Astronomical coordinate systems. ASTR320 Monday January 22, 2018

Transcription

1 Astronomical coordinate systems ASTR320 Monday January 22, 2018

2 Special public talk this week: Mike Brown, Pluto Killer Wednesday at 7:30pm in MPHY204

3 Other news Munnerlyn lab is hiring student engineers REU program application deadlines are approaching Homework #1 assigned

4 The Earth rotates about its axis Rotates west to east The sun rises and sets...

5 The Earth revolves about the Sun

6 The Earth rotates about its axis

7 Where was this picture taken?

8 Earth s annual and diurnal motion have various consequences Days, seasons (obvs) Location of Sun in the sky changes seasonally From Earth, the Sun appears to move in the sky along the ecliptic No, this is not an astrology class Difference in length of Solar and sidereal (star-based) day Solar day: average length of a day throughout the year Sidereal day: length of time it takes a star to return to the same place in the sky ~4 minutes shorter than a Solar day Summer (winter) solstice: Sun is at its highest (lowest) point in the sky Vernal, Autumnal equinox: day and night are of equal length Ecliptic: path of sun against background stars

9 Astrometry Measure the position of stars on the celestial sphere

10 Constellations The International Astronomical Union (IAU) divides the sky into 88 regions that it officially recognizes as constellations Equirectangular plot of the location in the sky of modern constellations. From wikipedia.org.

11 Angular measures 360 degrees in a circle 60 arcminutes in a degree 60 arcseconds in an arcminute ½ degree = angular size of Sun & Moon All astronomers know that there are arcseconds in 1 radian

12 Coordinate systems In astronomy we deal with spherical coordinate systems A spherical coordinate system is defined by two great circles, one goes through the poles of the other

13 Coordinate systems Any two great circles can define a celestial coordinate system, but only a few make sense: Coordinate system Principal great circle Prime meridian Altitude-azimuth Observer s horizon North-south meridian Equatorial/ celestial Ecliptic Galactic Projection of Earth s equator Plane of Earth s revolution Plane of Milky Way Head of Aries vernal equinox Head of Aries vernal equinox Galactic center Coordinates Altitude, azimuth Right ascension, α, declination δ Right ascension, α, declination δ Galactic longitude, l, Galactic latitude, b

14 The altitude-azimuth (observer s, horizon) coordinate system To use, need to know: North, horizon, zenith Zenith: point directly above the observer Altitude: angle from horizon to object along a great circle passing through zenith Azimuth: angle from N, measured along horizon Meridian passes through zenith and N,S pole points h=altitude z=zenith distance, 90 -h A=azimuth

15 That s nice, but But what if you want to tell an astronomer at another observatory to point their telescope at the object you just observed? A more general coordinate system, based on Earth s latitude/longitude system, would be more useful Celestial equator: projection of the Earth s equator onto the sky North celestial pole: Earth s rotation axis projected onto the sky (where the North Star is) Note also a challenge of the Alt-Az system is that the coordinates of a star in the sky changes throughout the night!

16 Equatorial coordinate system Right ascension, α, measured from the vernal equinox. Measured in hours, minutes, and seconds of time Declination, δ, measured from the celestial equator to the celestial poles. Measured in degrees, minutes, and seconds From Mihalas & Binney, Galactic Astronomy

17 Equatorial coordinate system For the advanced user: the Astronomical triangle Hour angle, t (an important angle for observers) Zenith angle, Z Parallactic angle, P (important, e.g., in spectroscopy and other applications where one needs to understand the effects of atmospheric refraction, which are always along the vertical circle) From Kaler, The Ever-Changing Sky.

18 Ecliptic coordinate system The ecliptic is the path of the Sun in the sky (Earth s orbital plane). The obliquity of the ecliptic is 23 o 27'. The moon orbits within 5 o of the ecliptic. Planets orbit within 7 o 0' of the ecliptic (except Pluto 17 o 09'). Zodiacal light, zodiacal dust, lie along this plane Intersection of the ecliptic and celestial equator define the vernal equinox (location of the Sun on March 21) and autumnal equinox (location of the Sun on Sep. 22). The Vernal equinox defines the zero-point of the right ascension coordinates. Ecliptic coordinate system is used mainly for objects in Solar System From Mihalas & Binney, Galactic Astronomy

19 Galactic coordinate system The Galactic equator is chosen to be that great circle on the sky approximately aligned with the Milky Way mid-plane. This plane is inclined by 62 o 36' to the celestial equator. The North Galactic Pole is at α = 12 h 49 m, δ = ' in 1950 equinox, and best observed at night in the Northern Hemisphere spring From Mihalas & Binney, Galactic Astronomy

20 Galactic coordinate system Galactic latitude, b, is measured from the Galactic equator to the Galactic poles. Galactic longitude, l, is measured eastward around the equator in degrees. The definition of l = 0 o is given by the location of the Galactic Center. From

21 Galactic coordinate system Use an Eulerian transformation to convert between coordinate systems (here, e.g., equatorial to Galactic): sinb = sinδ sinδ NGP - cosδ cosδ NGP sin(α - α 0 ) cos(l - l 0 ) cosb = cos(α - α 0 ) cosδ sin(l - l 0 ) cosb = sinδ cosδ NGP + cosδ sinδ NGP sin(α - α 0 ) With the definition of the North Galactic Pole: equinox α NGP δ NGP α 0 l :49.0 = o 27:24 12:51.4 = o 27:08 18:49.0 = o o 18:51.4 = o o

22 Precession of the equinoxes The precession of the Earth is a 25,800 year periodic wobble of the direction of the Earth's axis of rotation. This is a major effect that can be detected nightly, and which has a large effect on coordinates over the period of years.

23 Precession of the equinoxes Why does this happen? Because the Earth spins, it is in fact a little fatter around the equator by one part in 298. The Earth is 43 km larger in diameter across the equator than from pole to pole (a radius of 6378 km toward the equator compared to 6357 km toward the poles). Being 0.33% closer to the Earth's center at the pole, translates to 0.67% greater weights measured on the surface of the Earth at the poles than at the equator.

24 Precession of the equinoxes Because the Moon orbits the Earth in a plane that is within 5 degrees of the ecliptic, typically the Moon is not aligned with the Earth's equatorial bulge (unless the Moon is on the Celestial Equator). Thus the Moon generally is at an angle to the equatorial bulge, and tugs on the Earth's bulge. There are also smaller contributions from the Sun and planets attempting gravitationally to do the same thing (the Sun is only on the celestial equator twice a year and at all other times of the year it is pulling the Earth's bulge toward the ecliptic plane). These external forces on the spinning Earth creates the precessional "wobble" in the Earth's motion. From Abell's Exploration of the Universe, Ed. 3.

25 Precession of the equinoxes For the Earth, the precession acts to slowly change the direction that the Earth's rotational pole points. The direction of the Earth's North and South Celestial Poles rotate to different points on the Celestial Sphere with a 25,800 year cycle. The orbital axis of the Earth stays fixed in space but the rotational axis constantly changes direction. From Kaler, The Ever-Changing Sky.

26 Precession of the equinoxes Presently the Earth's North Pole points to Polaris, but 14,000 years ago it pointed towards Vega. The star gamma Cephei is the next northern pole star (it will be 3 degrees from the NCP in 2200 years). Note that it is not the location of the rotational pole on the Earth that is changing, but where that pole points on the Celestial Sphere Note also that if the direction of the poles is changing, so too is the direction of the equator of the Earth as projected on the sky.

27 Precession of the equinoxes If the position of the celestial poles and equators are changing on the celestial sphere, this means that the celestial coordinates of objects, which are defined by reference to the celestial equator and celestial poles, must also be constantly changing. Because of this change in the direction of the Earth's pole with time, the coordinate systems of RA and Dec that we adopt for one epoch are actually different for other epochs. The effects are quite noticeable, almost an arcminute per year along the ecliptic. What this means to you as an observer: when you give the coordinates of an object you also must specify the year that corresponds to those coordinates (because they will be significantly different in future years). This specified year for the coordinates is called the equinox of the coordinates. NOTE: A common mistake made by even senior astronomers is to call the year of the coordinates the "epoch" of the coordinates. This is wrong.

28 Precession of the equinoxes Astronomers tend to use "standard" years, like 1950, 2000, 2050 when they cite the Equinox of the coordinates. Presently we see most people using "J2000.0" coordinates. Coming to a telescope with coordinates precessed to the wrong year is a common mistake by observers. A mistake of 50 years in the coordinate system (most typical) will generally move your object of interest off a typical CCD field of view.

29 Precession of the equinoxes Because the plane of the Earth's orbit is fixed, the position of the ecliptic is fixed. But since the position of the Celestial Equator is changing, the position of the Vernal and Autumnal Equinoxes (where the Celestial Equator and the ecliptic cross) slowly shifts with time. In this figure, if the NCP is coming at you, the front side of the Celestial Equator is going down and the back side of the Celestial Equator is going up. This means that the position of the Vernal Equinox is sliding to the left (or, to the right from the Earth's point of view). The motion of the equinoxes is westward along the ecliptic because of the motion of the equator. From Kaler, The Ever-Changing Sky.

30 Precession of the equinoxes Since in a 25,800 year period the Vernal Equinox will slide 360 degrees, the annual motion of the Vernal Equinox (and Autumnal Equinox) is 360 o /(25800 yrs) = 50.3"/yr. Since the Vernal Equinox is slipping, the dates when the Sun is in a given constellation slowly changes. That s why the months associated with certain "signs of the zodiac" no longer match with the Sun's true position with respect to them the original definition of the dates of the "houses" happened a long time ago! From Kaler, The Ever-Changing Sky.