# In The Beginning and Cosmology Becomes a Science

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1 In The Beginning and Cosmology Becomes a Science

2 Naked-eye (unaided-eye) astronomy had an important place in ancient civilizations Positional astronomy the study of the positions of objects in the sky and how these positions change importance in navigation Naked-eye (unaided-eye) astronomy the sort that requires no equipment but human vision Extends far back in time, across all cultures British Isles Stonehenge Native American Medicine Wheel Aztec, Mayan and Incan temples Egyptian pyramids

3 Astronomical observations led to the development of the modern calendar The day based on the Earth s rotation The year based on the Earth s orbit The month based on the lunar cycle None of these are exactly the same as nature so astronomers use the average or mean day and leap years to keep the calendar and time consistent

4 Astronomers use angles to denote the positions and apparent sizes of objects in the sky The basic unit of angular measure is the degree ( ). Astronomers use angular measure to describe the apparent size of a celestial object what fraction of the sky that object seems to cover The angular diameter (or angular size) of the Moon is ½ or the Moon subtends an angle of ½.

5 If you draw lines from your eye to each of two stars, the angle between these lines is the angular distance between these two stars

6 The adult human hand held at arm s length provides a means of estimating angles

7 Angular Measurements Subdivide one degree into 60 arcminutes minutes of arc abbreviated as 60 arcmin or 60 Subdivide one arcminute into 60 arcseconds seconds of arc abbreviated as 60 arcsec or 60 1 = 60 arcmin = 60 1 = 60 arcsec = 60

8 Powers-of-ten notation a useful shorthand system for writing numbers

9 Common Prefixes for Powers of Ten Factor Name Symbol (billion) 10 9 Giga- G (million) 10 6 Mega- M (thousand) 10 3 kilo- k (hundredth) 10-2 centi- c (thousandth) 10-3 milli- m (millionth) 10-6 micro- μ (billionth) 10-9 nano- n

10 Astronomical distances are often measured in astronomical units, parsecs, or light-years Astronomical Unit (AU) One AU is the average distance between Earth and the Sun X 10 8 km or million miles Light Year (ly) One ly is the distance light can travel in one year at a speed of about 3 x 10 5 km/s or 186,000 miles/s 9.46 X km or 63,240 AU Parsec (pc) the distance at which 1 AU subtends an angle of 1 arcsec or the distance from which Earth would appear to be one arcsecond from the Sun 1 pc = km = 3.26 ly

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13 The parallax of stars reveals their distances Distances to the nearer stars can be determined by parallax, the apparent shift of a star against the background stars observed as the Earth moves along its orbit Parallax measurements made from orbit, above the blurring effects of the atmosphere, are much more accurate than those made with Earth-based telescopes Stellar parallaxes can only be measured for stars within a few hundred parsecs

14 Barnard s star has a parallax of 0.54 arcsec

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16 The Small Angle Formula D = linear size of object α d a = angular size of object (in arcsec) d = distance to the object D =

17 Small Angle Formula Example On July 26, 2003, Jupiter was 943 million kilometers from Earth and had an angular diameter of Using the small-angle formula, determine Jupiter s actual diameter. D = 31.2" km = km

18 iclicker Question The Sun and full Moon have about the same angular size on the sky of 0.5 degrees. Why? A. the sun and moon are the same size and the same distance from Earth, but always in different parts of the sky. B. the moon is bigger than the sun and farther from Earth C. all spherical objects have the same angular size on the sky D. the moon is smaller than the sun, but closer to Earth E. none of the above

19 Eighty-eight constellations officially cover the entire sky Ancient peoples looked at the stars and imagined groupings Pictures in the sky Different cultures different pictures We still refer to many of these groupings Astronomers call them constellations (from the Latin for group of stars ) Parts are asterisms

20 Modern Constellations On modern star charts, the entire sky is divided into 88 regions Each is a constellation Most stars in a constellation are nowhere near one another They only appear to be close together because they are in nearly the same direction as seen from Earth Need to think in three dimensions

21 The appearance of the sky changes during the course of the night and from one night to the next Stars appear to rise in the east, slowly rotate about the Earth and set in the west. This diurnal or daily motion of the stars is actually caused by the 24-hour rotation of the Earth.

22 Annual Motion The stars also appear to slowly shift in position throughout the year This is due to the orbit of the earth around the sun If you follow a particular star on successive evenings, you will find that it rises approximately 4 minutes earlier each night, or 2 hours earlier each month

23 It was common to imagine that the stars are located on a celestial sphere The celestial sphere is an imaginary object that has no basis in physical reality However it is still a model that remains a useful tool of positional astronomy Landmarks on the celestial sphere are projections of those on the Earth

24 Celestial equator divides the sky into northern and southern hemispheres Celestial poles are where the Earth s axis of rotation would intersect the celestial sphere Polaris is less than 1 away from the north celestial pole, which is why it is called the North Star or the Pole Star. Point in the sky directly overhead an observer anywhere on Earth is called that observer s zenith. Nadir is directly opposite the zenith

25 The Reason for the Seasons

26 The seasons are caused by the tilt of Earth s axis of rotation The Earth s axis of rotation is not perpendicular to the plane of the Earth s orbit It is tilted about 23½ away from the perpendicular The Earth maintains this tilt as it orbits the Sun, with the Earth s north pole pointing toward the north celestial pole

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28 Sept 21 Dec 21 June 21 March 21 The Sun appears to trace out a circular path called the ecliptic on the celestial sphere tilted at 23 ½ degrees to the equator The ecliptic and the celestial equator intersect at only two points Each point is called an equinox The point on the ecliptic farthest north of the celestial equator that marks the location of the Sun at the beginning of summer in the northern hemisphere is called the summer solstice At the beginning of the northern hemisphere s winter the Sun is farthest south of the celestial equator at a point called the winter solstice

29 The Moon helps to cause precession, a slow, conical motion of Earth s axis of rotation

30 Precession causes the gradual change of the star that marks the North Celestial Pole

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32 The Moon s rotation always keeps the same face toward the Earth this is synchronous rotation

33 Ancient astronomers measured the size of the Earth and attempted to determine distances to the Sun and Moon Observations In the town of Syene, the Sun shone directly down a vertical shafts on the summer solstice In Alexandria, the position of the sun changed by 7 or about one-fiftieth of a complete circle Conclusion Around 200 B.C., the Greek astronomer Eratosthenes used 50 x the distance between Alexandria and Syene to get a circumference of the earth of about km (the actual is about kilometers)

34 Aristarchus knew that the Sun, Moon, and Earth form a right triangle at first and third quarter phases Using geometrical arguments, he calculated the relative lengths of the sides of these triangles, thereby obtaining the relative distances to the Sun and Moon

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36 To understand the universe, astronomers use the laws of physics to construct testable theories and models Scientific Method A reiterative process based on observations, logic, and skepticism Hypothesis A concept or idea that seems to explain a phenomenon or set of observations Model A set of hypotheses that have withstood observational or experimental tests Theory A set of related hypotheses can be pieced together into a self consistent description of natural observations Laws of Physics Theories that accurately describe the workings of physical reality, and have stood the test of time and been shown to have great and general validity

37 Ancient astronomers invented geocentric models to explain planetary motions Like the Sun and Moon, the planets move on the celestial sphere with respect to the background of stars Most of the time a planet moves eastward in direct motion, in the same direction as the Sun and the Moon, but from time to time it moves westward in retrograde motion

38 Ancient astronomers believed the Earth to be at the center of the universe They invented a complex system of epicycles and deferents to explain the direct and retrograde motions of the planets on the celestial sphere

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43 Nicolaus Copernicus devised a comprehensive heliocentric model Copernicus s heliocentric (Sun-centered) theory simplified the general explanation of planetary motions In a heliocentric system, the Earth is one of the planets orbiting the Sun The sidereal period of a planet, its true orbital period, is measured with respect to the stars

44 Tycho Brahe s astronomical observations provided evidence for another model of the solar system

45 Parallax apparent difference in position of object viewed from two different locations

46 Johannes Kepler proposed elliptical paths for the planets about the Sun Using data collected by Tycho Brahe, Kepler deduced three laws of planetary motion: the orbits are ellipses With Sun at one focus Equal areas in equal times a planet s speed varies as it moves around its elliptical orbit The period squared equals the semi-major axis cubed the orbital period of a planet is related to the size of its orbit

47 Kepler s First Law

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49 Kepler s Second Law

50 Kepler s Third Law P 2 = a 3 P = planet s sidereal period, in years a = planet s semimajor axis, in AU

51 iclicker Question Kepler discovered his laws of planetary motion primarily from a study of the observations of A Copernicus B Galileo Galilei C Ptolemy D Tycho Brahe E Melvin Laird

52 Galileo s discoveries with a telescope strongly supported a heliocentric model Galileo s observations reported in 1610 the phases of Venus* the motions of the moons of Jupiter* mountains on the Moon Sunspots on the Sun *observations supporting heliocentric model

53 One of Galileo s most important discoveries with the telescope was that Venus exhibits phases like those of the Moon Galileo also noticed that the apparent size of Venus as seen through his telescope was related to the planet s phase Venus appears small at gibbous phase and largest at crescent phase

54 There is a correlation between the phases of Venus and the planet s angular distance from the Sun

55 Geocentric Model Issues To explain why Venus is never seen very far from the Sun, the Ptolemaic model had to assume that the deferents of Venus and of the Sun move together in lockstep, with the epicycle of Venus centered on a straight line between the Earth and the Sun In this model, Venus was never on the opposite side of the Sun from the Earth, and so it could never have shown the gibbous phases that Galileo observed

56 In 1610 Galileo discovered four moons of Jupiter, also called the Galilean moons or satellites This is a page from his published work in 1610

57 Isaac Newton formulated three laws that describe fundamental properties of physical reality Called Newton s Laws of Motion, they apply to the motions of objects on Earth as well as in space a body remains at rest, or moves in a straight line at a constant speed, unless acted upon by an outside force the law of inertia the force on an object is directly proportional to its mass and acceleration F = m x a the principle of action and reaction whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body

58 Newton s Law of Universal Gravitation F = gravitational force between two objects m 1 = mass of first object m 2 = mass of second object r = distance between objects G = universal constant of gravitation If the masses are measured in kilograms and the distance between them in meters, then the force is measured in Newtons Laboratory experiments have yielded a value for G of G = Newton m 2 /kg 2

59 Newton s description of gravity accounts for Kepler s laws and explains the motions of the planets and other orbiting bodies

60 Orbital Motion The law of universal gravitation accounts for planets not falling into the Sun nor the Moon crashing into the Earth Paths A, B, and C do not have enough horizontal velocity to escape Earth s surface whereas Paths D, E, and F do. Path E is where the horizontal velocity is exactly what is needed so its orbit matches the circular curve of the Earth

61 Orbits follow any one of the family of curves called conic sections

62 Gravitational forces between two objects produce tides in distant regions of the universe

63 Understanding Tidal Forces

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70 iclicker Question If the Earth's axis were not tilted with respect to its orbital plane, then A a mean solar day would be longer B a sidereal day would be longer C the tides would be much stronger D there would be virtually no seasons E the period of revolution and rotation would be equal

71 acceleration aphelion conic section conjunction deferent direct motion eccentricity ellipse elongation epicycle focus force geocentric model gravitational force gravity greatest eastern and western elongation heliocentric model hyperbola inferior conjunction inferior planet Kepler s laws law of equal areas law of inertia law of universal gravitation Key Words major axis mass Neap and spring tides Newtonian mechanics Newton s laws of motion Newton s form of Kepler s third law Occam s razor opposition parabola parallax perihelion period (of a planet) Ptolemaic system retrograde motion semimajor axis sidereal period speed superior conjunction superior planet synodic period tidal forces universal constant of gravitation velocity weight

72 Vocabulary angle angular diameter (angular size) angular distance angular measure arcminute arcsecond astronomical unit (AU) Big Bang black hole degree ( ) exponent galaxy gamma-ray burster hypothesis kiloparsec (kpc) laws of physics light-year (ly) megaparsec (Mpc) model

73 Antarctic and Arctic Circles apparent solar day apparent solar time autumnal equinox celestial equator celestial sphere circumpolar constellation declination diurnal motion ecliptic epoch equinox lower meridian mean solar day mean sun meridian meridian transit nadir north celestial pole Vocabulary positional astronomy precession precession of the equinoxes right ascension sidereal clock sidereal day sidereal time sidereal year south celestial pole summer solstice time zone tropical year Tropic of Cancer Tropic of Capricorn upper meridian vernal equinox winter solstice zenith zodiac

74 Vocabulary annular eclipse apogee eclipse eclipse path eclipse year first quarter moon full moon line of nodes lunar eclipse lunar phases new moon partial lunar eclipse partial solar eclipse penumbra penumbral eclipse perigee plane of the ecliptic saros sidereal month solar corona solar eclipse synchronous rotation synodic month third quarter moon totality total lunar eclipse total solar eclipse umbra waning crescent moon waning gibbous moon waxing crescent moon waxing gibbous moon

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