Astronomy Elementary Astronomy

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

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

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

Finding One’s Way in the Sky Ecliptic annual path of the Sun projected on celestial sphere 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 Locating Objects celestial sphere has 2-d surface two numbers to locate an object Origin reference point Units measuring system

Finding One’s Way in the Sky Linear vs. Angular Measurement linear distances meaningless on celestial sphere angular measurements 360o in a circle 60 minutes (`) in one degree 60 seconds (``) in one minute 43o52`34``

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

Latitude and Longitude

Latitude and Longitude

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

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

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

Motion of Heavenly Objects Observations and Explanations

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

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

June 20

July 20

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

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

Northern Summer Northern Winter Southern Summer Southern Winter

Seasons Northern Hemisphere summer solstice vernal equinox (Spring) 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 Northern Hemisphere winter solstice fall equinox 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 Solar Day Sidereal Day time between two successive crossings of the meridian by the Sun 24 hours 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 Tropical Year time for sun to complete one trip around ecliptic 365.242 solar days Sidereal Year time for constellations to complete one trip around the sky 365.256 solar days Difference due to Precession Difference due to precession time between two successive crossings of the meridian by a star 23 hrs 56 min

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

North Star and Precession

North Star

Planets (“wanderers”) 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 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 Opposition planet lies directly opposite the Sun in the sky only occurs for Mars, Jupiter & Saturn Opposition Superior Conjunction Earth Inferior Conjunction

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

Historical Perspective Explanations Historical Perspective

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

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

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

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

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

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

Johannes Kepler (1571 - 1630) analysis of Tycho’s data Three Laws of Planetary Motion Planets move in elliptical orbits with the Sun at one focus. Equal areas in equal times. P2 =k a3

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

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

Law 3 - P2 = ka3 P is the period of the planet how long it takes the planet to complete one orbit a is the length of the semimajor axis

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

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

Newton’s Laws of Motion

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

Changes in Motion 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 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" Non-uniform motion is accelerated motion.

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

Orbital Motion Law of Gravity described by Newton F = GMm/r2 M = mass of one object m = mass of the other object r = distance between the two objects G = 6.7 x 10-11 N-m2/kg2

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

Newton's Third Law action = reaction 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 Newton's laws of gravity and motion allow mass of object to be deduced from orbital motion of object moving around it Example using planets example using Galilean satellites

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

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