Astronomy lessons Astronomy 154
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This 11 page Class Notes was uploaded by Lauren Price on Monday September 19, 2016. The Class Notes belongs to Astronomy 154 at University of Tennessee - Knoxville taught by Sean Lindsay in Fall 2016. Since its upload, it has received 3 views. For similar materials see Stars/Galax/Cosmology Lecture in Physics and Astronomy at University of Tennessee - Knoxville.
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Date Created: 09/19/16
Astronomy 9/7/16 Kepler’s Law of Planetary Motion Empirical description of planetary orbits in our Solar System 1. Planetary orbits around the sun are elliptical, not circular, in shape, with the sun at one focus 2. Equal areas, equal times. Alternatively, planets travel faster in their orbits near Perihelion and slowest at Aphelion 3. The square of the period is proportional to the cube of the semimajor axis. P2 = a3, where P is in years, and A is in Au Kepler’s First Law Long axis is the major axis Short axis is the minor axis Half the major axis is the semimajor axis, a a is used to define planetary orbits Eccentricity, e, describes how “out of circular” the ellipse is e is used to define planetary objects Do not confused ecliptic with elliptical Perihelion: closest point to the sun Aphelion: farthest point from the sun Kepler’s Second Law Indicates that a planet is moving fastest at perihelion and moving slowest at aphelion Kepler’s Third Law Will be on quiz and tests States that the square of a planet’s orbital period, P, measured in years is equal to the cube of it’s semimajor axis, a, measured in Astronomical Units Au. P2 = a3 Planetary Motion Kepler’s three laws of planetary motion are observations and solutions based on mathematics fits to Brahe’s data. We call such a result an empirical result. One that is based on observations and data, but doesn’t explain the how/the physics of why that result occurred What is the reason that planets orbit our sun? Or, why do Kepler’s Three Laws of Planetary Motion work? Isaac Newton Newtonian Mechanics = the mechanism behind Kepler’s Laws Newton’s Laws of Motion Force (F): Any influence that tends to change the motion of an object Inertia: The resistance of an object to change its speed and direction Weight versus Mass (m or M) Mass is the amount of matter (protons, neutrons, electrons, etc) an object contains (SI unit: kg) Weight is the gravitational force exerted on an object with mass Speed versus Velocity (v) Velocity is the speed and direction with which an object is traveling Speed v. Velocity: (meters/seconds, m/s) Speed is just how fast it’s going Velocity is the speed and direction with which an object is traveling Acceleration (a): (m/s2, m/s) The rate of chance of velocity, i.e., how velocity (in speed and direction) is changing with time Acceleration is velocity per time, or (meters per second) per second Newtonian Mechanics Newton’s First Law of Motion Inertia An object will remain in a state of rest or uniform, straight line motion (constant velocity), unless acted upon by an outside force. Objects in motion tend to stay in motion unless something messes it up Newton’s Second Law of Motion, F = ma When a Force F acts on a body of mass m, it produces an acceleration a equal to the force divided by mass (a = F/m, F = ma) The acceleration of an object experiences is inversely proportional to the mass and directly proportional to the force exerted on it We can understand how a mass will accelerate (change velocity) if we know the force applied to it Apply more force to an object to induce a greater acceleration. Or, if something has more mass, it requires more force to accelerate Newton’s Second law commonly said as “F equals m a” or “force equals mass times acceleration” Newton’s Third Law of Motion; equal in magnitude, opposite in direction When one body exerts a force on a second body, the second body exerts a force equal in magnitude, but opposite in direction on the first body Newtonian Gravity Everything with mass is attractive Everything that has a mass exerts a gravitational force on every other object with a mass Masses attract one another How strong the gravitational force is depends only on two components: the masses involved, and the distance between them The force of gravity is proportional to the product of the masses divided by the square of the distance between them, usually labeled as r or R The InverseSquare Law Know this! Gravity only operates in one direction. IT IS ALWAYS ATTRACTIVE, AND NEVER REPULSIVE G, sometimes called “Big G” is the Gravitational Constant measured experimentally to be G = 6.67 x 10^11 N m^2/kg^2 Astronomy 9/9 Forget about G. Product of the masses divided by r squared. Answer: 4x weaker The Ms didn’t change but the R did. 1x1/(2)^2 = 1/4 Answer: m changed so (1)(2)/1 squared. So it gets stronger by 100% Newtonian Gravity The earth has mass… a lot of it at 5.97 x 10^24 kg (a trillion trillion kilograms. 1 kg = 2.2 pounds on earth) We live in the gravitational force so it is always acting on us On Earth, the acceleration due to Earth’s gravity, often written as g, is approximately constant and directed toward the center of the earth Earth’s gravitational acceleration is 9.8 m/s^2 It never stops and is always applying force to everything in the universe Putting something into orbit The speed at which the Force of Gravity balances out Centripetal Force (circular motion force) is orbital speed Set both forces equal to each other in balance Rocket Science If we fire a cannon ball with even more force then we can break orbit and go out into interplanetary space The speed to escape entirely, escape speed, is the square root of 2 greater than the orbital speed Using Newtonian Gravity to Weigh Things If we can measure the distance and period we can use Newtonian gravity to solve for mass Can also use these equations to determine the mass of the sun M = rv^2/G, the result is M = 2.0 x 10^30 kg Newton’s Modifications to Kepler’s Laws The planets are constantly being pulled toward the sun by the sun’s gravity But we are moving at the right speed to balance out the sun’s gravity Gravitational force equals centripetal force Two equal mass objects in orbit around a common focus, which is located at the Center of Mass, the point where masses perfectly balance Two objects with unequal mass orbit a common center of mass, with the more massive one having a smaller orbit, massive things are harder to move Note: the orbital periods of the two remain the same Common focus is at the center of mass The objects will always be perfectly opposite on another For our solar system, the center of mass is in the sun but not at the center of the sun. The sun orbits the common center of mass of all the planets Astronomy 9/12 Modified Kepler’s Laws With Newton’s modifications we can now apply Kepler’s Law to any system (earth, moon, etc) Chapter 3 Light: Our Source of Information Almost everything we know about the universe outside of the Solar System, we know through studying its light Looking through time and space Most of universe inaccessible except for its light Light, a form of radiation, carries a wealth of information to us Light and Radiation Radiation is any way in which energy is transmitted through space from one point to another without the need for a physical connection between the two locations Electromagnetic radiation, or light, is radiation cause by rapid variations in electric and magnetic fields What humans can see is called visible light However, visible light, is just a tiny portion of all the kinds of light that exist The Nature of Light Light is electromagnetic radiation Electric and magnetic field components Light is both a wave and a particle Here we discuss the wave nature of light Light is much more than what human’s see (visible light) All forms of light (red light, green light, infrared light, Xray light, etc.) travel at the same speed, the speed of light “Invisible” Light Human eye only capable of seeing visible light Other forms of light/electromagnetic radiation Radio waves, microwaves, infrared light, ultra violet light, xrays, and gamma rays All of which are invisible to the human eye Light It’s a Wave (and a particle) The wave travels across the surface transmitting energy, and therefore, carrying information Anatomy of waves Wave motion transmits energy/information without the physical transport of material Frequency is the number of crests that pass a given point per second The period is the time it takes the wave to travel from cresttocrest Frequency = 1/Period (unit: 1/seconds or Hertz) This is an inversely proportional relationship Wavelength is the cresttocrest, or equivalently, throughtothrough, distance The amplitude is how high or low a wave can get above or below its undisturbed state The velocity of a wave is the speed at which it travels, i.e., velocity = wavelength/period or wave velocity = wavelength x frequency (distance per time) The Visible Light Spectrum Spectrum: is dividing up the light to into its wavelength (equivalently frequencies) The longest wavelength is red while the shortest is the bluer and violet wavelength Redder have lower frequencies and bluer have higher frequencies Frequently Used Units The nanometer is frequently used for wavelength Nano is the prefix for 10^9, so 1nm = 1 x 10^9 m. 1 billion nanometers is one meter The micrometer, or micron, is also frequently used Micro is 10^6 of 1 millionth. 1 um = 1000 mn Sometimes astronomers use the Angstrom 1 A = 10^10m = .1nm Traveling Waves Water waves, sound waves, etc., travel in a medium (e.g., water, air) so what do light waves travel in? Electromagnetic waves require no medium Created by accelerating charged particles E.g., protons (positive charge) and electrons (negative charge) Electric Forces and Fields Analogous to gravitational force, all charged particles (electrons, protons, etc.) exert an electric force Unlike gravity, the electric force can be both attractive and repulsive If something happens that starts to make the charged particle vibrate Electric field changes, which is felt by all other charged particles in the universe The disturbance travels through space as a wave… an electromagnetic wave Electricity and Magnetism A Magnetic field induces a force on moving electric charges, electric currents Conversely, electric currents generate magnetic fields (electromagnets) Like gravity, electromagnetism is one of the four fundamental forces Electromagnetic Waves Electromagnetic waves: oscillating electric and magnetic fields. Changing electric field creates magnetic field, and vice versa The wavelength or frequency of an electromagnetic wave is what determines the color (blue, green, or red) of light Discovery 31 The “Single Slit Experiment” Thomas Young If light is a wave, it will exhibit diffraction (bending around obstacles) and a “fuzzy” shadow should result If particles, then perfect spot with no “fuzziness” Electromagnetic (EM) Waves Electromagnetic Radiation travel at the speed of light The speed of light is 3 x 10^5 kilometers/sec Exact value 299,792.458 km/sec Very fast but still finite For distant objects, light still takes millions to billions of years to traverse space
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