1. Review for Exam I Chapters 1, 2, 3,4 PHYS 1050 May, 2002

2. Purpose This document is a study guide, NOT a comprehensive list of all topics included on the exam. The exam will cover material from both the text and class notes.

3. Equations and Constants diameter/(2  x distance) = angular diameter/360 o small-angle formula: diameter = distance x (angular diameter/ 57.3 o ) F = ma F grav = Gm 1 m 2 /r 2 P 2 = a 3 speed of wave = wavelength x frequency period = 1/frequency energy of wave proportional to frequency (or 1/wavelength) circumference of circle = 2  x radius area of circle =  r 2 astronomical unit = 1 AU = 150 x 10 6 km = average distance from Earth to Sun speed of light = 300,000 km/sec light year = 1 LY = distance light travels in one year distance = speed x time

4. Definitions and Facts Age of the universe: ~ 12-17 billion years old Measuring distances –parallax –triangulation angles, baseline –angular measurement Stars and constellations –Polaris is “North Star”, marks the position in the sky of Earth’s rotation axis. –The “Big Dipper” is located in Ursa Major. –Orion is a prominent constellation in the winter sky. –Sirius is the brightest star in the sky. Celestial Sphere –North celestial pole, celestial equator, meridian –ecliptic, zodiac, equinoxes, solstices –right ascension, declination –altitude, azimuth, horizon, zenith

5. Motion of the Earth –rotation cause of day/night from WEST to EAST which causes objects to rise in EAST and set in WEST describe daily motion of stars, Sun, and Moon across sky at different latitudes –orbital motion seasonal variation of constellations –seasons rotational axis tilted at 23.5 o to ecliptic seasonal variation of Sun’s rising/setting/noon- time position

6. Motion of the Moon –orbital motion in eastward direction around Earth with angular speed of 0.5 o per hour lunar phases –new, full, first quarter, last quarter, gibbous and crescent (waxing/waning) –relationship between lunar phase and rising/setting time –rotation rotates once per orbit about Earth: synchronous rotation –always see same face of Moon from Earth

7. The Sky from Denton: 33.5 o N North Celestial Pole is 33.5 o above northern horizon. Celestial Equator is 56.5 o above southern horizon. Circumpolar stars lie within 33.5 o of North Celestial Pole. Rising & Setting stars are visible from 33.5 o away from South Celestial Pole. Stars within 33.5 o of South Celestial Pole are never visible from Denton.

8. The Earth’s Rotation The Earth's west to east rotation causes the celestial sphere to appear to rotate from east to west in 24 hours. LOOKING SOUTH –The Sun, Moon, planets, and stars appear to rise in the east, cross the meridian due south, and set toward the west. –Celestial objects are said to transit when the cross the celestial meridian in the southern sky. This is when they are highest in the sky. LOOKING NORTH –The stars appear to circle around the North Celestial Pole (near Polaris) once in 24 hours. –Stars within the angle of the observer's latitude away from the North Celestial Pole never rise or set. They are always above the horizon (circumpolar stars).

9. The Effects of Precession Causes the pole star to change. –Thuban (in Draco) was the pole star in 3,000 B.C.. –Polaris (in Ursa Minor) is the pole star now. –Vega (in Lyra) will be the pole star in 14,000 A.D. Causes intersection point of ecliptic and celestial equator to shift. –"Age of Aries" occurred 2,000 years ago. –"Age of Pisces" is now. –"Age of Aquarius" will begin about 400 years from now.

10. The Earth’s Orbital Motion The Earth’s orbital motion causes –the apparent eastward motion of the Sun along the ecliptic of about 1 o per day. –the annual motion of the Sun through the 13 zodiac constellations. –the seasonal visibility of stars and constellations. The tilt of Earth’s rotation axis by 23.5 o causes –tilt of the ecliptic with respect to the celestial equator. –the Sun's declination to change during the year. –seasonal variations in the altitude of the midday Sun, length of day & night, and rising & setting directions of the Sun.

11. Eclipses The Moon's orbit is inclined about 5 o to the ecliptic. That's why there are not eclipses every month. In order for an eclipse to occur, the Earth, Moon, and Sun must be nearly perfectly aligned. All eclipses occur when the Moon crosses the ecliptic. –Solar eclipses are possible only at the New Moon phase, when the Moon is crossing the Earth's orbital plane (ecliptic). –Lunar eclipses are possible only at Full Moon phase, when the Moon is crossing the ecliptic.

12. Solar and Lunar Eclipses Solar Eclipses –Earth moves into the Moon's shadow. –Occur only the the New Moon phase. –Visible only over a narrow path across the Earth. –Can be total, annular, or partial. –Total solar eclipses are possible because the angular size of the Sun and Moon are very nearly equal. Lunar Eclipses –Moon moves into Earth's shadow. –Occur only at the Full Moon phase. –Are visible over the entire night side of the Earth. –Can be total, partial, or penumbral. –A total lunar eclipse does not get completely black, because some light from the Sun is bent around the Earth by the Earth's atmosphere.

13. Planetary Motions and Configurations –all planets orbit EASTWARD around the Sun –the further from Sun, the slower the angular speed of the planet in orbit –describe cause of retrograde motion, observed planetary phases –define configurations inferior planets –conjunction »inferior »superior –maximum elongation superior planets –opposition, –conjunction, –quadrature

14. Planetary Motion and Models of the Solar System –retrograde motion –models geocentric –epicycles and deferents heliocentric –historical contributions to understanding of universe Aristotle Aristarchus Hipparchus Ptolemy Copernicus Galileo Brahe Kepler Newton

15. Kepler’s 3 Laws of Planetary Motion –1 st Law: law of ellipses –2 nd Law: law of equal areas –3 rd Law: “harmonic” law (P 2  a 3 ) –Ellipses and orbits eccentricity, semi-major axis, aphelion, perihelion Newton’s Laws of Motion and the Law of Gravity –1 st Law: law of inertia –2 nd Law: force law (F=ma) –3 rd Law: action-reaction law –Law of Gravity: gravitational force between two objects is proportional to the product of the mass of each object divided by the distance between their centers squared. –Concepts: Acceleration due to gravity same on objects of different mass, but force of gravity on each object is different. Force exerted on pebble by Earth is the same size, but opposite direction as force exerted on Earth by pebble. Why does the Moon orbit the Earth when the Earth’s gravity is pulling the Moon down toward Earth?

16. Forces and Motion –Definitions and Examples mass, inertia speed velocity acceleration force gravity weight

17. Waves and Wave Motion –definitions wavelength: distance between crests of a wave amplitude: intensity or height of a wave frequency: number of waves per second period: time between successive wave crests (1/frequency) wave speed: frequency x wavelength –transverse and longitudinal waves –properties of waves reflection refraction dispersion diffraction interference: constructive, destructive superposition –Doppler effect

18. Electromagnetic Spectrum –electromagnetic waves created by acceleration of charged particles transverse wave transmit energy through space need NO medium to propagate all wavelengths travel at same speed in a vacuum, c = 3x10 5 km/s –components in order of increasing wavelength gamma rays, X-rays, ultraviolet light, visible light, infrared light, radio waves –relationship between energy, frequency, and wavelength of light E  f or E  1/ high energy radiation: high frequency, small wavelengths, “blue” color low energy radiation: low frequency, large wavelengths, “red” color Kirchoff’s Laws –relate patterns within an observed spectrum to the object producing the spectrum –understand how features are produced continuous spectrum emission spectrum absorption spectrum

19. Atomic Structure –protons, electrons, neutrons –Bohr model of atom “solar system” model with quantized electron energy levels –ground state, excited states, ionization –transitions between states »electron “excited” by absorbing photon with right energy »electron “de-excited” by emitting a photon –relationship between electron energy levels and atomic spectra each element has unique emission/absorption spectrum –properties of objects determined by studying spectra they produce temperature, motions, composition, etc. –sources of spectral line broadening

20. Example Questions 1 According to Newton, if the mass of the Earth tripled, your weight would _________. A. remain the same B. be one half of its current value C. be one third of its current value D. Three times its current value E. quadruple its current value The distance between successive wave crests is defined as the _________ of that wave. A. frequency B. amplitude C. period D. wavelength E. wave speed 1. A comet orbiting the Sun has an aphelion distance of 90 AU and a perihelion distance of 70 AU. The semi-major axis of the asteroid's orbit is ________. A. 10 AU B. 20 AU C. 80 AU D.160 AU E.714 AU

21. Example Questions If the same net force is applied to two objects, one with a mass of 10-kg and the other with a mass of 5-kg, which of the following statements is TRUE? A. A. The 10-kg mass will have twice the acceleration of the 5-kg mass. B. B. The 5-kg mass will have twice the acceleration of the 10-kg mass. C. C. Both objects will have the same acceleration, since the force determines the acceleration. What is emitted from an atom when one of its electrons makes a transition from a higher energy state to a lower energy state? A.A photon. B.A neutron. C.An electron. D.A proton. E.Nothing, the atom becomes smaller.