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Review for First Exam Astronomy 1010, Fall 2009

Review for First Exam Astronomy 1010, Fall 2009. Practice Questions Equations Your Questions New Material. T/F Practice Questions. 1) 4.0 10 6  0.0050 = 2.0  10 3 False: 4.0 10 6  5.010 -3 = 20.  10 6+(-3) = 20.  10 3 = 2.0  10 4

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Review for First Exam Astronomy 1010, Fall 2009

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  1. Review for First Exam Astronomy 1010, Fall 2009 Practice Questions Equations Your Questions New Material

  2. T/F Practice Questions 1) 4.0106  0.0050 = 2.0  103 • False: 4.0106  5.010-3 = 20.  106+(-3) • = 20.  103 = 2.0  104 2)A true science must allow for hypotheses to be tested, and if found to contradict newer experiments or observations, the hypotheses should be modified or discarded. • True 3)One of Ptolemy’s main contributions to astronomy consisted of writing down and summarizing the discoveries of earlier Greek astronomers. • True

  3. 4) The third quarter moon rises around noon. • False (it rises around midnight -- 1st Q rises around noon) 5) An astronomer living at 60oN latitude will see fewer different stars during the course of a year than will an astronomer living at 30oS latitude. • True (at 60oN there are more South circumpolar stars that are never seen than N circumpolar stars for 30oS) 6) Kepler’s third law says that a planet moves fastest when closest to the Sun. • False: it says planets closer to the Sun move faster, (but Kepler’s 2nd law says this). 7) If the Moon’s mass suddenly became only only half of what it actually is, the gravitational force between the earth and the moon would be halved. • True, as Fgrav= GmEmM/d2

  4. Multiple Choice Practice Questions 8) Given that the radius of Jupiter is 68,700 km and the radius of Venus is 6.05  108 cm, what is the ratio of Venus’ radius to Jupiter’s? • 1.14  10-4 • 1.14  10-2 • 8.81  10-2 • 1.14  101 • 8.81  102

  5. 8) Given that the radius of Jupiter is 68,700 km and the radius of Venus is 6.05  108 cm, what is the ratio of Venus’ radius to Jupiter’s? • 1.14  10-4 • 1.14  10-2 • 8.81  10-2 • 1.14  101 • 8.81  102 RV = 6.05  108 cm = 6.05  106 m = 6.05  103 km So, RV/RJ = 6.05  103 km / 6.87  104 km = 0.881  10-1 = 8.81  10-2

  6. 9. On the vernal (spring) equinox • A. the number of hours of light equals the number of hours of dark • B. the Sun crosses the Celestial Equator moving from North to South • C. the Sun rises due East and sets due West • D. both A. and C. are true • E. all of A., B., and C. are true

  7. 9. On the vernal (spring) equinox • A. the number of hours of light equals the number of hours of dark • B. the Sun crosses the Celestial Equator moving from Nouth to Sorth • C. the Sun rises due East and sets due West • D. both A. and C. are true • E. all of A., B., and C. are true

  8. 10. A total solar eclipse can only occur when: • the moon’s phase is new. • the line of intersection of the earth’s and moon’s orbital planes (line of nodes) runs through the sun. • the moon is not at apogee (apogee is when a satellite is furthest from its planet). • Both A. and B., but not C., are necessary. E. All of A., B. and C. are necessary.

  9. 10. A total solar eclipse can only occur when: • the moon’s phase is new. (only for solar) • the line of intersection of the earth’s and moon’s orbital planes (line of nodes) runs through the sun. (for both lunar & solar) • the moon is not at apogee (apogee is when a satellite is furthest from its planet). • Both A. and B., but not C., are necessary. E. All of A., B. and C. are necessary. (otherwise only an annular eclipse)

  10. 11. Which of the following situations describes an acceleration: • A. a planet traveling around the sun • B. a car traveling at a constant speed down a straight street • C. a car decreasing speed while traveling down a straight street • D. a car waiting at a stop light for the light to turn green • E. both A. and C. are accelerations

  11. 11. Which of the following situations describes an acceleration: • A. a planet traveling around the sun • B. a car traveling at a constant speed down a straight street • C. a car decreasing speed while traveling down a straight street • D. a car waiting at a stop light for the light to turn green • E. both A. and C. are accelerations

  12. 12. Galileo used his telescope to discover all but which of the following: • A. the phases of Venus • B. the mountains on the Moon • C. the rings of Saturn • D. the rotation of the Sun • E. the moons of Jupiter

  13. 12. Galileo used his telescope to discover all but which of the following: • A. the phases of Venus • B. the mountains on the Moon • C. the rings of Saturn (his telescope not quite good enough) • D. the rotation of the Sun (via sunspots) • E. the moons of Jupiter

  14. 13. Compared to its angular momentum when it is farthest from the Sun, Earth’s angular momentum when it is closest to the Sun is • A. greater. • B. the same. • C. less.

  15. 13. Compared to its angular momentum when it is farthest from the Sun, Earth’s angular momentum when it is closest to the Sun is • A. greater. • B. the same. (Conservation of AM) • C. less.

  16. Your questions?

  17. Review of Scientific Notation • 102 = 100, 101=10, 100 = 1, 10-1=0.1, 10-2=0.01 • 1012=1,000,000,000,000=trillion (Tera-) • 109 =1,000,000,000 = billion (Giga-) • 106 = 1,000,000 = million (Mega-) • 103 = 1,000 = thousand (kilo-) • 10-2= 0.01=one-hundredth (centi-) • 10-3= 0.001=one-thousandth (milli-) • 10-6= 0.000001=one-millionth (micro-) • 10-9= 0.000000001=one-billionth (nano-) • 5.4x103=5,400 7.05x10-3=0.00705 • 4,700=4.7x103 0.017 = 1.7x10-2

  18. Powers of Ten Arithmetic Multiplication: (5.3x103) x (6x10-5) = 31.8x103+(-5) =31.8x10-2 = 3.18x10-1 =0.318 = 0.3 One significant figure! Keep only the minimum number of significant figures going into the calculation in the answer. Division: (9.3 x10-4)/(3.10x10-6) = 3.0 x10-4-(-6) = 3.0 x102 = 300 BUT, 3.0x102 is the better answer, as it CLEARLY has two significant figures; scientific notation is PRECISE.

  19. The Scales of the Universe We deal with the largest possible things -- the whole universe -- and with the smallest -- nuclei of atoms. This requires us to use a wide range of PHYSICAL UNITS and we USE THE METRIC SYSTEM. Length: m or cm Mass: kg or g Time: s or yr Temperature: K(elvins) 1 pc = 3.26 light-yr = 3.085678 x 1018cm=3.1x1013km 1AU = 1.496x1013cm = 150,000,000 km (astronomical unit = mean distance between earth and sun)

  20. Celestial Coordinates: Latitude & Longitude taken to the Sky • BUT ALL STARS (AND GALAXIES) ARE LOCATED IN CELESTIAL COORDINATES. • Equivalent to LATITUDE is DECLINATION (); degrees (), minutes (') and seconds(") (of arc) • from +90 deg (NCP) to -90 deg (SCP). • 1 circle = 360 deg() • 1 deg = 60 arcmin • 1 arcmin = 60 arcsec, so • 1 arcsec = 1/3600 th of a degree or 1/1,296,000 th of a circle. • Sirius has a declination of: -16, 41', 58"

  21. Equivalent to LONGITUDE is RIGHT ASCENSION; (R.A. or ): Zero = spring equinox (where Sun on Ecliptic crosses Celestial Equator) • measured in units of time: hours, minutes and seconds, from 0 hours to 23 h, 59 m, 59.999 s. • One hour of RA = 15 deg of angle (360 degrees/24 hr/day) • Sirius: right ascension of: 6 h, 45 m, 09 s. • Vega has dec=+38O44’ and RA=18h35.2m

  22. At positive latitiude L (example is 40 N), • stars within L deg of the NCP will be circumpolar and these stars have Declinations,  > (90-L) deg. • At latitude L, stars with Declinations, , satisfying: • (90-L) > > (L-90) are equatorial, • Stars with  < (L-90) are "south-polar”: never seen.

  23. Lunar Phases and Approximate Time

  24. Eclipse Geometry

  25. Distances and Sizes • Angular diameter = Diameter/Distance •  = D/d • Theta (angular diameter) is measured in RADIANS, with 2 radians = 360 degrees or 1 rad =57.296 • Example: We know the distance to the Sun and the Diameter of the Sun. • What is the angular size of the Sun? •  = 2 R / 1 AU = 1.392 x 106 km / 1.496 x 108 km • = 9.305 x 10-3 rad = 0.5331 deg = 31.99 arcmin

  26. Distances from Parallax • Key tool in measuring distances to nearby stars. • Apparent shift in position due to Earth’s orbit around the Sun. • One PARSEC (PARallax SECond) = distance at which a star would subtend a 1 arcsec angle from a 1 AU baseline. • As there are 206,265”/rad, 1 pc = 206,265 AU • 1 pc = 3.26 ly = 3.085678 x 1016m • Always a SMALL angle, so • d (pc) = 1/p(arcsec), • so if p = 0.1”, d = 10 pc, or if d = 50 pc, then p = 0.02”

  27. The Size of the Earth • Eratosthenes (276--195 BCE) used geometry and simple astronomy to make an accurate measurement of the Earth's radius. • He realized the difference in the altitude of the noonday Sun in Syene and Alexandria equaled the latitude difference between the cities. • That gave the ratio: • circumference of the Earth / 360 = distance / 7.2 • Accuracy determined by distance in stadia --- measured by foot and uncertain, but around 40,000 km, and probably good to 10% • (Correct value: 40,074 km or 24,890 miles)

  28. Kepler’s Laws of Planetary Motion • Ten more years of work led to the THREE EMPIRICAL LAWS: • 1. All planets follow elliptical orbits, with the Sun located at one focus. (Nothing is at the other focus.) • 2. Every planet sweeps out equal areas in equal times as it orbits the Sun. • In other words, planets move fastest when closest to the Sun (near PERIHELION) and slowest when furthest away (APHELION).

  29. Kepler’s Second Law: Equal Areas Swept out in Equal Times

  30. Sidebar on Ellipses: 1 • To draw one, loop a string around two tacks, holding it taught with a pencil point. • Definition: the locus of points the sum of whose distances from two other points (the foci) is constant. • The longest axis through an ellipse is the MAJOR AXIS One half of that is the SEMI-MAJOR AXIS, a • One half of the shortest axis ( perpendicular to the major axis) is the SEMI-MINOR AXIS, b • Distance from the Center to each Focus is semi-major axis times the ECCENTRICITY or FC = ae • e = [1 - (b/a)2]1/2 OR: b2 = a2(1 - e2) • If e = 0 we have a circle (b=a; foci and center coincide); • if e = 1 we have a line-segment

  31. Ellipses and Planetary Orbits

  32. Kepler’s Third Law of Planetary Motion • 3. The cube of the semi-major axis of a planet's orbit is proportional to the square of its period. • a3 = P2 if a is in units of AU and P is in years (in OUR solar system). • Examples: • aMars = 1.524 AU so PMars = (1.524)3/2 = 1.881 years; aJupiter= 5.20 AU so PJupiter = (5.20)3/2 = 11.86 years. • More generally, a  P2/3 or P  a3/2 • Later Newton showed that these general proportionalities (but not equality) was always true for systems with a single dominating mass, not just our solar system.

  33. NEWTON'S LAWS OF MOTION • 1. An object at rest remains at rest and an object moving at a certain velocity retains that velocity unless a FORCE acts on it. • Aristotle's view: forces were needed merely to keep something moving at a constant speed • Newton realized friction or air resistance were forces that slowed things down • Galileo had already understood this.

  34. Newton’s SECOND LAW • The core of Newtonian mechanics, it allows trajectories of cannon balls, rockets, planets, comets, stars and galaxies to be computed. • F = m a • is the most important relation in physics; one can equivalently write • a = F/m • This clearly says less massive objects obtain larger accelerations from the same force. • Think of stepping on the gas and going from 0 mph to 60 mph in 10 seconds: your acceleration is 6 mph/s (forwards)

  35. More on the 2nd Law • Breaking takes you from 60 mph back to 0 in 4 sec • or a negative acceleration of 15 mph/s. • These are VECTOR equations -- with magnitude and direction • Velocity = distance covered / time • V = d/t • Acceleration = change in velocity/time change • a= V/t • - both the Speed and Direction are needed • I.e. 50 mph to the East is the same speed, but different velocity, from 50 mph to the North • Going around a curve at a constant speed DOES involve an acceleration (you feel pushed to one side of the car, right?)

  36. Newton’s Third Law • 3. EVERY ACTION (FORCE) HAS AN EQUAL AND OPPOSITE REACTION. • Forces don't act in isolation: • the Earth pulls the Moon and the Moon pulls back on the Earth; • we push down and back on the ground with our muscles, it pushes us up and forward; • a rower or gondolier pushes water (or canal bottom) in one direction and the scull or gondola goes the other way; • a rocket expels gases rearward and it flies forward.

  37. Conservation Laws in Astronomy • Momentum • Angular Momentum • Energy Conservation of (linear) Momentum is implied by Newton’s Laws of Motion. One ball hits another, exerts a force, which accelerates Second ball (2nd law); 3rd Law says opposite force decelerates the first ball

  38. Angular Momentum Conservation • AM = m x v x r (mass x velocity x distance) • Orbital AM conservation says no push needed to keep Earth orbiting and also faster motion at perihelion than aphelion: v x r = constant • Rotational AM conservation says Earth keeps spinning on its axis and also faster spin when contracted: ballerina, gas cloud making planets

  39. Conservation of Energy • Energy comes in many forms but three classes can contain them all: • Kinetic (energy of motion) • Radiative (energy of light or electromagnetic radiation) • Potential (stored energy -- gravitational, chemical, atomic, mass-energy)

  40. Gravitational Potential and Kinetic Energy • No KE, maximum gravitational potential energy at top of throw • Maximum KE, minimum gravitational PE when thrown and when caught • KE = (1/2)mv2

  41. NEWTON'S LAW OF GRAVITY • The ATTRACTIVE FORCE OF GRAVITY IS DIRECTLY PROPORTIONAL TO THE PRODUCT OF THE MASSES • AND INVERSELY PROPORTIONAL TO THE SQUARE OF THE DISTANCE, r, BETWEEN THEM. • where Newton’s gravitational constant • G = 6.673 x 10-11 m3 kg-1 s-2

  42. Gravitational Acceleration: 1 • Combine 2nd Law of Motion w/ Law of Gravity • ACCELERATION DUE TO GRAVITY, g, OF AN OBJECT IS PROPORTIONAL TO ITS MASS AND INVERSELY PROPORTIONAL TO THE SQUARE OF THE DISTANCE FROM ITS CENTER.

  43. Weight v. Mass • Weight (Newtons, dynes) is the force due to gravity acting on a mass (amount of matter, kilograms, grams) so • W = m g (special case of F = m a). Since gravity gets weaker a greater distances, you actually weigh less at the top of a building than you do at its base, even though your mass hasn't changed. • Since Atlanta is about 300 m above sea level, you weigh a little less here than in Savannah • -- at sea level, and closer to the center of the earth. • You weigh more in an elevator as it just accelerates to go up and less in one that accelerates to go down; • you are weightless in one that is falling w/o support!

  44. Circular Velocity and Escape Velocity • Newton also showed that the general shape of a BOUND ORBIT was an ELLIPSE (with a circle as a special situation) • and that the general shape of an ESCAPE ORBIT was a HYPERBOLA (with a parabola as a special case). • The simplest case: a CIRCULAR orbit, just skimming the earth

  45. Orbit Shape Depends on Speed • v = vc : circular orbit • vc < v < vesc : elliptical orbit w/ center of E at near focus; • Both BOUND (NEGATIVE ENERGY ORBITS) • v = vesc: parabolic escape orbit: reaches infinity with no energy left (ZERO ENERGY ORBIT) • v > vesc • hyperbolic escape orbit: reaches infinity still moving away (POSITIVE ENERGY ORBIT) • For earth, vesc = 11.2 km/s, or about 25,000 mph!

  46. Weighing Astronomical Bodies • For example, to get the mass of the Sun + Earth (basically just Sun) m = 2.0 x 1030 kg

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