Astronomy. A Study of the Planets, Solar System, and Universe My Notes. Richard Pichora. Copyright 2017, 2018 Richard Pichora

Transcription

1 Astronomy A Study of the Planets, Solar System, and Universe My Notes Richard Pichora Copyright 2017, 2018 Richard Pichora

2 This page intentionally left blank II

3 Contents Astronomy... 1 Astronomy Mathematics... 1 Constants... 1 Astronomical Unit... 1 Light Year... 1 Parsec... 1 Meter... 1 Speed of Light... 2 Astronomical Unit of Time... 2 Tropical Year... 2 Light Year for Unit Distance... 2 Mean Solar Day... 2 Mean Solar Day... 2 Mean Sidereal Day... 2 Mean Sidereal Day... 2 Sidereal Year... 2 Sidereal Year... 2 Anomalistic Year... 2 Anomalistic Year... 2 Civil Year... 2 Sidereal Day... 3 Sidereal Year... 3 Tropical Year... 3 Anomalistic year... 3 The Ecliptic... 3 Trigonometric Functions... 4 Useful Formulae... 5 Absolute Magnitude... 5 Absolute Magnitude... 5 Apparent Magnitude... 5 Distance Magnitude... 6 III

4 Difference in Magnitude... 6 Distance and Parallax... 6 Light Gathering Power... 6 Resolving Power... 6 Faintest Star Visible in any Telescope... 7 True and Apparent Angular Fields... 7 Image Scale at Prime Focus... 7 Magnification... 7 Magnification Prime Focus Photography... 7 F Ratio... 8 Eyepiece Projection Photography... 8 Length of Star Trails on Film... 8 Area Covered by Photography... 8 Conversion of One Degree of Latitude/Longitude to Meters... 9 Rotation of Earth... 9 Transit of Celestial Objects... 9 Conversion of Days and Decimal Days to Hours, Minutes, Seconds... 9 Conversion of Days, Hours, Minutes, Seconds to Days and Decimal Days Time Zones Johannes Kepler 3 Laws of Planetary Motion Miles to Kilometers The Moon Radius Distance Periods of the Moon Inclination The Planets Definition Planet Information Dwarf Planet Definition Dwarf Planet Names IV

5 Pluto s Moons Planet and Dwarf Planet Comparison The Zodiac Star Configurations Winter W Summer Triangle Winter Triangle Reference V

6 Astronomy Astronomy is the study of the sun, moon, stars, planets, comets, gas, galaxies, gas, dust and other non-earthly bodies and phenomena. Astronomy Mathematics Constants Astronomical Unit (1) (AU) An astronomical unit is the distance from the Sun to the Earth. 149,597,870.0 KM x 10 8 KM x M LY x 10-5 LY parsecs x 10-6 parsecs Light Year (2) (LY) The distance light travels in one (1)-year x KM x M 63, AU parsecs Parsec (3) A unit of astronomical length based on the distance from Earth at which stellar parallax is one second of arc 1 2 = ½ = O 1 AU/2 = 149,597,870/2 = 74,789,935 KM adj = opp/tan(ά) = 74,789,935/tan( ) = x KM x KM x M ly 206, AU Meter (3) x AU x LY x parsecs 1

7 Speed of Light (c) (1) 299, KM/S x 10 5 KM/S x 10 8 M/S Astronomical Unit of Time (1) 1 day = 24 hours 1 day = 1440 minutes 1 day = 86,400 seconds Tropical Year (1) days x 10 7 seconds Light Year for Unit Distance (1) seconds minutes Mean Solar Day (4) 1 mean solar day = mean sidereal days 1 mean solar day = 24 hours 03 minutes seconds of sidereal time Mean Solar Day (3) 1 mean solar day = 86,400 seconds Mean Sidereal Day (4) 1 mean sidereal day = mean solar days 1 mean sidereal day = 23 hours 56 minutes seconds of mean solar time Mean Sidereal Day (3) 1 mean sidereal day = 86, seconds Sidereal Year (16) 1 sidereal year = mean solar days Sidereal Year (3) 1 sidereal year = x 10 7 seconds Anomalistic Year (16) 1 anomalistic year = mean solar days Anomalistic Year (3) 1 anomalistic year = x 10 7 seconds Civil Year (16) 1 civil year = days 1 civil year = days during leap year 2

8 Sidereal Day (16) The interval of two successive passages of a catalogue equinox across a given meridian. It is divided into 24 sidereal hours. The sidereal day is 3 minutes 56 seconds shorter than the mean solar day. Sidereal Year (16) The average time the Earth takes to complete one (1)-revolution measured with respect to a fixed direction in space Tropical Year (16) The year measured by the changing seasons, is that which the mean longitude of the Sun moves through 360 O The interval between two successive passages of the sun through the vernal equinox Anomalistic year (16) The time period between two successive passages of the earth through the perihelion of its orbit The Ecliptic (33) Approximately 23 ½ O Year 1980 = 23 O ( O ) 3

9 Trigonometric Functions 4

10 Useful Formulae Magnitude M = Absolute Magnitude m = Apparent Magnitude D = Distance in Parsecs Absolute Magnitude (5) M = m log D Example: D = 1.7 m = 1 M = * log(1.7) M = * M = M = Absolute Magnitude (6) M = m 5 * log(d 10 parsecs) Example: D = 1.7 m = 1 M = 1 5 * log(1.7 10) M = 1 5 * log(0.17) M = 1 5 * M = 1 ( ) M = Apparent Magnitude (7) m = 5 log D 5 + M Example: D = 1.7 M = m = 5 * log(1.7) m = 5 * m = m = m = m = 1.0 5

11 Distance Magnitude (7) log D = (5 + m M) 5 Example: M = m = 1 log(d) = ( ) 5 log (D) = log (D) = D = 1.7 Difference in Magnitude (39) d = difference in magnitude of two (2)-objects d = difference in brightness 5 Note: is an approximation. The true number is 100, or about A difference in magnitude of 5 should be 100 times in brightness. Distance and Parallax (10) p = parallax of object in seconds of arc r = distance in parsecs o r = 1/p o p = 1/r Light Gathering Power (40) Calculate the light gathering power of a telescope or binoculars L = Light gathering power of the instrument D 1 = Diameter of the first instrument D 2 = Diameter of the second instrument (the eye) L = D 1 2 / D 2 2 Example: D 1 = 150 mm telescope (6 ) D 2 = human eye (7mm) L = = 22, = A 150mm telescope will gather 459 times the light as the human eye. Resolving Power (11) I = Diameter in inches of the instrument C = Diameter in centimeters of the instrument r = Resolving power of the instrument in seconds of arc r = 4.6/I r = 11.7/C Note: This is under perfect seeing conditions 6

12 Faintest Star Visible in any Telescope (22) D = Diameter of telescope in inches δ = Diameter of the eye pupil in inches m = Apparent magnitude m = 6.5 5log δ + 5 logd Note: This is under the most favorable conditions and is assuming the human eye can see (unaided) an object with an apparent magnitude of 6.5 Example: Pupil diameter = 7mm (0.28 ) Telescope = 150mm (6 ) M = * log(0.28) + 5 * log(6) m = * ( ) + 5 * m = 6.5 (-2.764) m = m = True and Apparent Angular Fields (18) M = Magnification of ocular on a telescope α = Apparent angular field θ = True angular field θ = α / M M = α / θ Image Scale at Prime Focus (19) h = linear height in the same units as F F = Focal length θ = Angular height of object in degrees h = θf / 57.3 Magnification (14) F = Focal length of telescope f = Focal length of eyepiece M = Magnification M = F / f Magnification Prime Focus Photography (15) θ r = Angular size of object in radians θ d = Angular size of object in degrees F = Focal length of telescope X = Measured distance on film of object in the same units as F X = Fθ r X = 0.017Fθ d 7

13 F Ratio (9) F ratio = Focal Length / Diameter Diameter = Focal Length / F Ratio Example: Telescope Focal Length = 750 mm Telescope Diameter = 150mm F Ratio = 750 / 150 = 5 Eyepiece Projection Photography (23) EFL = Effective Focal Length DF = Distance from the center of the eyepiece to the film EFL = DF * (telescope focal length) / (eyepiece focal length) Length of Star Trails on Film (24) Photography with a Stationary Camera l = tf(cosξ)/13,750 l = length of star trails t = exposure time in seconds F = focal length of lens in millimeters ξ = declination of star Area Covered by Photography (27) A = 2 arctan (S/2F) A = Angle in degrees S = Side of frame in millimeters F = focal length in millimeters 35 mm frame = 24 mm X 36 mm Example: 28 mm lens = o X o 50 mm lens = o X o 80 mm lens = o X o 200 mm lens = 6.87 o X o 750 mm lens = 1.83 o X 2.75 o 8

14 Conversion of One Degree of Latitude/Longitude to Meters (12) (Circumference of earth) / (360 o ) X COS of latitude equals the length of 1 o of longitude More exact: (13) Φ = latitude 1 o of latitude in meters = 111, (COS 2 Φ) (COS 4 Φ) 1 o of longitude in meters = 111, (COS Φ) (COS 3 Φ) (COS 5 Φ) Rotation of Earth (9) Time = Arc 1 hour = 15 o 1 minute = 15 1 second = 15 Arc = Time 1 o = 4 minutes 1 = 4 seconds 1 = seconds Transit of Celestial Objects (32) Objects will cross the meridian earlier on succeeding days: 4 minutes earlier each day 1 hour earlier each 15 days Conversion of Days and Decimal Days to Hours, Minutes, Seconds (9) 1. Multiply decimal portion of day by 24. This will give the number of hours. 2. Multiply the decimal portion of hours by 60. This will give the number of minutes. 3. Multiply the decimal portion of minutes by 60. This will give the number of seconds 4. Use the integer portion of the results of each for the final Hours-Minutes-Seconds Example: day 6.56 of March * 24 = * 60 = * 60 =24.0 Answer: March 6 1:26:24 PM 9

15 Conversion of Days, Hours, Minutes, Seconds to Days and Decimal Days (9) 1. Divide seconds by Add to minutes 3. Divide minutes by Add to hours 5. Divide hours by Add to days Example: March 6 1:26:24 PM / 60 = = / 60 = = / 24 = = 6.56 Answer: Day 6.56 of March Time Zones (9) UT = Universal Time EST = Eastern Standard Time EDT = Eastern Daylight Time CST = Central Standard Time CDT = Central Daylight Time MST = Mountain Standard Time MDT = Mountain Daylight Time PST = Pacific Standard Time PDT = Pacific Daylight Time AKST = Alaska Standard Time AKDT = Alaska Daylight Time Hawaii = Hawaii Time Zone HAST = Hawaii -Aleutian Standard Time HADT = Hawaii - Aleutian Daylight Time UT 5 hours = EST UT 4 hours = EDT UT - 6 hours = CST UT 5 hours = CDT UT 7 hours = MST UT 6 hours = MDT UT 8 hours = PST UT 7 hours = PDT UT 9 hours = AKST UT 8 hours = AKDT UT 10 hours = Hawaii UT 10 hours = HAST UT 9 Hours = HADT 10

16 Johannes Kepler 3 Laws of Planetary Motion (17, 30, 31) 1. Each planet follows an elliptical path around the Sun, which is at one focus of the ellipse. 2. An imaginary line, or spoke, connecting the planet with the Sun sweeps across equal areas of space in equal time. 3. If two or more planets are compared, the length of each planets year proves to be related in a perfectly regular way to its average distance from the Sun. The distance cubed is always proportional to the square of the planet s period, or year: d 3 = p 2 d = Distance in Astronomical Units p = Period in Earth years p = d d d = d 3/2 3 d = p p = p 2/3 Miles to Kilometers (37) 1 mile = KM Miles * = KM KM / = miles 11

17 The Moon Radius (34) 1738 km Distance (34) Average distance from earth = 384,400 km Periods of the Moon (34) Sidereal period = days (Fixed star to fixed star) Synodic period = days (New Moon to New Moon) Inclination (34) 5 O 8 43 to the ecliptic (5.145 O ) 12

18 The Planets Definition (35) A celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighborhood around its orbit Planet Information Each of the planets in our solar system, our Sun, and our Moon, has a corresponding symbol. The characteristics of our planets and solar system include (28) (29) (36) (38) : Object Average Distance from Sun Diameter Orbital Period Rotation Name The Sun 1,391,016 KM 34 earth days Mercury 57.9 million KM (0.387 a.u.) 4,878 KM 88.0 earth days 58.6 earth days Venus million KM (0.723 a.u.) 12,104 KM earth days 243 earth days Earth million KM (1.0 a.u.) 12, KM 1 year 24 hours Mars million KM (1.524 a.u.) 6,794.4 KM earth days 24.6 earth hours Jupiter million KM (5.203 a.u.) 142,796 KM earth years 9.93 earth hours Saturn 1,427 million KM (9.539 a.u.) 120,000 KM earth years earth hours Uranus 2,869 million KM ( a.u.) 50,800 KM earth years 17.2 earth hours Neptune 4,496.6 million KM ( a.u.) 48,600 KM earth years 16.1 earth hours The planets from largest to smallest: 1. Jupiter 2. Saturn 3. Uranus 4. Neptune 5. Earth 6. Venus 7. Mars 8. Mercury Planet Name (Number of Moons) Name of Moon(s) Mercury (0) Venus (0) Earth (1) Moon Mars (2) Phobos Deimos Jupiter (67) Adrastea S/2003 J2 Aitne S/2003 J3 Amalthea S/2003 J4 Ananke S/2003 J5 G = Galilean Satellite Aoede S/2003 J9 Arche S/2003 J10 Autonoe S/2003 J12 13

19 Callirrhoe S/2003 J15 Callisto (G) S/2003 J16 Carme S/2003 J18 Carpo S/2003 J19 Chaldene S/2003 J23 Cyllene S/2011 J1 Dia S/2011 J2 Elara Erinome Eukelade Euanthe Euporie Europa (G) Eurydome Ganymede (G) Harpalyke Hegemone Helike Hermippe Herse Himalia Io (G) Iocaste Isonoe Jupiter LI Jupiter LII Kale Kallichore Kalyke Kore Leda Lysithea Megaclite Metis Mneme Orthosie Pasiphae Pasithee Praxidike Sinope Sponde Thebe Themisto Taygete Thelxinoe Thelxinoe Saturn (62) Aegaeon Aegir Albiorix Anthe Atlas Bebhionn Bergelmir Bestla Calypso Daphnis Dione Enceladus Epimetheus Erriapus Farbauti Fennir Forjot Greip Hati Helene Hyperion Hyrrokkin Iapetus Ijiraq Janus Jarnsaxa Kari Kiviuq Loge Methone Mimas Mundlifari Narvi Paaliaq Pallene Pan Pandora Phoebe Polydeuces Prometheus Skathi Skoll Surtur Suttungr Tarqeq Tarvos 14

20 Telesto Tethys Thrymr Titan Ymir S/2004 S7 S/2004 S12 S/2004 S13 S/2004 S17 S/2006 S1 S/2006 S3 S/2007 S2 S/2007 S3 S/2009 S1 Uranus (27) Cordelia Ophelia Bianca Cressida Desdemona Juliet Portia Rosalind Mab Belinda Perdita Puck Cupid Miranda Francisco Ariel Umbriel Titania Oberon Caliban Stephano Trinculo Sycorax Margaret Prospero Setebos Ferdinand Neptune (14) Triton Nereid Naiad Thalassa Despina Galatea Larissa Proteus Halimede Psamathe Sao Laomedeia Neso S/2004/N1 The Planets and their Moons (29) Dwarf Planet Definition (35) A celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, (c) has not cleared the neighborhood around its orbit, and (d) is not a satellite Dwarf Planet Names (29) Ceres o Pluto o Dwarf planet Ceres is the largest object in the asteroid belt between Mars and Jupiter and the only dwarf planet located in the inner solar system. It was the first member of the asteroid belt to be discovered when Giuseppe Piazzi spotted it in And when Dawn arrived in 2015, Ceres became the first dwarf planet to receive a visit from a spacecraft. Discovered in 1930, Pluto was long considered our solar system's ninth planet. But after the discovery of similar intriguing worlds deeper in the distant Kuiper Belt, icy Pluto was reclassified as a dwarf planet. Findings by NASA's New Horizons in 2015 revealed for the first time how that Pluto is a complex and mysterious world. Information about Pluto and its 15

21 Eris o Haumea o Makemake o largest moon, Charon, provide insight into the collision believed to have formed the dwarf planet and moons we see today. It takes icy Eris 557 Earth years to complete a single orbit around our sun. The plane of Eris' orbit is well out of the plane of the solar system's planets and extends far beyond the Kuiper Belt, a zone of icy debris beyond the orbit of Neptune. All the asteroids in the asteroid belt would easily fit inside Eris. However, Eris, like Pluto, is still smaller than the Earth's Moon. Oddly-shaped Haumea is one of the fastest rotating large objects in our solar system. It completes a turn on its axis every four hours. The quick spin elongated the dwarf planet into the unique shape astronomers discovered in It is roughly the same size as Pluto. Like Pluto and Eris, Haumea orbits our Sun in the Kuiper Belt, a distant zone of icy objects beyond the orbit of Neptune.It takes 285 Earth years for Haumea to make one orbit around our sun. Along with fellow dwarf planets Pluto and Haumea, Makemake is located in the Kuiper Belt, a region outside the orbit of Neptune. Astronomers believe it is slightly smaller than Pluto. It takes 310 Earth years for this dwarf planet to make one orbit around our Sun. Pluto s Moons (29) The known moons of Pluto are: Charon: Discovered in 1978, this small moon is almost half the size of Pluto. It is so big Pluto and Charon are sometimes referred to as a double planet system. Nix and Hydra: These small moons were found in 2005 by a Hubble Space Telescope team studying the Pluto system. Kerberos: Discovered in 2011, this tiny moon is located between the orbits of Nix and Hydra. Styx: Discovered in 2012, this little moon was found by a team of scientists searching for potential hazards to the New Horizons spacecraft flyby in

22 Planet and Dwarf Planet Comparison (29) What makes a planet according to the definitions adopted by the International Astronomical Union: Characteristic Planet Dwarf Planet Is in orbit around the Sun X X Has sufficient mass to assume a nearly round shape X X Is not a satellite X X Has cleared the neighborhood around its orbit X Has not cleared the neighborhood around its orbit X 17

23 The Zodiac Name Dates Description Aries March 21 April 20 The Ram Taurus April 21 May 21 The Bull Gemini May 22 June 21 The Twins Cancer June 22 July 23 The Crab Leo July 24 August 23 The Lion Virgo August 24 September 23 The Maiden Libra September 24 October 23 The Scales Scorpio October 24 November 22 The Scorpion Sagittarius November 23 December 21 The Archer Capricorn December 22 January 20 The Goat Aquarius January 21 February 19 The Water Bearer Pisces February 20 March 20 The Fish Star Configurations Winter W Procyon Sirius Betelgeuse Rigel Aldebaran Summer Triangle Deneb Altair Vega Winter Triangle Procyon Sirius Betelgeuse 18

24 Reference 1. Planetary and Lunar Coordinates for the Years page 310 Prepared by: H.M. Nautical Almanac Office Royal Greenwich Observatory and The Nautical Almanac Office United States Naval Observatory 2. My own calculations based on the speed of light per second multiplied by the number of seconds in a tropical year. Both constants are defined in reference #1. 3. My own calculations 4. The Astronomical Almanac 1997 page B6 Issued by: U.S. Naval Observatory and Royal Greenwich Observatory 5. Asimov on Astronomy by Isaac Asimov; page Principles of Astronomy by Stanley Wyatt; third edition; page My own calculations based on formulae in reference # 5 8. Entry removed 9. Based on acquired knowledge 10. Principles of Astronomy by Stanley Wyatt; third edition; page A Field Guide to the Stars and Planets by Donal H. Menzel and Jay M. Pasachoff; page Astronomy Magazine 13. The Astronomical Almanac page K5 14. Principles of Astronomy by Stanley Wyatt; third edition; page Principles of Astronomy by Stanley Wyatt; third edition; page The Facts on File Dictionary of Astronomy Edited by Valerie Illingworth 17. The Attractive Universe; Gravity and the Shape of Space by E.G. Valens; pages Amateur Astronomer s Handbook by J.B. Sidgwick; page Amateur Astronomer s Handbook by J.B. Sidgwick; pages 52, 346, Entry removed 21. Entry removed 22. Amateur Astronomical Handbook page Astronomy Magazine February 1978 pages Sky and Telescope Magazine August 1989 page

25 25. Entry Removed 26. Mathematical Physics by Donald H. Menzel; page Astronomy Magazine September 1989 page SKYGUIDE A Field Guide for Amateur Astronomers by Mark R. Chartrand III 29. NASA web site 30. Asimov On Astronomy by Isaac Asimov; pages The Facts on File of Astronomy edited by Valerie Ellingworth; Pages Dynamic Astronomy Sixth Edition by Robert T. Dixon; pages The Astronomical Companion by Guy Ottewell; Pages The Astronomical Companion by Guy Ottewell; Pages International Astronomical Union (IAU) web site 36. The Astronomical Almanac page K7 37. Metric Units and Conversion Charts by Theodore Wildi; Page The Planets by The Smithsonian Institute 39. Principles of Astronomy by Stanley Wyatt; third edition; page Principles of Astronomy by Stanley Wyatt; third edition; page