Monte Carlo Model of Comet Dust
|
|
- Eustacia Hampton
- 5 years ago
- Views:
Transcription
1 Monte Carlo Model of Comet Dust Computational Physics Monte Carlo Model of Comet Dust Project 1
2 About Comets... Coma (Head) Dust Tail Ion Tail Nucleus 10^4-10^5 km 10^5-10^6 km 10^5-10^6 km 1 km All the comet activity starts with the nucleus and sublimation of ices. We'd like to understand that better, so we need to look at the process up close. The materials in the comet nucleus are some of the least altered materials left from formation of the solar system.
3 Project Overview Submillimeter-wave Observations of Comet Churyumov-Gerasimenko (67P) by the MIRO instrument on the Rosetta Spacecraft show enhanced emission above the limb of the comet nucleus. MIRO Team thinks this is due to large (several millimeters) dust particles lifted off of the nucleus as ice sublimates and streams away from the surface. Our project will be to construct a model of this process and see if we can match the observations.
4 MIRO Instrument 30 cm Observe at 0.5 mm 1.6 mm
5 MIRO Observation
6 What's going on here?? SubMM Channel Map
7 Basic Dust Observation DUST EMISSION
8 log TA (K) Analysis of Radial Profiles log r (km) Dust coming from sunlit side of the nucleus -1.6 Radial fall-off goes as r
9 Our Problem Simple model of uniform spherical expansion at constant velocity would expect that dust signal would decrease as r. So, why r? Ideas: Dust grains accelerate as they are pushed away from the nucleus by the gas. Large dust grains seen by MIRO get smaller as they go out. Eventually they are too small to be seen at millimeter wavelengths. The flow of material from the nucleus is highly nonuniform. Perhaps a different pattern of dust flow can account for the difference?
10 How can we test this? Construct a model of the outflow and compare to observations Given the radial distribution of dust around the nucleus, we may integrate the density distribution along the line of sight. Our signal is proportional to this quantity. s r b x0
11 For outflow at constant speed, number density, n, ( number of particles per cubic meter): Integrate number density to get column density total number along line of sight per area. s r R Expect: b x0 N(b) goes as 1/b
12 Problems In our real comet, the function n(r) will be complicated: Speed is not constant Particles destroyed n(r) not symmetric but could depend on lots of horrible stuff. When confronted with lots of complexity, sometimes the best bet is to simulate what is going on and observe it to model the result.
13 Simulation Particles originate at surface of spherical nucleus (radius R). We can choose to start particles from anywhere on the nucleus. Particles go in some direction with a velocity profile that might include acceleration. We integrate the velocity profile to get location of particle as a function of time. Particles may be destroyed on a particular efolding time scale.
14 Geometry X Particle Location: r Z to Sun Y to MIRO
15 How do we specify location? Need to determine r, theta, and phi of a lot of particles. r depends on velocity of the particles and time that particle has been traveling before we observe it. We need to know the time since creation before observation. We need to know r(t) profile consistent with velocity model. theta, phi must be selected according to where the particle originated.
16 r location Time of Simulation t1 Time of Flight, t Observation Time Time of creation of particle 0 Given time of simulation, t1, we will say that a particle could originate at any time between 0 and t1 with equal probability. A UNIFORM distribution. t1 must be selected so that we properly sample all particles along our line of sight. Since we need to look out to infinity, it follows that t1 will be big enough that the distance travelled by the particle will be pretty large compared to the distance we'd like to calculate column density. Given t1, we select t, the time of flight for a particular particle. Then we need to know r(t) to know its distance from the nucleus.
17 Choice of t1 MIRO 100km r = v t1 We are interested in column densities out to 100 km from nucleus. t1 must be chosen so that maximum distance a particle can travel is very large compared to 100 km in order to compute good column densities.
18 r(t) models NOTE: r(t) assumes v(t) Constant Speed Accelerating Speed We will consider three models: MODEL Particle Size v0 (m/s) tau0 (s) A Small B Medium C Large
19 Direction Models Select theta and phi according to probability that emission will be into a particular solid angle. For isotropic emission All phi's are equally likely: Uniform Distribution All values of cos(theta) are equally likely:
20 Procedure Given t1 and R (assume 2000 m): For each particle: Draw 3 random numbers: r1, r2, r3. Compute time: t = t1*r1 Compute cos(theta) = 1-2*r2 Compute phi = 2pi *r3 Use r(t) formula to find r. Location is then > Do this LOTS of times
21 Observables By LOTS I really mean a lot certainly millions, maybe a billion. It is NOT advisable to keep all locations in memory. Better to compute the observables as particles are calculated. Observables How many particles in a bin at a particular radius? How many particles in a bin of b the impact parameter? How many particles in bins in the X-Z plane this makes an image of the emission.
22 Binning Results Accumulate particle into Bin in radius. r R R+dr R+2dr R+3dr R+4dr r Accumulate total number of particles in each radius bin. This gives the radial distribution of the particles in the simulation. Note that for the radial distribution you are counting numbers in concentric shells around the nucleus.
23 Other Bins For simplicity, we will assume MIRO at infinite distance. The plane of the sky seen from MIRO Is the X-Z plane In our coordinate system. X Column Density is found by counting in annular rings around nucleus. b Bin for Ring b + db Z X An image may be computed by accumulating points in pixels. A pixel is a small box in the x-z plane. z+dz x+dx Bin for pixel z+dz, x+dx Z
24 What to do with Numbers in Bins? Total number of particles divided by time of simulation is proportional to rate of emission. Note that the number of particles that wind up in a bin divided by the total number of particles in the simulation is the fraction of all particles in the bin. Number Density (n)versus radius is proportional to fraction in a radial shell divided by volume of shell. Column Density (N) is fraction in annular ring divided by area of ring. Image Intensity (I) in image is fraction of particles in a pixel divided by area of the pixel.
25 How Many Particles? That's ultimately up to you. Justify your choice. Things to consider: In the simulation, the number in a particular bin will change from one simulation to the next. There will be noise on our radial profiles. How does amount of noise depend on total numbers? What is acceptable level of noise in the result?
26 Example Uniform Distribution 10 bins Two experiments with 1000 particles. Note change and noise in simulation. Two additional experiments with many more particles. Note decrease in noise.
27 Development Steps Isotropic Particle Direction at Constant Velocity Provides case where answer is known (see previous slides). number density proportional to 1/r^2 column density proportional to 1/b Compute constant velocity cases for models: A,B,C How do quantities depend on value of velocity? Isotropic Particle Direction using r(t) model for acceleration. How do the number density and column density change compared to constant velocity case? Do any of the column density models match the MIRO observation that column density falls as 1/b^1.6??
28 Development Steps (continued) Add particle destruction to the model: Particles may breakup or evaporate with time. The probability of a particle existing at time t, P(t), will decrease exponentially with some lifetime L: To consider this effect, accumulate particles into bins with a weight P(t). Consider constant velocity and accelerated velocity models. How do results change when this effect is added to the calculation? How does radial falloff in column density change with lifetime? Can we do a better job of matching the observed radial falloff in column density?
29 More things to try (extra credit) Observation shows that dust is coming from the day side of the nucleus. Modify particle production so that particles come from day side only. Consider what happens to images of the emission when we get production from day hemisphere or from even smaller angles. How does the program need to change to consider the true observation from a finite distance of, say 150 km, from the nucleus? Does this affect our results computed for infinite distance?
30 Still more things to try... How would we handle time variability of the emission in the model? Comet rotates with 12.4 hour period. What happens if there is an active spot which turns on when it is in the sun? What happens if the rate of emission changes during the time of the simulation?
31 What am I supposed to do? Write Python program to do the simulation. Compute observables for basic cases: Constant V models (use V0 for models A,B,C) Accelerating V models (use models A,B,C) Particle destruction models. For each model characterize r behavior of n and b behavior of N as a power law and derive exponent for comparison to MIRO observation. Consider other suggested calculations if inclined to do so...
32 Write Report Background Describe Numerical Method and Rationale for selecting this method. Demonstrate checks you have made to be sure that the program is correct. Write description of results; answer any questions posed. Include copy of scripts.
Rosetta activity variation and evolution
Cometary Activity Rosetta activity variation and evolution Understanding activity understanding ice inside the nucleus Understanding ice understanding early solar system history/conditions Understand link
More informationToday. life the university & everything. Reminders: Review Wed & Fri Eyes to the web Final Exam Tues May 3 Check in on accomodations
life the university & everything Phys 2130 Day 41: Questions? The Universe Reminders: Review Wed & Fri Eyes to the web Final Exam Tues May 3 Check in on accomodations Today Today: - how big is the universe?
More informationPHYSICS 107. Lecture 27 What s Next?
PHYSICS 107 Lecture 27 What s Next? The origin of the elements Apart from the expansion of the universe and the cosmic microwave background radiation, the Big Bang theory makes another important set of
More informationComets and KBO's. Comets. Halley's Comet. Far outside the orbit of Neptune are an overwhelming number of small icy bodies
Comets and KBO's Far outside the orbit of Neptune are an overwhelming number of small icy bodies The Kuiper belt is a ring of icy material located in the plane of the Solar System Comets were known and
More informationSolar System Debris: Comets and Asteroids
1 Solar System Debris: Comets and Asteroids Primarily found in two zones in the solar system. The Asteroid Belt (rocky, between Jupiter and Mars) The Edgeworth/Kuiper Belt (beyond Neptune) and Oort Cloud
More informationPhysics I : Oscillations and Waves Prof. S. Bharadwaj Department of Physics and Meteorology Indian Institute of Technology, Kharagpur
Physics I : Oscillations and Waves Prof. S. Bharadwaj Department of Physics and Meteorology Indian Institute of Technology, Kharagpur Lecture - 21 Diffraction-II Good morning. In the last class, we had
More informationIntroduction and Fundamental Observations
Notes for Cosmology course, fall 2005 Introduction and Fundamental Observations Prelude Cosmology is the study of the universe taken as a whole ruthless simplification necessary (e.g. homogeneity)! Cosmology
More informationQuantum Mechanics-I Prof. Dr. S. Lakshmi Bala Department of Physics Indian Institute of Technology, Madras. Lecture - 21 Square-Integrable Functions
Quantum Mechanics-I Prof. Dr. S. Lakshmi Bala Department of Physics Indian Institute of Technology, Madras Lecture - 21 Square-Integrable Functions (Refer Slide Time: 00:06) (Refer Slide Time: 00:14) We
More informationReach for the Stars Science Olympiad Division B Saturday, February 24, 2007 Case Western Reserve University
Reach for the Stars Science Olympiad Division B Saturday, February 24, 2007 Case Western Reserve University Names School/Team Total Score You have 50 minutes to complete this test. 1) What are some of
More informationGriffith Observatory Samuel Oschin Planetarium. Griffith Observatory Samuel Oschin Planetarium. Griffith Observatory Samuel Oschin Planetarium
Test 04 Chapters 15-20 Limited Copies Are available Griffith Observatory Samuel Oschin Planetarium June 4 th from 8:00 pm - 10:00 pm Covering ALL Tests Slide 1 Slide 2 Griffith Observatory Samuel Oschin
More informationSmall Bodies in our Solar System. Comets, Asteroids & Meteoroids
Small Bodies in our Solar System Comets, Asteroids & Meteoroids * A Small Body is any object in the solar system that is smaller than a planet or moon, such as a comet, an asteroid, or a meteoroid. Compiled
More informationMechanics, Heat, Oscillations and Waves Prof. V. Balakrishnan Department of Physics Indian Institute of Technology, Madras
Mechanics, Heat, Oscillations and Waves Prof. V. Balakrishnan Department of Physics Indian Institute of Technology, Madras Lecture - 21 Central Potential and Central Force Ready now to take up the idea
More information4 HOW DID THE EARTH FORM?
4 HOW DID THE EARTH FORM? New stars and space debris spinning like pizza dough are a couple of the things that explain the formation of solar systems like ours. In this three-part lecture, David Christian
More informationWEEK 7 NOTES AND EXERCISES
WEEK 7 NOTES AND EXERCISES RATES OF CHANGE (STRAIGHT LINES) Rates of change are very important in mathematics. Take for example the speed of a car. It is a measure of how far the car travels over a certain
More informationIllustrate It! You will need to set out colored pencil and markers at this station.
Kesler Science Station Lab Comets, Meteors, and Asteroids Teacher Directions Explore It! I will spend much of my time at this station making sure that the students are doing the orbits correctly. I have
More informationConduction and Radiation Prof. C. Balaji Department of Mechanical Engineering Indian Institute of Technology, Madras
Conduction and Radiation Prof. C. Balaji Department of Mechanical Engineering Indian Institute of Technology, Madras Module No. # 01 Lecture No. # 16 Reflectivity We will continue with our discussion on
More informationThe Cosmic Perspective Seventh Edition. Asteroids, Comets, and Dwarf Planets: Their Natures, Orbits, and Impacts. Chapter 12 Review Clickers
Review Clickers The Cosmic Perspective Seventh Edition Asteroids, Comets, and Dwarf Planets: Their Natures, Orbits, and Impacts Asteroids a) are rocky and small typically the size of a grain of rice or
More informationPossible Extra Credit Option
Possible Extra Credit Option Attend an advanced seminar on Astrophysics or Astronomy held by the Physics and Astronomy department. There are seminars held every 2:00 pm, Thursday, Room 190, Physics & Astronomy
More informationAstron 104 Laboratory #7 Sunspots and the Solar Cycle
Name: Section: Astron 104 Laboratory #7 Sunspots and the Solar Cycle Section 9.4 In this exercise, you will observe how the physical appearance of the Sun changes from day to day over the period of one
More informationHomework 6 Name: Due Date: June 9, 2008
Homework 6 Name: Due Date: June 9, 2008 1. Where in the universe does the general expansion occur? A) everywhere in the universe, including our local space upon Earth, the solar system, our galaxy and
More informationAddition of Opacities and Absorption
Addition of Opacities and Absorption If the only way photons could interact was via simple scattering, there would be no blackbodies. We ll go into that in much more detail in the next lecture, but the
More informationThe interpretation is that gravity bends spacetime and that light follows the curvature of space.
7/8 General Theory of Relativity GR Two Postulates of the General Theory of Relativity: 1. The laws of physics are the same in all frames of reference. 2. The principle of equivalence. Three statements
More informationAdvanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati
Advanced Hydraulics Prof. Dr. Suresh A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati Module - 2 Uniform Flow Lecture - 1 Introduction to Uniform Flow Good morning everyone,
More informationASTR/PHYS 109 Dr. David Toback Lectures 22,23,24 & 25
Big Bang, Black Holes, No Math ASTR/PHYS 109 Dr. David Toback Lectures 22,23,24 & 25 Big Bang, Black Evidence for the Big Bang Holes, No MathTopic 3: Photons and Hydrogen in the Universe 1 Was due Today
More informationThe State of the Universe [2010] There is only data and the interpretation of data (green text = assumptions)
The State of the Universe [2010] There is only data and the interpretation of data (green text = assumptions) Current thinking in cosmology says that the universe is filled with dark matter and dark energy.
More informationAstronomy 102: Stars and Galaxies Review Exam 3
October 31, 2004 Name: Astronomy 102: Stars and Galaxies Review Exam 3 Instructions: Write your answers in the space provided; indicate clearly if you continue on the back of a page. No books, notes, or
More informationAstronomy 10 Test #2 Practice Version
Given (a.k.a. `First ) Name(s): Family (a.k.a. `Last ) name: ON YOUR PARSCORE: `Bubble your name, your student I.D. number, and your multiple-choice answers. I will keep the Parscore forms. ON THIS TEST
More information21/11/ /11/2017 Space Physics AQA Physics topic 8
Space Physics AQA Physics topic 8 8.1 Solar System, Orbits and Satellites The eight planets of our Solar System Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune As well as the eight planets, the
More informationChapter 13 Notes The Deaths of Stars Astronomy Name: Date:
Chapter 13 Notes The Deaths of Stars Astronomy Name: Date: I. The End of a Star s Life When all the fuel in a star is used up, will win over pressure and the star will die nuclear fuel; gravity High-mass
More informationScientists named the space rock NT7 and clocked its speed at 7 miles per second. The scientists thought the asteroid was heading straight for Earth!
Asteroid Attack! A few years ago, astronomers discovered a mile-wide rock tumbling through space. At first, the scientists feared that the newly discovered space rock would plow into Earth on February
More informationEQ: How do I convert between standard form and scientific notation?
EQ: How do I convert between standard form and scientific notation? HW: Practice Sheet Bellwork: Simplify each expression 1. (5x 3 ) 4 2. 5(x 3 ) 4 3. 5(x 3 ) 4 20x 8 Simplify and leave in standard form
More informationASTRO 114 Lecture Okay. We re gonna continue our discussion today on galaxies and quasars, and
ASTRO 114 Lecture 52 1 Okay. We re gonna continue our discussion today on galaxies and quasars, and all the strange objects that are out there in the universe. I wanted to mention a little bit more about
More informationEngineering Mechanics Prof. U. S. Dixit Department of Mechanical Engineering Indian Institute of Technology, Guwahati Kinematics
Engineering Mechanics Prof. U. S. Dixit Department of Mechanical Engineering Indian Institute of Technology, Guwahati Kinematics Module 10 - Lecture 24 Kinematics of a particle moving on a curve Today,
More informationMITOCW big_picture_derivatives_512kb-mp4
MITOCW big_picture_derivatives_512kb-mp4 PROFESSOR: OK, hi. This is the second in my videos about the main ideas, the big picture of calculus. And this is an important one, because I want to introduce
More informationCS 361: Probability & Statistics
October 17, 2017 CS 361: Probability & Statistics Inference Maximum likelihood: drawbacks A couple of things might trip up max likelihood estimation: 1) Finding the maximum of some functions can be quite
More informationInstability and different burning regimes
1 X-ray bursts Last time we talked about one of the major differences between NS and BH: NS have strong magnetic fields. That means that hot spots can be produced near the magnetic poles, leading to pulsations
More informationAt this point of its orbit, any solar satellite such as a comet or a planet is farthest away from the sun. What is the aphelion?
At this point of its orbit, any solar satellite such as a comet or a planet is farthest away from the sun. What is the aphelion? These small, rocky worlds orbit the sun generally between the orbits of
More informationEinstein s Gravity. Understanding space-time and the gravitational effects of mass
Einstein s Gravity Understanding space-time and the gravitational effects of mass Albert Einstein (1879-1955) One of the iconic figures of the 20 th century, Einstein revolutionized our understanding of
More informationAST5220 lecture 2 An introduction to the CMB power spectrum. Hans Kristian Eriksen
AST5220 lecture 2 An introduction to the CMB power spectrum Hans Kristian Eriksen Cosmology in ~five slides The basic ideas of Big Bang: 1) The Big Bang model The universe expands today Therefore it must
More informationMain Event: Comets by Paul Jenkins
Main Event: Comets by Paul Jenkins Most people realise that comets come from the Oort Cloud, a huge ball of objects surrounding the solar system but which has a bias of objects towards the plane of the
More informationMITOCW watch?v=m00pjhtq6ju
MITOCW watch?v=m00pjhtq6ju The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To
More informationPredictions for Dusty Mass Loss from Asteroids during Close Encounters with Solar Probe Plus
Predictions for Dusty Mass Loss from Asteroids during Close Encounters with Solar Probe Plus Steven R. Cranmer University of Colorado Boulder, LASP Paper: http://arxiv.org/abs/1606.01785 Introduction
More informationInstructor (Brad Osgood)
TheFourierTransformAndItsApplications-Lecture26 Instructor (Brad Osgood): Relax, but no, no, no, the TV is on. It's time to hit the road. Time to rock and roll. We're going to now turn to our last topic
More informationMITOCW ocw lec8
MITOCW ocw-5.112-lec8 The following content is provided by MIT OpenCourseWare under a Creative Commons license. Additional information about our license and MIT OpenCourseWare in general is available at
More informationLecture 3: Specific Intensity, Flux and Optical Depth
Lecture 3: Specific Intensity, Flux and Optical Depth We begin a more detailed look at stellar atmospheres by defining the fundamental variable, which is called the Specific Intensity. It may be specified
More informationWho was here? How can you tell? This is called indirect evidence!
1 Who was here? How can you tell? This is called indirect evidence! 2 How does a planetary system form? The one we can study in the most detail is our solar system. If we want to know whether the solar
More informationThe Interstellar Medium (ch. 18)
The Interstellar Medium (ch. 18) The interstellar medium (ISM) is all the gas (and about 1% dust) that fills our Galaxy and others. It is the raw material from which stars form, and into which stars eject
More informationPlasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi
Plasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi Module No. # 01 Lecture No. # 22 Adiabatic Invariance of Magnetic Moment and Mirror Confinement Today, we
More informationMITOCW MIT6_041F11_lec17_300k.mp4
MITOCW MIT6_041F11_lec17_300k.mp4 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality, educational resources for
More informationIn other words, we are interested in what is happening to the y values as we get really large x values and as we get really small x values.
Polynomial functions: End behavior Solutions NAME: In this lab, we are looking at the end behavior of polynomial graphs, i.e. what is happening to the y values at the (left and right) ends of the graph.
More informationOrigin of the Solar System
Origin of the Solar System and Solar System Debris 1 Debris comets meteoroids asteroids gas dust 2 Asteroids irregular, rocky hunks small in mass and size Ceres - largest, 1000 km in diameter (1/3 Moon)
More information23.1 The Solar System. Orbits of the Planets. Planetary Data The Solar System. Scale of the Planets The Solar System
23.1 The Solar System Orbits of the Planets The Planets: An Overview The terrestrial planets are planets that are small and rocky Mercury, Venus, Earth, and Mars. The Jovian planets are the huge gas giants
More informationMITOCW 6. Standing Waves Part I
MITOCW 6. Standing Waves Part I The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free.
More informationPROFESSOR: WELCOME BACK TO THE LAST LECTURE OF THE SEMESTER. PLANNING TO DO TODAY WAS FINISH THE BOOK. FINISH SECTION 6.5
1 MATH 16A LECTURE. DECEMBER 9, 2008. PROFESSOR: WELCOME BACK TO THE LAST LECTURE OF THE SEMESTER. I HOPE YOU ALL WILL MISS IT AS MUCH AS I DO. SO WHAT I WAS PLANNING TO DO TODAY WAS FINISH THE BOOK. FINISH
More informationLec 9: Stellar Evolution and DeathBirth and. Why do stars leave main sequence? What conditions are required for elements. Text
1 Astr 102 Lec 9: Stellar Evolution and DeathBirth and Evolution Why do stars leave main sequence? What conditions are required for elements Text besides Hydrogen to fuse, and why? How do stars die: white
More informationLUNAR OBSERVING. What will you learn in this lab?
LUNAR OBSERVING What will you learn in this lab? The Moon is the second most noticeable object in the sky. This lab will first introduce you to observing the Moon with a telescope. You will be looking
More informationAnnouncements. Problem Set 6 due next Monday, February 25, at 12:50PM. Midterm graded, will be returned at end of lecture.
Turing Machines Hello Hello Condensed Slide Slide Readers! Readers! This This lecture lecture is is almost almost entirely entirely animations that that show show how how each each Turing Turing machine
More informationChaos and stability in the vicinity of a Jovian planet
BEREA COLLEGE Chaos and stability in the vicinity of a Jovian planet by Shiblee Ratan Barua Berea College /22/28 It has been widely known that the influence of large bodies (the Sun, the terrestrial and
More informationJAMES: HEY THERE STAR GAZERS. I'M JAMES ALBURY, DIRECTOR OF THE KIKA SILVA PLA PLANETARIUM IN GAINESVILLE, FLORIDA.
STAR GAZERS SG 1745 5-MINUTE "THE LEONID METEOR SHOWER" HEY THERE STAR GAZERS. I'M JAMES ALBURY, DIRECTOR OF THE KIKA SILVA PLA PLANETARIUM IN GAINESVILLE, FLORIDA. AND I'M DEAN REGAS, ASTRONOMER FOR THE
More informationMATH 308 COURSE SUMMARY
MATH 308 COURSE SUMMARY Approximately a third of the exam cover the material from the first two midterms, that is, chapter 6 and the first six sections of chapter 7. The rest of the exam will cover the
More informationQuantum Mechanics - I Prof. Dr. S. Lakshmi Bala Department of Physics Indian Institute of Technology, Madras. Lecture - 16 The Quantum Beam Splitter
Quantum Mechanics - I Prof. Dr. S. Lakshmi Bala Department of Physics Indian Institute of Technology, Madras Lecture - 16 The Quantum Beam Splitter (Refer Slide Time: 00:07) In an earlier lecture, I had
More informationChapter 3 ALGEBRA. Overview. Algebra. 3.1 Linear Equations and Applications 3.2 More Linear Equations 3.3 Equations with Exponents. Section 3.
4 Chapter 3 ALGEBRA Overview Algebra 3.1 Linear Equations and Applications 3.2 More Linear Equations 3.3 Equations with Exponents 5 LinearEquations 3+ what = 7? If you have come through arithmetic, the
More informationPrentice Hall EARTH SCIENCE
Prentice Hall EARTH SCIENCE Tarbuck Lutgens 23.1 The Solar System The Planets: An Overview The terrestrial planets are planets that are small and rocky Mercury, Venus, Earth, and Mars. The Jovian planets
More informationComets. Ancient Ideas about comets. Draft Dec 11, Edmund Halley ( ) Great Comet of 1680
Comets Ancient Ideas about comets kometes = `the hairy one (hairy star) 550 BC Pythagoreans thought they were wandering planets. Draft Dec 11, 2006 Aristotle (350 BC) thought that, like meteors, they were
More informationAST5220 lecture 2 An introduction to the CMB power spectrum. Hans Kristian Eriksen
AST5220 lecture 2 An introduction to the CMB power spectrum Hans Kristian Eriksen Cosmology in ~five slides The basic ideas of Big Bang: 1) The Big Bang model The universe expands today Therefore it must
More informationThe Magnetic Sun. CESAR s Booklet
The Magnetic Sun CESAR s Booklet 1 Introduction to planetary magnetospheres and the interplanetary medium Most of the planets in our Solar system are enclosed by huge magnetic structures, named magnetospheres
More informationMITOCW watch?v=ko0vmalkgj8
MITOCW watch?v=ko0vmalkgj8 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To
More informationReview: HR Diagram. Label A, B, C respectively
Stellar Evolution Review: HR Diagram Label A, B, C respectively A C B a) A: White dwarfs, B: Giants, C: Main sequence b) A: Main sequence, B: Giants, C: White dwarfs c) A: Main sequence, B: White Dwarfs,
More informationUltimate Events. Galaxy clustering in ever deeper surveys. Models of universe and its fates
ASTR 1040 Accel Astro: Stars & Galaxies Ultimate Events Prof. Juri Toomre TA: Nicholas Nelson Lecture 30 Thur 28 Apr 2011 zeus.colorado.edu/astr1040-toomre toomre Allen Telescope Array Review current big
More informationMITOCW ocw-18_02-f07-lec17_220k
MITOCW ocw-18_02-f07-lec17_220k The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free.
More informationAST 101 Introduction to Astronomy: Stars & Galaxies
The H-R Diagram review So far: AST 101 Introduction to Astronomy: Stars & Galaxies - Stars on Main Sequence (MS) - Pre MS (Star Birth) Next: - Post MS: Giants, Super Giants, White dwarfs Evolution of Low
More informationThe Hubble Deep Field
The Hubble Deep Field Introduction This is a picture of the Hubble Deep Field (HDF). The deepest image of the sky ever taken, it was made in 1996 using the Hubble Space Telescope by effectively leaving
More informationPrentice Hall EARTH SCIENCE
Prentice Hall EARTH SCIENCE Tarbuck Lutgens Chapter 23 Touring Our Solar System 23.1 The Solar System The Planets: An Overview The terrestrial planets are planets that are small and rocky Mercury, Venus,
More informationMarine Hydrodynamics Prof.TrilochanSahoo Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur
Marine Hydrodynamics Prof.TrilochanSahoo Department of Ocean Engineering and Naval Architecture Indian Institute of Technology, Kharagpur Lecture - 10 Source, Sink and Doublet Today is the tenth lecture
More information8 Estimating the Earth s Density
Name: Date: 8 Estimating the Earth s Density 8.1 Introduction We know, based upon a variety of measurement methods, that the density of the Earth is 5.52 grams per cubic centimeter. [This value is equal
More informationNuclear Physics Fundamentals and Application Prof. H. C. Verma Department of Physics Indian Institute of Technology, Kanpur. Lecture 2 Nuclear Size
Nuclear Physics Fundamentals and Application Prof. H. C. Verma Department of Physics Indian Institute of Technology, Kanpur Lecture 2 Nuclear Size So, I have given you the overview of nuclear physics.
More informationWHAT WE KNOW. Scientists observe that every object in the universe is moving away from each other. Objects furthest away are moving the fastest. So..
ASTRONOMY THE BIG BANG THEORY WHAT WE KNOW Scientists observe that every object in the universe is moving away from each other. Objects furthest away are moving the fastest. So.. WHAT DOES THIS MEAN? If
More informationPlantwide Control of Chemical Processes Prof. Nitin Kaistha Department of Chemical Engineering Indian Institute of Technology, Kanpur
Plantwide Control of Chemical Processes Prof. Nitin Kaistha Department of Chemical Engineering Indian Institute of Technology, Kanpur Lecture - 41 Cumene Process Plantwide Control (Refer Slide Time: 00:18)
More informationClouds and Rain Unit (3 pts)
Name: Section: Clouds and Rain Unit (Topic 8A-2) page 1 Clouds and Rain Unit (3 pts) As air rises, it cools due to the reduction in atmospheric pressure Air mainly consists of oxygen molecules and nitrogen
More informationBig Bang, Black Holes, No Math
ASTR/PHYS 109 Dr. David Toback Lectures 21 and 22 1 Was Due Today L22 Reading: (BBBHNM Unit 3) Pre-Lecture Reading Questions (PLRQ) Unit 3: Let us know if you think you were misgraded Unit 3 Revision (if
More informationSTEP Support Programme. Mechanics STEP Questions
STEP Support Programme Mechanics STEP Questions This is a selection of mainly STEP I questions with a couple of STEP II questions at the end. STEP I and STEP II papers follow the same specification, the
More informationMiARD. Deliverable Report
Ref. Ares(2017)5878072-30/11/2017 MiARD H2020 grant number 686709 Deliverable Report Work Package and Leader WP2, Nicolas Thomas Deliverable Number Title D2.5 3D gas and dust distributions at one or more
More informationAY2 Introduction to Astronomy Winter quarter, 2013
AY2 Introduction to Astronomy Winter quarter, 2013 Instructor: Maria Fernanda (Feña) Duran (mfduran@ucolick.org) Teaching assistants: Jieun Choi (jchoi37@ucsc.edu) Katie Hamren (khamren@ucolick.org) Course
More information=.55 = = 5.05
MAT1193 4c Definition of derivative With a better understanding of limits we return to idea of the instantaneous velocity or instantaneous rate of change. Remember that in the example of calculating the
More informationClicker Question: Clicker Question: Clicker Question:
Test results Last day to drop without a grade is Feb 29 Grades posted in cabinet and online F D C B A In which direction would the Earth move if the Sun s gravitational force were suddenly removed from
More informationMITOCW MIT8_01F16_W01PS05_360p
MITOCW MIT8_01F16_W01PS05_360p You're standing at a traffic intersection. And you start to accelerate when the light turns green. Suppose that your acceleration as a function of time is a constant for
More informationPrimary KS1 1 VotesForSchools2018
Primary KS1 1 Do aliens exist? This photo of Earth was taken by an astronaut on the moon! Would you like to stand on the moon? What is an alien? You probably drew some kind of big eyed, blue-skinned,
More informationLine Broadening. φ(ν) = Γ/4π 2 (ν ν 0 ) 2 + (Γ/4π) 2, (3) where now Γ = γ +2ν col includes contributions from both natural broadening and collisions.
Line Broadening Spectral lines are not arbitrarily sharp. There are a variety of mechanisms that give them finite width, and some of those mechanisms contain significant information. We ll consider a few
More informationThe Electric Field of a Finite Line of Charge The Electric Field of a Finite Line of
The Electric Field of a Finite Line of Charge The Electric Field of a Finite Line of Charge Example 26.3 in the text uses integration to find the electric field strength at a radial distance r in the plane
More information9/10/2018. An Infinite Line of Charge. The electric field of a thin, uniformly charged rod may be written:
The Electric Field of a Finite Line of Charge The Electric Field of a Finite Line of Charge Example 26.3 in the text uses integration to find the electric field strength at a radial distance r in the plane
More informationSolar System Junk however, a large number of bodies were left over as Junk or the debris of planet building
Solar System Junk So far, we ve taken a brief look at the 8 planets of the solar system, their array of moons or natural satellites, and how we think such a system formed. Most of the material in the solar
More informationWeek 8: Stellar winds So far, we have been discussing stars as though they have constant masses throughout their lifetimes. On the other hand, toward
Week 8: Stellar winds So far, we have been discussing stars as though they have constant masses throughout their lifetimes. On the other hand, toward the end of the discussion of what happens for post-main
More informationBig Bang, Black Holes, No Math
ASTR/PHYS 109 Dr. David Toback Lectures 25 & 26 1 Was due Today L26 Reading: (Unit 4) Pre-Lecture Reading Questions (PLRQ) Unit 4: Grades posted soon Unit 4 Revision (if desired): Due Wednesday before
More informationa c = v2 F = ma F = Gm 1m 2 r d out RMA = F out r 2 " = Fd sin# IMA = d in eff = RMA F in IMA = W out
Name: Physics Chapter 7 Study Guide ----------------------------------------------------------------------------------------------------- Useful Information: a c = v2 F = ma F = Gm 1m 2 r r 2 " = Fd sin#
More informationScale in the Universe and Star Life Cycles
Scale in the Universe and Star Life Cycles Author: Richard Beare - Faulkes Telescope Project Scale in the Universe and Star Life Cycles Measuring objects in the Solar System Jupiter 2.45 arcmin 4.59 AU
More informationNews. Exam 4/Final is Saturday December 9 at 2:00 p.m. here in Clark 107
News Exam 4/Final is Saturday December 9 at 2:00 p.m. here in Clark 107 A review session will be held on Friday December 8 at 5:15 p.m. (most likely here in this room) A sheet of review questions is available
More informationNote: Please use the actual date you accessed this material in your citation.
MIT OpenCourseWare http://ocw.mit.edu 18.02 Multivariable Calculus, Fall 2007 Please use the following citation format: Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of
More informationConvection causes granules. Photosphere isn t actually smooth! Granules Up-Close: like boiling water. Corona or of the Sun. Chromosphere: sphere of
Overview Properties of the Sun Sun s outer layers Photosphere Chromosphere Corona Solar Activity Sunspots & the sunspot cycle Flares, prominences, CMEs, aurora Sun s Interior The Sun as an energy source
More informationSun s Properties. Overview: The Sun. Composition of the Sun. Sun s Properties. The outer layers. Photosphere: Surface. Nearest.
Overview: The Sun Properties of the Sun Sun s outer layers Photosphere Chromosphere Corona Solar Activity Sunspots & the sunspot cycle Flares, prominences, CMEs, aurora Sun s Interior The Sun as an energy
More information