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Positional Astronomy Coordinate Systems

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Positional Astronomy Coordinate Systems Positional Astronomy Observational Astronomy 2019 Part 2 Prof. S.C. Trager Coordinate systems We need to know where the astronomical objects we want to study are located in order to study them! We need a system (well, many systems!) to describe the positions of astronomical objects. The Celestial Sphere First we need the concept of the celestial sphere. It would be nice if we knew the distance to every object we’re interested in — but we don’t. And it’s actually unnecessary in order to observe them! The Celestial Sphere Instead, we assume that all astronomical sources are infinitely far away and live on the surface of a sphere at infinite distance. This is the celestial sphere. If we define a coordinate system on this sphere, we know where to point! Furthermore, stars (and galaxies) move with respect to each other. The motion normal to the line of sight — i.e., on the celestial sphere — is called proper motion (which we’ll return to shortly) Astronomical coordinate systems A bit of terminology: great circle: a circle on the surface of a sphere intercepting a plane that intersects the origin of the sphere i.e., any circle on the surface of a sphere that divides that sphere into two equal hemispheres Horizon coordinates A natural coordinate system for an Earth- bound observer is the “horizon” or “Alt-Az” coordinate system The great circle of the horizon projected on the celestial sphere is the equator of this system. Horizon coordinates Altitude (or elevation) is the angle from the horizon up to our object — the zenith, the point directly above the observer, is at +90º Horizon coordinates We need another coordinate: define a great circle perpendicular to the equator (horizon) passing through the zenith and, for convenience, due north This line of constant longitude is called a meridian Horizon coordinates The azimuth is the angle measured along the horizon from north towards east to the great circle that intercepts our object (star) and the zenith. Horizon coordinates The origin of these angles (coordinates) is the observer Note that this is a left- handed coordinate system! The William Herschel Telescope is an alt-az telescope, as are the VLTs. Horizon coordinates Nearly all big telescopes (diameter ≥ 4m, telescopes built after ~1990, most “classical” radio telescopes) are in alt-az mounts This is the natural coordinate system for these telescopes But this system is dependent on the location of the observer and time of the observation: makes consistent cataloguing of objects difficult! Equatorial coordinates +90º Let’s consider a coordinate system that is tied to the astronomical objects themselves — and preferably those that don’t move! ♈ –90º Equatorial coordinates +90º In equatorial coordinates, the celestial equator is the great circle that intersects both the celestial sphere and the Earth’s equator: it’s the projection of the ♈ equator onto the celestial sphere –90º Equatorial coordinates +90º The declination δ is the celestial latitude and is measured in degrees, with 0º at the equator, +90º at the North Celestial Pole (NCP) — the intersection of the Earth’s north (rotational) pole with the ♈ celestial sphere — and –90º at the South Celestial Pole –90º Equatorial coordinates +90º The right ascension (RA) α is the celestial longitude and is measured in units of time, 0–24 hours, from west to east, with 0h at the Sun’s position when it crosses the equator from ♈ south to north, approximately at noon on 21 March in Greenwich, UK. –90º Equatorial coordinates +90º The position α=0h, δ=0º is called the vernal equinox ♈ this is the sign of the constellation Aries, where the vernal equinox happened 2500 years ago ♈ The equatorial system is a right-handed system –90º Equatorial coordinates +90º Because the Earth precesses around an average direction perpendicular to the ecliptic (the plane of the Earth’s orbit around the Sun) due to the torques exerted on by the Moon, Sun, and Jupiter (more ♈ later!), the equatorial system slowly changes with time. –90º Equatorial coordinates +90º This means that the vernal equinox and the celestial equator move with respect to the distant background objects (galaxies, quasars). There we need to assign an epoch — a date — to ♈ any equatorial coordinate. (We’ll return to this shortly!) –90º Our Gratama Telescope is a polar-axis telescope, as the Isaac Newton The local equatorial system Telescope on La Palma The local equatorial system is used to point polar-axis (or “equatorial”) mount telescopes These telescopes rotate around an axis parallel to the Earth’s rotation axis In the Northern Hemisphere, this means that the primary mount axis always points north The local equatorial system These telescopes track a star by rotation around only one axis Note that this means that the field of the image does not rotate, like it does for an alt-az telescope The local equatorial system In the local equatorial system, the hour angle HA replaces the right ascension: HA=LST–α Here LST is the local sidereal time (which we’ll define shortly!) So knowing the time of day (the LST) and the α,δ of an object, it’s very easy to locate your object with a polar-axis telescope. HA varies from –6 h at the eastern horizon (rising) to 0 h at the zenith to +6 h at the western horizon (setting) Note that the minus sign makes this a left-handed coordinate system! Equatorial coordinates A note about fixed angular sizes in (any) equatorial coordinate system: Fixed angular sizes get longer in longitude of the coordinate system (e.g., right ascension) as one goes goes towards the pole – i.e., towards higher absolute latitude |δ| – by a factor that goes as 1/cos(δ) Galactic coordinates It is sometimes convenient to use the Milky Way itself to define a coordinate system For example, if you want to know the positions of globular clusters relative to the bugle and disk or need an estimate of the interstellar dust extinction or the stellar density towards an object Galactic coordinates It is sometimes convenient to use the Milky Way itself to define a coordinate system For example, if you want to know the positions of globular clusters relative to the bugle and disk or need an estimate of the interstellar dust extinction or the stellar density towards an object Galactic coordinates In galactic coordinates, the plane of the Galaxy defines the (celestial) equator, assuming that the Sun sits exactly in the plane (which isn’t quite true) Galactic coordinates In this system, the galactic longitude l (often written lII) is measured in degrees, with 0º on a line connecting the Sun with the center of the Galaxy (roughly...) and increasing in a right- handed fashion Galactic coordinates The galactic latitude b (bII) is also measured in degrees, with b=0º at the equator. Galactic coordinates The system is precisely defined by the direction of the North Galactic Pole (NGP): h m ↵NGP(B1950) = 192.25◦ = 12 49 δNGP(B1950) = +27.4◦ = +27◦240 and by the Galactic longitude of the North Celestial Pole: lNCP = 123◦ Galactic coordinates The first set of coordinates α=12h49m NCP l=123º implies that the celestial δ=27.4º and galactic equators are tilted by 90º–27.4º=62.6º line of nodes These two great circles cross at two nodes, and the line of nodes that l=33.0º connect them is the axis α=18h49m that transforms one plane to the other Galactic coordinates α=12h49m NCP l=123º The equators cross at δ=27.4º lnode = 123◦ 90◦ = 33◦ B1950 h −m h h m ↵node = 12 49 +6 = 18 49 line of nodes for the ascending node the extra 90º angles in l and α shift from the l=33.0º NCP and the galactic α=18h49m equator to the nodes Galactic coordinates Using the cosine law of spherical trigonometry, one can show that the transformation from α,δ to l,b is cos b cos(l 33◦) = cos δ cos(↵ 282.25◦) − − cos b sin(l 33◦) = cos δ sin(↵ 282.25◦) cos 62.6◦ +sinδ sin 62.6◦ − − sin b =sinδ cos 62.6◦ cos δ sin(↵ 282.25◦) sin 62.6◦ − − where the last equation gives the sign of b — i.e., the proper quadrant of the Galaxy Galactic coordinates To transform from l,b to α,δ use cos δ sin(↵ 282.25◦) = cos b sin(l 33◦) cos 62.6◦ sin b sin 62.6◦ − − − sin δ = cos b sin(l 33◦) sin 62.6◦ sin b cos 62.6◦ − − Note in both transformations that α,δ must be in B1950 coordinates! Other coordinate systems Ecliptic coordinates used mostly for satellite navigation, where knowledge of the Sun–spacecraft angle is critical; uses the plane of the ecliptic as the celestial equator Supergalactic coordinates used for determining the positions of galaxies and clusters of galaxies relative to the Virgo Cluster–Local Group–Coma Cluster plane; rarely used Two issues... 1. Epoch: For the equatorial coordinate system, a date must be specified to know where the vernal equinox was when the positions where defined. Two epochs are commonly used: B1950, based on the Besselian year and refers to the Earth’s orientation at 22h 09m UT on 1949 December 31 J2000, based on the Julian year and refers to the Earth’s orientation at ≈noon in Greenwich UK on 2000 January 1. Nearly all astronomers now use J2000, but older papers use B1950 (and the Galactic coordinate system is specified in B1950) Gaia’s DR2 catalogue will replace Hipparcos in the next few weeks! Two issues..
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