Lecture 3: The Sun-Earth-Moon System Coordinate Systems, Moon Phases, Tides, and Calendars Elizabeth Charlton, 2016 1 Elizabeth Charlton, 2016 2 ! Used to describe the apparent size of an object or the apparent distance between objects in space. http://coolcosmos.ipac.caltech.edu/cosmic_classroom/cosmic_reference/angular.html Elizabeth Charlton, 2016 3 ! Usually expresses in degrees, arcminutes, and arcseconds " 1°=1/360 of a circle " 1 arcmin = 1’= 1/60 of a degree " 1 arcsec = 1’’ = 1/60 of an arcmin =1/3600 of a degree Elizabeth Charlton, 2016 4 ! Rough Estimates " Extending your fist against the night sky should cover roughly 10 degrees " Your thumb should cover roughly 2 degrees " Your little finger should cover roughly 1 degree https://www.timeanddate.com/astronomy/measuring-the-sky-by-hand.html Elizabeth Charlton, 2016 5 ! Angular Measurements and Distance " the parsec – corresponds to the distance at which the mean radius of the earth’s orbits subtends an angle of one arcsecond. " measure used for large distances outside the solar system. " equal to about 3.26 light-years Elizabeth Charlton, 2016 6 By Srain at English Wikipedia - This image is an altered version of :Image:Stellarparallax2.svg, which is an SVG version of :Image:Stellarparallax2.png. Stellarparallax2.svg was released into the public domain by its creator, Booyabazooka., Public Domain, https://commons.wikimedia.org/w/ index.php?curid=4196613 Elizabeth Charlton, 2016 7 ! For objects such as the Sun and stars, we cannot directly perceive their distance ! Historically the sky was perceived as a sphere with little lights on it Earth within celestial sphere" by Tfr000 (talk) 20:06, 29 March 2012 (UTC) - Own work. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/ File:Earth_within_celestial_sphere.gif#mediaviewer/File:Earth_within_celestial_sphere.gif Elizabeth Charlton, 2016 8 ! The apparent eastward path of the Sun throughout the year " the plane of the Earth’s orbit "Ecliptic with earth and sun animation" by Tfr000 (talk) 16:54, 15 March 2012 (UTC) - Own work. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons - http:// " tilted with respect to the commons.wikimedia.org/wiki/File:Ecliptic_with_earth_and_sun_animation.gif#mediaviewer/ File:Ecliptic_with_earth_and_sun_animation.gif celestial equator due to the tilt of the Earth’s axis (23.5o) Elizabeth Charlton, 2016 9 ! Equinox – point where the ecliptic crosses the celestial equator ! Solstice – point where the ecliptic and celestial equator are at the maximum 23.5o separation "Earths orbit and ecliptic" by Tfr000 (talk) 01:59, 15 March 2012 (UTC) - Own work. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons - http:// commons.wikimedia.org/wiki/File:Earths_orbit_and_ecliptic.PNG#mediaviewer/ File:Earths_orbit_and_ecliptic.PNG Elizabeth Charlton, 2016 10 ! Just like the curved surface of the earth has a coordinate system … ! So does the sky, 2 systems in fact " Altitude and Azimuth " Right Ascension and Declination Elizabeth Charlton, 2016 11 ! Also known as the Horizontal coordinate system " The observer’s local horizon is the fundamental plane separating the hemisphere’s " Altitude – or elevation. The angle between the object and the local horizon " Azimuth – the angle of the object around the horizon " Zenith – the point directly overhead " Zenith Distance – the distance from zenith Elizabeth Charlton, 2016 12 "Azimuth-Altitude schematic" by TWCarlson - http://commons.wikimedia.org/wiki/ File:Azimut_altitude.svg. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Azimuth-Altitude_schematic.svg#mediaviewer/ File:Azimuth-Altitude_schematic.svg Elizabeth Charlton, 2016 13 ! Celestial Coordinate System – Analogous to the Longitude-Latitude Coordinate System on Earth " The projection of the Earth’s equator onto the Celestial Sphere is the fundamental plane (units: degrees arcsec arcmin) " Right Ascension – Measures the angular distance of an object eastward along the celestial equator from the vernal equinox (units: hr min sec) " Declination – Measures the angular distance of an object perpendicular to the celestial equator Elizabeth Charlton, 2016 14 "Ra and dec demo animation small" by Tfr000 (talk) 20:50, 17 April 2012 (UTC) - Own work. Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons - http:// commons.wikimedia.org/wiki/File:Ra_and_dec_demo_animation_small.gif#mediaviewer/ File:Ra_and_dec_demo_animation_small.gif Elizabeth Charlton, 2016 15 Elizabeth Charlton, 2016 16 ! The observed motion of the Sun and Stars is due to the motions of the Earth – rotation, revolution, precession "AxialTiltObliquity" by Dna-webmaster - self-made by Dna-webmaster; earth-image from NASA. Licensed under Creative Commons Attribution 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/ File:AxialTiltObliquity.png#mediaviewer/File:AxialTiltObliquity.png Elizabeth Charlton, 2016 17 ! Observing from the Earth, how does the Sun move? " Daily Motion " Yearly Motion Copyright © James B. Kaler. All rights reserved. These contents are the property of the author and may not be reproduced in whole or in part without the author's express consent except in fair use for educational purposes. Thanks to reader number counter on blogger. Elizabeth Charlton, 2016 18 ! Daily Motion – What do we observe? " Due to the rotation of the Earth " Day – 86,400 SI seconds (24 hours) is the Astronomical unit of time " Astronomical Definitions ! Mean Solar Day – average time of a single rotation of the planet with respect to the Sun (average over the year = 24 hours) ! Sidereal Day – an entire rotation of the planet with respect to the stars (3min 56sec shorter than solar day) Elizabeth Charlton, 2016 19 ! Sidereal Day is shorter than the Solar Day 1 to 2 is one sidereal day 1 to 3 is one solar day "Sidereal day (prograde)". Licensed under Creative Commons Attribution-Share Alike 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/ File:Sidereal_day_(prograde).png#mediaviewer/File:Sidereal_day_(prograde).png Elizabeth Charlton, 2016 20 ! Yearly Motion – What do we observe? " Due to the revolution of the Earth " Year – A Julian year is defined as exactly 365.25 days of 86,400 SI seconds (24 hours). " Other Astronomical Years ! Sidereal Year – the time it takes the Earth to complete one revolution with respect to the fixed stars (fixed frame of reference) ! Tropical year – the time it takes the Sun to return to the same position in the cycle of the seasons (for example: vernal equinox to vernal equinox) Elizabeth Charlton, 2016 21 ! Using the position of the Sun or stars to keep time " Astrolabes " Sundials "Iranian Astrolabe 14" by Jacopo Koushan (User:Jacopo188)Photograph by Masoud Safarniya "Equatorial sundial topview" by WillowW - Own work. Licensed under Creative Commons Attribution 3.0 (User:M.safarniya) - Own work. Licensed under Creative Commons Attribution-Share Alike 3.0 via via Wikimedia Commons - http://commons.wikimedia.org/wiki/ Wikimedia Commons - http://commons.wikimedia.org/wiki/ File:Equatorial_sundial_topview.gif#mediaviewer/File:Equatorial_sundial_topview.gif File:Iranian_Astrolabe_14.jpg#mediaviewer/File:Iranian_Astrolabe_14.jpg Elizabeth Charlton, 2016 22 ! At local noon the sun is at its highest point in the sky (crosses the meridian) ! This is different for every longitude " Time Zones – Offset from Universal Time "Meridian on celestial sphere" by Tfr000 (talk) 16:56, 18 June 2012 (UTC) - Own work. Licensed under CC BY-SA 3.0 via Commons - "World Time Zones Map" by TimeZonesBoy - Own work. Licensed under Creative Commons Attribution- https://commons.wikimedia.org/wiki/ Share Alike 3.0 via Wikimedia Commons - http://commons.wikimedia.org/wiki/ File:Meridian_on_celestial_sphere.png#/media/ File:World_Time_Zones_Map.png#mediaviewer/File:World_Time_Zones_Map.png File:Meridian_on_celestial_sphere.png Elizabeth Charlton, 2016 23 ! How does the motion of the sun depend on the time of year? ! How does the motion of the sun depend on the location of the observer? Elizabeth Charlton, 2016 24 ! At the equator – path during the solstices "Solstice-0" by Tauʻolunga - Own work. Licensed under Creative Commons Attribution-Share Alike 2.5 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Solstice-0.jpg#mediaviewer/ File:Solstice-0.jpg Elizabeth Charlton, 2016 25 ! At 20o latitude – path during the solstices "Solstice-20" by Tauʻolunga - Own work. Licensed under Creative Commons Attribution-Share Alike 2.5 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Solstice-20.jpg#mediaviewer/ File:Solstice-20.jpg Elizabeth Charlton, 2016 26 ! At 50o latitude – path during the solstices "Solstice-50" by Tauʻolunga - Own work. Licensed under Creative Commons Attribution-Share Alike 2.5 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Solstice-50.jpg#mediaviewer/ File:Solstice-50.jpg Elizabeth Charlton, 2016 27 ! At 70o latitude – path during the solstices "Solstice-70" by Tauʻolunga - Own work. Licensed under Creative Commons Attribution-Share Alike 2.5 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Solstice-70.jpg#mediaviewer/ File:Solstice-70.jpg Elizabeth Charlton, 2016 28 ! At 90o latitude – path during the solstices "Solstice-90" by Tauʻolunga - Own work. Licensed under Creative Commons Attribution-Share Alike 2.5 via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:Solstice-90.jpg#mediaviewer/