Positions on the Celestial Sphere

1. Positions on the Celestial Sphere • How to locate (and track) objects from a spinning, orbiting platform in space….

2. Homework 1 due Tuesday Jan 15

3. Pointing and Tracking Astrophysical Objects Frisco Peak Telescope – Pointing and Tracking Precision less than 10 arcsec (Angle subtended by a penny at roughly 200 yards) Frisco Peak Telescope Control Panel 1 radian=206,264.98 arcsec

4. Positions on the Celestial SphereThe Altitude-Azimuth Coordinate System • Coordinate system based on observers local horizon • Zenith - point directly above the observer • North - direction to north celestial pole NCP projected onto the plane tangent to the earth at the observer’s location • h: altitude - angle measured from the horizon to the object along a great circle that passes the object and the zenith • z: zenith distance - is the angle measured from the zenith to the object z+h=90 • A: azimuth - is the angle measured along the horizon eastward from north to the great circle used for the measure of the altitude

5. Equatorial Coordinate System • Coordinate system based on a projection of the Earth’s geographic poles and equator onto the celestial sphere • Celestial Poles - Points on celestial sphere intersected by line coincident with Earth’s rotation axis. North and South. • Celestial Equator - Projection of Earth’s Equator onto the the celestial sphere. • : Declination - The latitudinal angle measured from the celestial equator to the object along a great circle that passes through the object and the celestial poles. Objects north of the celestial equator have declinations in the range from 0 to +90 degrees. Objects south of the celestial equator have declinations in the range from 0 to -90 degrees. • : Right Ascension - The longitudinal angle measures the angle of how far east an object lies from the Vernal Equinox. • : Vernal Equinox - Point on celestial equator where the path of the sun crosses the celestial equator.

6. Positions on the Celestial SphereMeridian • Meridian- Imaginary line through the Zenith and North Celestial Pole extended along a great circle on the celestial sphere to the northern and southern horizon

7. Positions on the Celestial SphereHour Angle and Local Sidereal Time • Local Sidereal Time (LST) - The amount of time that has elapsed since the Vernal Equinox (point) last traversed the local meridian. • Hour Angle- The hour angle (HA) of an object is equal to the difference between the current local sidereal time (LST) and the right ascension (α) of that object:

8. Precession of the Equinoxes • Due to slow wobble of Earth’s rotation axis caused by Earth’s non-spherical shape and gravitational interaction with the Sun and planets • Precession period is 25,770 years • Pole will sweep out a circle on the sky with angular diameter of nearly 47 degrees!!! • Impacts the values of RA and DEC of objects over time ==> Epochs. The change in values of RA and DEC from their values in the year 2000.0 are given by:

9. Even More Astronomical Coordinate Systems… Other coordinate systems may be more appropriate … For instance mapping objects in the milky way is best done using galactic coordinates Conversions between coordinate systems are possible…with a little math!!!

10. Changes in the Sky • Coordinates continuously changing in alt-az system for all celestial objects (except geo-stationary satellites) • Earth’s rotation • Earth’s orbit about Sun • Proper motion of objects • The moon • Planets • Asteroids • Comets • Satellites…. Milky Way From Frisco Peak. Paul Ricketts 

11. Earth’s Rotation • Earth’s rotation is responsible for the “rapid” motion of objects through the sky Mud springs point 2 hour exposure of NCP. Paul Ricketts

12. Tilt of Earth’s Axis • The rotation axis of the Earth is tilted at 23.5 degrees from the normal of the Ecliptic plane.

13. The Sun’s motion in the skySeasonal Changes • The Sun’s motion across the sky changes over the course of the year. This is due mainly to the tilt of the Earth’s rotation axis. • The maximum angular height above the horizon at a location in the Northern Hemisphere is maximum on the Summer Solstice and minimum on the Winter Solstice. This results in sunlight being spread over a larger area during Winter causing a reduction in heating of the surface of the Earth at Northern latitudes during Winter. • The values of the Sun’s RA and DEC change over the year as shown in the graph.

14. Earth’s Orbit about the Sun Due to the Earth’s motion about the Sun : • Line of sight to the sun sweeps through the constellations. The sun apparently moves through the constellations of the zodiac along a path known as the Ecliptic • The constellations that are visible each night at the same time changes with the season • A given star will rise approximately 4 minutes earlier each day The Ecliptic.The path of the sun through the year in equatorial coordinates.

15. What is a day? • The period (sidereal) of earth’s revolution about the sun is 365.26 solar days. The earth moves about 1 around its orbit in 24 hours. • Solar day • Is defined as an average interval of 24 hours between meridian crossings of the Sun. • The earth actually rotates about its axis by nearly 361 in one solar day. • Sidereal day • Time between consecutive meridian crossings of a given star. The earth rotates exactly 360 w.r.t the background stars in one sidereal day = 23h 56m 4s

16. Annalemma • The curve traced on the sky by the position of the Sun at local noon over the course of the year. • The change in altitude (declination) is the result of the tilt of the earth’s rotation axis. • The change in hour azimuth (hour angle) is due mainly to the variation in the length of the solar day resulting from the Earth’s elliptical orbit. • For more info see.… • http://www.annalemma.com

17. Proper Motions Celestial objects may have their own proper motion…including stars, galaxies… Radial motion is along the line of sight. Transverse motion is the component of motion perpendicular to the line of sight to the object.

18. Measurements of Time • Gregorian Calendar - Calendars which label months and dates for each year need to account for the fact that Earth’s revolution period is not an integer number of days…--> Leap Years, Leap Seconds,… • Julian Date - Astronomers typically refer to the times when observations were made in terms of elapsed time since some specified zero time. The zero time that is used is noon on January 1,4713 BC…JD0.0. The Julian date of J2000.0 is JD2451545.0. Times other than noon Universal time are specified as a fraction of a day. MJD=JD-2400000.5. MJD begins at midnight instead of noon…

19. Celestial Sphere and Spherical Trigonometry Law of Sines Law of Cosines for sides Side= arc of great circle Angle=angle between sides Sum of angles of spherical triangle<180 degrees Law of Cosines for angles

20. Celestial Sphere and Spherical Trigonometry Want to find opening angle Dq Given Da andDd Apply law of sines Small angle approximation Apply law of cosines Small angle approximation (again) Angular distance in terms of changes in RA and DEC

21. Celestial Sphere and Spherical Trigonometry from a rotating platform http://en.wikipedia.org/wiki/Celestial_sphere "A Compendium of Spherical Astronomy".

22. Planetarium/Telescope Control Software Starry Night Stellarium Your Phone…