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