Astronomy Elementary Astronomy Astronomy 4 Study of the

Astronomy Elementary Astronomy

Astronomy 4 Study of the Heavens 4 Science – verifiable predictions 4 Physics (some math)

Finding One’s Way in the Sky 4 Celestial Sphere – imaginary sphere 4 Horizon – line where sky meets ground 4 Zenith – point on celestial sphere directly overhead 4 Meridian – imaginary line running N-S that passes through zenith

Finding One’s Way in the Sky 4 Celestial Poles – projection of Earth’s rotation axis on celestial sphere 4 Celestial Equator – imaginary circle lying halfway between north and south poles – projection of Earth’s equator

Finding One’s Way in the Sky 4 Ecliptic – annual path of the Sun projected on celestial sphere 4 Zodiac – narrow band, around the ecliptic – many of the constellations have animal names – zoo zodiac

Finding One’s Way in the Sky

Finding One’s Way in the Sky 4 Locating Objects – celestial sphere has 2 -d surface – two numbers to locate an object 4 Origin – reference point 4 Units – measuring system

Finding One’s Way in the Sky 4 Linear vs. Angular Measurement – linear distances meaningless on celestial sphere – angular measurements – 360 o in a circle – 60 minutes (`) in one degree – 60 seconds (``) in one minute – 43 o 52`34``

Finding One’s Way in the Sky 4 Earth – Latitude • natural reference points, poles and equator • 90 o N=north pole, 90 o S=south pole, 0 o =equator – Longitude • arbitrary reference point • prime meridian through Greenwich, England = 0 o

Latitude and Longitude

Latitude and Longitude

Finding One’s Way in the Sky 4 Celestial Sphere – need way of measuring angles (compass, sextant, protractor) 4 Two systems for determining position – Altitude-Azimuth – Equatorial

Altitude - Azimuth Coordinates 4 Altitude – angular distance above horizon 4 Azimuth – angular distance measured in CW direction from N* 4 Advantages – very easy to determine 4 Disadvantages – depends on location

Equatorial Coordinates 4 Declination – angular distance from celestial equator – north (+), south (-) celestial poles 90 o 4 Right Ascension – measured in an easterly direction from the location of the vernal equinox 4 Advantages – same for all observers 4 Disadvantages – more difficult to determine

Motion of Heavenly Objects Observations and Explanations

Sun 4 Observation – rises in East, sets in West – daily (diurnal) 4 Explanations – Sun moves through the sky (old) – Earth rotates on axis once per day (accepted)

Sun 4 Observation – moves west to east wrt to stars – yearly (annual)

June 20

July 20

Sun 4 Observation – moves west to east wrt to stars – yearly (annual) 4 Explanation – Earth orbits Sun 4 Ecliptic – apparent path of the Sun through sky

Sun 4 Observation – sunrise and sunset move north and south – hours of daylight increase and decrease – annual 4 Explanation – Earth’s rotation axis is tilted with respect to plane of orbit

Northern Summer Northern Winter Southern Summer

Seasons 4 Northern Hemisphere – summer solstice • rotational axis points toward Sun • most hours of daylight • Sun rises northernmost along eastern horizon – vernal equinox (Spring) • equal hours of day and night • Sun rises directly East • moving north

Seasons 4 Northern Hemisphere – winter solstice • axis points away from Sun • fewest hours of daylight • Sun rises southernmost along eastern horizon – fall equinox • equal hours of day and night • Sun rises directly East • moving south

Seasons and the Celestial Sphere

Keeping Time 4 Solar Day – time between two successive crossings of the meridian by the Sun – 24 hours 4 Sidereal Day – time between two successive crossings of the meridian by a star – 23 hrs 56 min

Day 2 Day 1 difference between sidereal day and solar day: sidereal day is shorter

Keeping Time 4 Tropical Year – time for sun to complete one trip around ecliptic – 365. 242 solar days 4 Sidereal Year – time for constellations to complete one trip around the sky – 365. 256 solar days 4 Difference due to Precession

North Star 4 Observation – different stars play the role of north star – difficult observation to make – time scale of 26, 000 years 4 Explanation – Earth’s rotation axis wobbles – precession

North Star and Precession

North Star

Planets (“wanderers”) 4 Observation – five visible to naked eye • Mercury, Venus, Mars, Jupiter, Saturn – east to west • daily – west to east • move in zodiac (narrow band surrounding ecliptic) – retrograde (east to west)

Planetary Configurations 4 Conjunction – lies in same direction of the sky as the Sun – Superior • Sun between planet and us – Inferior • planet between Sun and us • only occurs for Mercury and Venus

Planetary Configurations 4 Opposition – planet lies directly opposite the Sun in the sky – only occurs for Mars, Jupiter & Saturn Superior Conjunction Inferior Conjunction Earth Opposition

Planetary Configurations 4 Transit – object moves across the Sun’s disk – occurs only for inferior planets 4 Greatest Elongation – greatest angular separation of a planet from Sun – Mercury - 28 o – Venus - 47 o – superior planets - 180 o

Explanations Historical Perspective

Shape of the Earth (Sphere) 4 Pythagoras – sphere is perfect shape 4 Aristotle – change in stars with change in latitude – appearance of ships’ sails – shadow of Earth during lunar eclipse

Size of Earth 4 Erastothenes (276 - 195 B. C. ) – geometry Parallel Light Rays (40, 000 km at equator)

Sun, Earth and Moon 4 Aristarchus – Moon about 1/3 size of Earth – Sun about 20 times farther away than Moon – Sun bigger than Earth – heliocentric theory

Geocentric Theory 4 Earth is center of motion. – Sun, Moon, planets, stars all move around Earth 4 Fast moving objects are near Earth 4 Epicycle (Ptolemy ) – circles on circles – could explain retrograde motion

Heliocentric Theory 4 Copernicus (1473 - 1543) 4 Sun is center of motion – Earth, planets, stars move around Sun in circles 4 explains retrograde motion 4 allows calculation of relative distances 4 Problems: – no parallax observed – predictions were not much better

Tycho Brahe (1546 -1601) 4 superior observations 4 Heavens are changeable – supernova • beyond planets – comet • outside of Earth’s atmosphere 4 compromise – all planets orbit Sun – Sun orbits Earth

Johannes Kepler (1571 - 1630) 4 analysis of Tycho’s data 4 Three Laws of Planetary Motion 1 Planets move in elliptical orbits with the Sun at one focus. 2 Equal areas in equal times. 3 P 2 =k a 3

Law 1 - Ellipse 4 squashed circle 4 eccentricity – measure of flattening – ratio of distance between foci to length of major axis • 0 = perfect circle 4 most orbits have small e semimajor axis

Law 2 - Equal Areas 4 Planets move faster when closer to the Sun

Law 3 - 2 P = 3 ka 4 P is the period of the planet – how long it takes the planet to complete one orbit 4 a is the length of the semimajor axis

Galileo Galilei (1564 - 1642) 4 observed moons of Jupiter – orbiting something other than the Earth 4 phases of Venus – Venus in orbit around Sun 4 Sunspots – Sun is not unchanging 4 Craters on the Moon – ordinary rock

Isaac Newton (1642 - 1727) 4 Laws of Motion 4 Theory of Gravity

Newton’s Laws of Motion

Describing the Motion 4 position – location 4 velocity – speed and direction 4 acceleration – change in velocity • changing speed • changing direction • both changing

Changes in Motion 4 Galileo – rolling on inclines – inertia • tendency of an object at rest to remain at rest and an object in motion to keep moving

Changes in Motion 4 Newton=s First Law of Motion – An object at rest remains at rest. – An object in motion continues to move in a straight line at a constant speed unless a net force acts on it. – Such motion is called "uniform" 4 Non-uniform motion is accelerated motion.

Orbital Motion 4 non-uniform – object follows a curved path – even if speed is constant 4 First Law º a force must act on it – astronomical objects • force is Gravity

Orbital Motion 4 Law of Gravity – described by Newton – F = GMm/r 2 • • M = mass of one object m = mass of the other object r = distance between the two objects G = 6. 7 x 10 -11 N-m 2/kg 2

Newton's Second Law of Motion 4 F = ma – change in motion depends on force – change in motion depends on mass • mass measures amount of material • more technically, its inertia 4 allows shape of orbit and details of motion to be worked out

Newton's Third Law 4 action = reaction 4 the force that the Earth exerts on you is equal in size to the force you exert on the Earth

Measuring a Body's Mass 4 Newton's laws of gravity and motion allow mass of object to be deduced from orbital motion of object moving around it 4 Example using planets 4 example using Galilean satellites

Gravity 4 Surface Gravity – gravitational force of planet on object – this is the weight of object

Gravity 4 Escape Velocity – speed needed to move away from an object and not fall back – depends on gravitational force – higher speed • mass will go higher • escape velocity for Earth = 11 km/s

Gravity 4 Escape Velocity – atmospheres • low escape velocity • high temperature • little atmosphere – black holes • escape velocity exceeds speed of light