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Astronomy Sec. 3 08/31/
Terrestrial Globe [globe, voyage/set location] Meridians( Latin for midday) and parallels. Latitude (N/S of Equator) and longitude (E/W of Prime Meridian). Directions. East is rotational direction. Relative directions. Measures in degrees(°), arcminutes(‘), and arcseconds(“). 1° = 60’ = 3600”. Meridians converge at poles (length of 1 degree of longitude shrinks as poles are approached). Zenith and nadir (Arabic for “overhead” and “opposite of overhead”). 3. Days and Time - Sidereal day. 23h 56m = time for 360° rotation [globe, voyager view from sun]. - Apparent solar day. Range is 24h +-30s = time between successive sunrises, etc. Corrosponds to 360°-362° rotation. Earth’s changing orbital speed and tilted axis cause the variation. - Mean Solar day. 24h 00m= average length of the apparent solar day (wristwatch time). - Time Zones. About 15° wide, make travel convenient. Each longitude really has its own apparent solar time. 3. Years and Calendars - Sidereal year. 365.2564 days = time for one true orbit (360° revolution).
- tropical year. 365.2422 days = time for season repetition (359°. revolution.) - Gregorian calendar. Instituted 1582 to match calendar to the tropical year, I.E., the seasons. Rule: years have 365 days usually, but have 266 days when the year is… [divisible by 4] AND [not divisible by 4000] AND [if a century year, divisible by 400]. Thus, average length of year = 365 + ¼ - 1/4000 – 3/400 = 365. days
Metric System and Powers of Ten Metric units and prefixes, powers of ten, astronomical data [book]
Practice with Big Numbers Keck 10 m telescope; 70M$ = 70 x 10 to the 6th^ $ = new 737 Annual ground-based astronomy budget (mainly NASA & NSF): ~300 M$ = 2 big movies HST, spread over 10 years: 1.5 G$ = 1.5 x 10(to the 9th) $
Astronomy Sec. 4 08/31/
Law of 72 After n years of growth at given annual % rate (APR), accumulation is (1+ APR/100)^n times the original amount. Example: after 5 years with APR = 3%, the growth factor is (1+0.03)^5 (1.03)^5 = 1. Doubling time in years is T double = 0.693/ = 72 years/ 1n (1+APR/100) = APR 4. The celestial Sphere [sphere, p2, voyager Help/Basic concepts]. Reality for ancients, computational convenience for moderns. Stars actually at various distances. Features based on Earth’s axis: Celestial poles – Celestial Equator – Celestial meridians and parallels. Celestial meridians converge at poles. These features move relative to the stars over 26,000 years due to precession of Earth’s axis [Voyager demo Basics/ Prec of the Eq] Features based on Earth’s orbit: [voyager cel. Sph. w/ ecl. Coord.] Ecliptic – ecliptic plane – ecliptic poles. The Zodiac. Stars like Polaris are fixed for our lifetime, but not over thousands of years. Eqyptians had a different north star.
4.3 Altazimuth Coordinates [globe, p3, altaz, math guide dwg, voyager local hor. w/ altaz. Coord.] Specify directions relative to observer on ground, depending on observer’s position and the time. Coordinates are… Altitude (alt.): Angle above below horizon (=0°) Azimuth (az.): angle clockwise relative to due North (=0°). Meanings of N, S, E, W. 4. Equatorial Coordinates [spere, eq, voyager local hor. w/ eq. coord.) Specify directions relative to celestial meridians and parallels. Therefore, are almost time-independent (but precession causes the coordinates to very slowly change). Coordinates are… Declination (De., or ) Angle N or S of celestial equator )=0° 00’ 00”) celestial poles at +-90° Right Ascension (A.A., or a): Angle E vernal Equinox (= 0(h)00(m)00(s). Measures in time units, where 360° = 24 hours. Vernal Equinox in sun’s celestial meridian on first day of spring in northern hemisphere (exactly 12 h of daylight.) 4. Seasons [Flashlight & globe, JP] Daylight amounts. Season dates. USA vs. Chile. Heating vs. sunlight’s angle of incidence. Combined effect of illumination time, angle of incidence, and distance from sun. Role of atmosphere’s thermal inertia. 4.6 Precession [falling wheel] A spinning wheel’s responses to torques (twisting forces). Earth is a gyro with 26,000 year period (tabletop example]. Therefore, celestial poles and equatorial coordinates slowly change, and seasonal cycle (tropical year) < 360° orbital time (sidereal year). Sidereal year - tropical year = (1/26,000) x 365.2564 days = 20 minutes
Astronomy Sec. 5 08/31/
Sections: 8.1-8.2, 8.4-8.5, 8.7, 8.10-8. 5. Long-term astronomical Influences on Climate Milankovitch hypotheses (1920): Apart from variations in sun’s light, solar heating depends on ellipticity of Earth’s orbit, and on inclination and precession of Earth’s axis. All three vary with time, so Earth’s climate should also vary. Supporting evidence only recently [Fig. 2-12] Ellipticity: Other planets’ gravitational tug on Earth, parallel to ecliptic plane, cause its orbit’s ellipticity to vary over ~10(to the 5th) yr: Aphelion/perihelion distance ratio can be as high as 1.15. Inclination: Other planets’ tugs on Earth, perpendicular to its orbital plane, cause the inclination of the axis to oscillate between 22° and 24.5° over 41,000 yr. This affects the contrast between seasons. 5. Planetary Motions Names and order. Planets orbit in the same direction, and all orbits are roughly in the ecliptic plane [demonstrator, Voyager]. The naked-eye planets, their appearance to the eye. Special locations: conjunction, opposition, and maximum elongations (inner planets only). (When they’re in conjunction with the sun (Mercury and Venus) 5. Lunar Orbit and Phases Elliptical orbit, mean radius 1.3 light sec, inclined 5° to ecliptic plane [JP]. Sidereal period 27.3 d = lunar day also. Phase names, shapes, and causes [JPs, flashlight & Moon]. Synodic period = 29.5 days (how long it takes the moon to go around the Earth). Riding and setting times of the phases. Takes a month for moon to go around the Earth. Phases: Crescent, Waxing Crescent, half moon (1/4), waxing Gibbous, full, waning Gibbous, Third Quarter, Waning Crescent Half of the moon is always lit by the Sun.
5.4 Origin of Tides Earth and Moon orbit their center of mass, ¼ Earth radius below Earth’s surface [model]. Moon’s tidal force = difference in the Moon’s gravitational force between any two parts of the Earth. Tidal and centrifugal forces distort Earth’s oceans and its rocky globe (20 cm) into a football shape [draw]. Ocean-bottom friction holds ocean’s bulge ahead of the Earth-Moon axis! Water tide doesn’t point straight toward the Moon 5. Lunisolar Tides Sun also causes tides on Earth, but the effect is half the Moon’s. Two spring and two neap tides occur per synodic month, when lunar and solar tides reinforce or partly cancel each other. Spring Tides – High tides and Low Tides 5. Astronomical Effects of Tides [p15a] Regular variations in thickness of tidal sediment layers from 9x 10(to the 8th) yr ago reveal the year had 481 days of 18.2 hr, and the month lasted 23.4 present days, meaning the Moon was 10% closer! Now: Moon’s orbital radius grows 3.8 cm/yr, and Earth days lengthen ~0.002 sec/century [p15b] Causes: ocean-bottom friction and Earth’s “leading” tidal bulge. Reasoning: layers vary regularly in thickness and composition. Annual variations in the layering mark the passage of one year (a constant). Four neap-spring layers mark one month, so the number of months per year can be counted. The number of layers per month gives the number of days per month. (So days have been shorter in the past according to layers in ground)
Stonehenge (ca. 3000-1000 BC) – most famous ancient stone structure [4 JPs. Cartoon]. Demonstrates recognition of solar, lunar, seasonal (agricultural), and eclipse patterns. – Heel stone – where the sun rises on the first day of summer. 57 – 3 x 19 = cycle of solar eclipses takes 19 years – after 3 times they repeat. 6. A Half-Millennium of Greek Astronomy (500 BC-100 AD) Pythagoras (500s BC) – spherical Earth is center of Universe, surrounded by 8 concentric celestial spheres and air [sphere]. Their uniform circular motion produces inaudible music of the spheres. Aristotle (300s BC) – 56 spheres. Deduced spherical shape of Earth. Non-detection of stellar parallax made him believe Universe is geocentric [try]. Eratosthenes (200s BC) – Estimates Earth’s circumference (~10% high) [JP]. Aristarchus (200s BC) – Geometrically determined that Sun is 19x farther than Moon (via phase timings) and 7x bigger than Earth (via total eclipses and observed size of Earth’s shadow). Correct values are 400x and 109x. Concluded Sun is at center of Universe, and stars are distant. Hipparchus (100s BC) – Used off-center circles (eccentrics) for Sun’s and Moon’s orbits in his geocentric model to produce observed variations in their “orbital speeds [sketch]. Ptolemy (100s AD) – Devised epicycles, deferents and equants to explain retrograde motion of planets (an asymmetry: Mercury’s and Venus’s epicycles centered on Earth-Sun axis) [JP].
Sec. 7 08/31/
A “century” of European Astronomy (1540-1620) Nicolaus Copernicus o [2JPs] Re-emphasized heliocentric model as simpler and better than geocentric model in De Revolutionibus Orbium Coelestium (1543) [demonstrator]. Heliocentric model predicted gibbous and crescent phases for Mercury and Venus, whereas geocentric one predicted only crescents. However, predicted planetary positions were not much better (only good to within 2 degrees = 4 moon diameters). [F&E 5/27]. Reminder: Aristarchus also though Universe was helopcentric. Nicholas of Cusa (1400?-1464), cardinal and philosopher, wrote that Earth is not center of Universe, other celestial bodies are like Earth, and all follow non-circular paths. Tycho Brahe o [JP] He and his staff observed Sun, Moon, and planets daily (1576-96) with best precision yet (1/7 moon diamtere). Described the “new star” supernova SN 1572 in De Stella Nova (1573). Johannes Kepler o [JP] Succeeded Tycho in 1601, used Tycho’s data to discover three laws of planetary motion: the first two are in Astronomia Nova (1609), third is in Harmonice Mudi (1619). First Law: orbits are ellipses. Second Law: equal areas (radius vector area will always be the same). Third Law: [period P in yr](to the 2nd) = [semimajor axis A in AU](to the 3rd) [F&E 12/07]. Galileo Galilei o [4 JPs, telescope] Professor at Padua and Pisa who began automatic observations with 30 mm telescope in 1609, and reported them in Sirereus Nuncius (1610). Some demystified the heavens: sunspots [p35], solar rotation, and lunar feature. Others supported the heliocentric model: Jovian disk and satellites, and gibbous Venus. 7.
Sect. 8 08/31/
Newton and Orbits Newton used his laws of motion to derive and improve Kepler’s laws Kelper #1: Planetary orbits are ellipses with the Sun at one focus. Newton: (1) orbits can also be circles, parabolas, or hyperbolas, and (2) the objects orbit their center of mass [JP, model]. Kelper #2: A planet’s radius vector sweeps out equal areas in equal time. Newton: same. Kepler #3: p^2= A^3 Newton: p^2 = A^3 (1+ MPLanet/ MSun) 8. Circular Orbits For an orbit of radius A and period P [stopper], Orbital velocity is Vcirc = 2(pie)A/ P Escape velocity is just Vesc = squareroot2 Vcirc = 1.4 Vcirc 8. Electromagnetic (EM) Radiation EM radiation is light. EM waves are traveling ripples in the patterns of electrical and magnetic force produced by an accelerating electrical charge: a line of electrons would oscillate in response to a passing EM wave. Sometimes a particle (photon) model is better. Wavelength and frequency (f) [wave machine]. Wave speed = c=f (wavelength) in a vacuum (f and wavelength vary inversely. EM spectrum regions [#87]. Different wavelengths cause different color sensations.
Atmosphere is a filter that transmits only optical radio, and some IR and UV to ground [#87]. Air turbulence and light pollution degrade observations, so high observatories are best [p24, p25, p8, 4 JPs]. 8. Optical Telescopes Refractors [show]: Convex objective lens light bends rays to produce image, and eyepieces magnify the image [beaker, laser, lens]. Main defects are chromatic aberration, weights, expense. Reflectors [sketch[: Concave objective mirror at back reflects light rays to produce image [concave mirror]. A secondary mirror reflects image to eyepiece. Main defect is spherical aberration. Mountings allow telescopes to be smoothly moved to compensate for Earth’s rotation. Altazimuth mount: one axle vertical with motors on both axles. Equatorial mount: one axle aimed at the celestial pole with motor on that axle only [HSMO home page]. Newest and notable ground telescope designs seek better performance at lower cost. Features: altazimuth mounts, segmented mirrors, active optics, spin casting, liquid mirrors, robotic control; (like OSU’s telescope) [ JPs, p94, p84, p16, p23, p54, GTC, pp21-25, p26, 11JPs]. – 1789 telescope (reflector, altazimuth)
Focal length (f) = 4800 mm (distance from mirror to image) Light collected depends on mirror’s area = (pie) d^2(4) [partly covered lens] Resolving power is limited by light’s wavelike nature. Smallest resolved angle for visible wavelengths is about 0=116/d(sub)mm), in arcseconds [compute] Eye’s resolution about 60” (max pupil diamtere = 7mm). Air turbulence limit about 1”. Magnification equals ratio of focal lengths: ftelescope/ feyepiece [eyepieces, compute]. Practical minimum and maximum values are 0.2 d(sub(mm)) and 2 d(sub(mm) [compute]. 9. UV, Optical and IR Instruments Cameras: [camera, p160, JP]. Use a telescope’s optics to focus an object’s image onto a detector such as a charge-coupled device (CCD). A CCD is a miniature checkerboard where each square converts the light received into electrical charge that is later “read” by a computer. Filters can be used to select the wavelengths observed. Image processing is the calibration and analysis of these matrix-like image files [3 JPs]. Photometers: Cameras optimized to measure only brightness of objects, especially stars (no imaging). Filters can be used [p68]. Spectrographs: Use a grating or prism to produce an object’s spectrum. A spectrum is a band of light that reveals how much of each color is present. The spectrum is recorded by a camera [CD. Grating, prism; show spectra of flashlight and laser].
