep objects like moons and ring particles in orbit. Students use the contexts of the Solar System and the Saturn system MEETS NATIONAL to explore the nature of orbits. The lesson SCIENCE EDUCATION enables students to correct common mis- STANDARDS: conceptions about gravity and orbits and to Science as Inquiry • Abilities learn how orbital speed decreases as the dis- Prometheus and Pandora, two of Saturn’s moons, “shepherd” necessary to Saturn’s F ring. scientific inquiry tance from the object being orbited increases. Physical Science • Motions and PREREQUISITE SKILLS BACKGROUND INFORMATION forces Working in groups Background for Lesson Discussion, page 66 Earth and Space Science Reading a chart of data Questions, page 71 • Earth in the Plotting points on a graph Answers in Appendix 1, page 225 Solar System 1–21: Saturn 22–34: Rings 35–50: Moons EQUIPMENT, MATERIALS, AND TOOLS For the teacher Materials to reproduce Photocopier (for transparencies & copies) Figures 1–10 are provided at the end of Overhead projector this lesson. Chalkboard, whiteboard, or large easel FIGURE TRANSPARENCY COPIES with paper; chalk or markers 11 21 For each group of 3 to 4 students 31 Large plastic or rubber ball 4 1 per student Paper, markers, pencils 5 1 1 per student 6 1 for teacher 7 1 (optional) 1 for teacher 8 1 per student 9 1 (optional) 1 per student 10 1 (optional) 1 for teacher 65 Saturn Educator Guide • Cassini Program website — http://www.jpl.nasa.gov/cassini/educatorguide • EG-1999-12-008-JPL Background for Lesson Discussion LESSON 3 Science as inquiry The nature of Saturn’s rings and how (See Procedures & Activities, Part I, Steps 1-6) they move (See Procedures & Activities, Part IIa, Step 3) Part I of the lesson offers students a good oppor- tunity to experience science as inquiry. -
Instructor's Guide for Virtual Astronomy Laboratories
Instructor’s Guide for Virtual Astronomy Laboratories Mike Guidry, University of Tennessee Kevin Lee, University of Nebraska The Brooks/Cole product Virtual Astronomy Laboratories consists of 20 virtual online astronomy laboratories (VLabs) representing a sampling of interactive exercises that illustrate some of the most important topics in introductory astronomy. The exercises are meant to be representative, not exhaustive, since introductory astronomy is too broad to be covered in only 20 laboratories. Material is approximately evenly divided between that commonly found in the Solar System part of an introductory course and that commonly associated with the stars, galaxies, and cosmology part of such a course. Intended Use This material was designed to serve two general functions: on the one hand it represents a set of virtual laboratories that can be used as part or all of an introductory astronomy laboratory sequence, either within a normal laboratory setting or in a distance learning environment. On the other hand, it is meant to serve as a tutorial supplement for standard textbooks. While this is an efficient use of the material, it presents some problems in organization since (as a rule of thumb) supplemental tutorial material is more concept oriented while astronomy laboratory material typically requires more hands-on problem-solving involving at least some basic mathematical manipulations. As a result, one will find material of varying levels of difficulty in these laboratories. Some sections are highly conceptual in nature, emphasizing more qualitative answers to questions that students may deduce without working through involved tasks. Other sections, even within the same virtual laboratory, may require students to carry out guided but non-trivial analysis in order to answer questions. -
Lecture 12 the Rings and Moons of the Outer Planets October 15, 2018
Lecture 12 The Rings and Moons of the Outer Planets October 15, 2018 1 2 Rings of Outer Planets • Rings are not solid but are fragments of material – Saturn: Ice and ice-coated rock (bright) – Others: Dusty ice, rocky material (dark) • Very thin – Saturn rings ~0.05 km thick! • Rings can have many gaps due to small satellites – Saturn and Uranus 3 Rings of Jupiter •Very thin and made of small, dark particles. 4 Rings of Saturn Flash movie 5 Saturn’s Rings Ring structure in natural color, photographed by Cassini probe July 23, 2004. Click on image for Astronomy Picture of the Day site, or here for JPL information 6 Saturn’s Rings (false color) Photo taken by Voyager 2 on August 17, 1981. Click on image for more information 7 Saturn’s Ring System (Cassini) Mars Mimas Janus Venus Prometheus A B C D F G E Pandora Enceladus Epimetheus Earth Tethys Moon Wikipedia image with annotations On July 19, 2013, in an event celebrated the world over, NASA's Cassini spacecraft slipped into Saturn's shadow and turned to image the planet, seven of its moons, its inner rings -- and, in the background, our home planet, Earth. 8 Newly Discovered Saturnian Ring • Nearly invisible ring in the plane of the moon Pheobe’s orbit, tilted 27° from Saturn’s equatorial plane • Discovered by the infrared Spitzer Space Telescope and announced 6 October 2009 • Extends from 128 to 207 Saturnian radii and is about 40 radii thick • Contributes to the two-tone coloring of the moon Iapetus • Click here for more info about the artist’s rendering 9 Rings of Uranus • Uranus -- rings discovered through stellar occultation – Rings block light from star as Uranus moves by. -
The Rings and Inner Moons of Uranus and Neptune: Recent Advances and Open Questions
Workshop on the Study of the Ice Giant Planets (2014) 2031.pdf THE RINGS AND INNER MOONS OF URANUS AND NEPTUNE: RECENT ADVANCES AND OPEN QUESTIONS. Mark R. Showalter1, 1SETI Institute (189 Bernardo Avenue, Mountain View, CA 94043, mshowal- [email protected]! ). The legacy of the Voyager mission still dominates patterns or “modes” seem to require ongoing perturba- our knowledge of the Uranus and Neptune ring-moon tions. It has long been hypothesized that numerous systems. That legacy includes the first clear images of small, unseen ring-moons are responsible, just as the nine narrow, dense Uranian rings and of the ring- Ophelia and Cordelia “shepherd” ring ε. However, arcs of Neptune. Voyager’s cameras also first revealed none of the missing moons were seen by Voyager, sug- eleven small, inner moons at Uranus and six at Nep- gesting that they must be quite small. Furthermore, the tune. The interplay between these rings and moons absence of moons in most of the gaps of Saturn’s rings, continues to raise fundamental dynamical questions; after a decade-long search by Cassini’s cameras, sug- each moon and each ring contributes a piece of the gests that confinement mechanisms other than shep- story of how these systems formed and evolved. herding might be viable. However, the details of these Nevertheless, Earth-based observations have pro- processes are unknown. vided and continue to provide invaluable new insights The outermost µ ring of Uranus shares its orbit into the behavior of these systems. Our most detailed with the tiny moon Mab. Keck and Hubble images knowledge of the rings’ geometry has come from spanning the visual and near-infrared reveal that this Earth-based stellar occultations; one fortuitous stellar ring is distinctly blue, unlike any other ring in the solar alignment revealed the moon Larissa well before Voy- system except one—Saturn’s E ring. -
Planetary Rings
CLBE001-ESS2E November 10, 2006 21:56 100-C 25-C 50-C 75-C C+M 50-C+M C+Y 50-C+Y M+Y 50-M+Y 100-M 25-M 50-M 75-M 100-Y 25-Y 50-Y 75-Y 100-K 25-K 25-19-19 50-K 50-40-40 75-K 75-64-64 Planetary Rings Carolyn C. Porco Space Science Institute Boulder, Colorado Douglas P. Hamilton University of Maryland College Park, Maryland CHAPTER 27 1. Introduction 5. Ring Origins 2. Sources of Information 6. Prospects for the Future 3. Overview of Ring Structure Bibliography 4. Ring Processes 1. Introduction houses, from coalescing under their own gravity into larger bodies. Rings are arranged around planets in strikingly dif- Planetary rings are those strikingly flat and circular ap- ferent ways despite the similar underlying physical pro- pendages embracing all the giant planets in the outer Solar cesses that govern them. Gravitational tugs from satellites System: Jupiter, Saturn, Uranus, and Neptune. Like their account for some of the structure of densely-packed mas- cousins, the spiral galaxies, they are formed of many bod- sive rings [see Solar System Dynamics: Regular and ies, independently orbiting in a central gravitational field. Chaotic Motion], while nongravitational effects, includ- Rings also share many characteristics with, and offer in- ing solar radiation pressure and electromagnetic forces, valuable insights into, flattened systems of gas and collid- dominate the dynamics of the fainter and more diffuse dusty ing debris that ultimately form solar systems. Ring systems rings. Spacecraft flybys of all of the giant planets and, more are accessible laboratories capable of providing clues about recently, orbiters at Jupiter and Saturn, have revolutionized processes important in these circumstellar disks, structures our understanding of planetary rings. -
Abstracts of the 50Th DDA Meeting (Boulder, CO)
Abstracts of the 50th DDA Meeting (Boulder, CO) American Astronomical Society June, 2019 100 — Dynamics on Asteroids break-up event around a Lagrange point. 100.01 — Simulations of a Synthetic Eurybates 100.02 — High-Fidelity Testing of Binary Asteroid Collisional Family Formation with Applications to 1999 KW4 Timothy Holt1; David Nesvorny2; Jonathan Horner1; Alex B. Davis1; Daniel Scheeres1 Rachel King1; Brad Carter1; Leigh Brookshaw1 1 Aerospace Engineering Sciences, University of Colorado Boulder 1 Centre for Astrophysics, University of Southern Queensland (Boulder, Colorado, United States) (Longmont, Colorado, United States) 2 Southwest Research Institute (Boulder, Connecticut, United The commonly accepted formation process for asym- States) metric binary asteroids is the spin up and eventual fission of rubble pile asteroids as proposed by Walsh, Of the six recognized collisional families in the Jo- Richardson and Michel (Walsh et al., Nature 2008) vian Trojan swarms, the Eurybates family is the and Scheeres (Scheeres, Icarus 2007). In this theory largest, with over 200 recognized members. Located a rubble pile asteroid is spun up by YORP until it around the Jovian L4 Lagrange point, librations of reaches a critical spin rate and experiences a mass the members make this family an interesting study shedding event forming a close, low-eccentricity in orbital dynamics. The Jovian Trojans are thought satellite. Further work by Jacobson and Scheeres to have been captured during an early period of in- used a planar, two-ellipsoid model to analyze the stability in the Solar system. The parent body of the evolutionary pathways of such a formation event family, 3548 Eurybates is one of the targets for the from the moment the bodies initially fission (Jacob- LUCY spacecraft, and our work will provide a dy- son and Scheeres, Icarus 2011). -
Tidal Forces - Let 'Er Rip! 49
Tidal Forces - Let 'er Rip! 49 As the Moon orbits Earth, its gravitational pull raises the familiar tides in the ocean water, but did you know that it also raises 'earth tides' in the crust of earth? These tides are up to 50 centimeters in height and span continent-sized areas. The Earth also raises 'body tides' on the moon with a height of 5 meters! Now imagine that the moon were so close that it could no longer hold itself together against these tidal deformations. The distance were Earth's gravity will 'tidally disrupt' a solid satellite like the moon is called the tidal radius. One of the most dramatic examples of this is the rings of Saturn, where a nearby moon was disrupted, or prevented from forming in the first place! Images courtesy NASA/Hubble and Cassini. Problem 1 - The location of the tidal radius (also called the Roche Limit) for two 1/3 bodies is given by the formula d = 2.4x R (ρM/ρm) where ρM is the density of the primary body, ρm is the density of the satellite, and R is the radius of the main body. For the Earth-Moon system, what is the Roche Limit if R = 6,378 km, ρM = 3 3 5.5 gm/cm and ρm = 2.5 gm/cm ? (Note, the Roche Limit, d, will be in kilometers if R is also in kilometers, and so long as the densities are in the same units.) Problem 2 - Saturn's moons are made of ice with a density of about 1.2 gm/cm3 .If Saturn's density is 0.7 gm/cm3 and its radius is R = 58,000 km, how does its Roche Limit compare to the span of the ring system which extends from 66,000 km to 480,000 km from the planet's center? Problem 3 - In searching for planets orbiting other stars, many bodies similar to Jupiter in mass have been found orbiting sun-like stars at distances of only 3 million km. -
Moving Pictures: the History of Early Cinema by Brian Manley
Discovery Guides Moving Pictures: The History of Early Cinema By Brian Manley Introduction The history of film cannot be credited to one individual as an oversimplification of any his- tory often tries to do. Each inventor added to the progress of other inventors, culminating in progress for the entire art and industry. Often masked in mystery and fable, the beginnings of film and the silent era of motion pictures are usually marked by a stigma of crudeness and naiveté, both on the audience's and filmmakers' parts. However, with the landmark depiction of a train hurtling toward and past the camera, the Lumière Brothers’ 1895 picture “La Sortie de l’Usine Lumière à Lyon” (“Workers Leaving the Lumière Factory”), was only one of a series of simultaneous artistic and technological breakthroughs that began to culminate at the end of the nineteenth century. These triumphs that began with the creation of a machine that captured moving images led to one of the most celebrated and distinctive art forms at the start of the 20th century. Audiences had already reveled in Magic Lantern, 1818, Musée des Arts et Métiers motion pictures through clever uses of slides http://en.wikipedia.org/wiki/File:Magic-lantern.jpg and mechanisms creating "moving photographs" with such 16th-century inventions as magic lanterns. These basic concepts, combined with trial and error and the desire of audiences across the world to see entertainment projected onto a large screen in front of them, birthed the movies. From the “actualities” of penny arcades, the idea of telling a story in order to draw larger crowds through the use of differing scenes began to formulate in the minds of early pioneers such as Georges Melies and Edwin S. -
American Scientist the Magazine of Sigma Xi, the Scientific Research Society
A reprint from American Scientist the magazine of Sigma Xi, The Scientific Research Society This reprint is provided for personal and noncommercial use. For any other use, please send a request to Permissions, American Scientist, P.O. Box 13975, Research Triangle Park, NC, 27709, U.S.A., or by electronic mail to [email protected]. ©Sigma Xi, The Scientific Research Society and other rightsholders Engineering Next Slide, Please Henry Petroski n the course of preparing lectures years—against strong opposition from Ibased on the material in my books As the Kodak some in the artistic community—that and columns, I developed during the simple projection devices were used by closing decades of the 20th century a the masters to trace in near exactness good-sized library of 35-millimeter Carousel begins its intricate images, including portraits, that slides. These show structures large and the free hand could not do with fidelity. small, ranging from bridges and build- slide into history, ings to pencils and paperclips. As re- The Magic Lantern cently as about five years ago, when I it joins a series of The most immediate antecedent of the indicated to a host that I would need modern slide projector was the magic the use of a projector during a talk, just previous devices used lantern, a device that might be thought about everyone understood that to mean of as a camera obscura in reverse. Instead a Kodak 35-mm slide projector (or its to add images to talks of squeezing a life-size image through a equivalent), and just about every venue pinhole to produce an inverted minia- had one readily available. -
Shepherd Moon Face-Off! 21 December 2012, by Jason Major
Shepherd Moon face-off! 21 December 2012, by Jason Major Here's Pandora, as seen by Cassini on September 5, 2005: False-color image of Pandora. Credit: NASA/JPL/SSI Raw Cassini image acquired on Dec. 18, 2012. Credit: NASA/JPL/SSI …and here's Prometheus, seen during a close pass in 2010 and color-calibrated by Gordan Ugarkovic: Two of Saturn's shepherd moons face off across the icy strand of the F ring in this image, acquired by the Cassini spacecraft on December 18, 2012. In the left corner is Pandora, external shepherd of the ropy ring, and in the right is Prometheus, whose gravity is responsible for the subtle tug on the wispy ring material. (Please don't blame the moon for any recent unsatisfying sci-fi films of the same name. There's no relation, we promise.) Similar in size (Pandora is 110 x 88 x 62 km, Prometheus 148 x 100 x 68 km) both moons are porous, icy, potato-shaped bodies covered in craters—although Prometheus' surface is somewhat smoother in appearance than Pandora's, perhaps due to the gradual buildup of infalling material from the F ring. Check out some much closer images of these two moons below, acquired during earlier flybys: 1 / 2 Prometheus casting a shadow through F ring haze. Credit: NASA/JPL/SSI/Gordan Ugarvovic The external edge of the A ring with the thin Keeler gap and the wider Encke gap can be seen at the right of the top image. Both of these gaps also harbor their own shepherd moons—Daphnis and Pan, respectively.