Astronomical Coordinates

Easiest Conceptually: Altitude-Azimuth (AltAz)

Zenith: straight up!

Meridian: N/S line going through the zenith

Altitude: height above the horizon

Zenith angle: 90-Altitude

Azimuth: where great circle connecting star and zenith touches horizon, measured N through E.

Airmass or secz: another measure of altitude is Airmass, which measures path-length through the atmosphere.

For z<60, Airmass=secant(Zenith angle).

What's good about this definition? What's bad about it?

Earth's rotation: Hour angles and such

Stars rise and set, over a 12 hour period. (Thought question: In the northern hemisphere, stars rise in the East and set in the West. What about in the southern hemisphere?)

Transit: When a star crosses the meridian, it is its highest elevation.
Hour angle: How many hours since an object transited. e.g., HA = -2hrs means it is rising and will transit in 2 hours.

So we can think of coordinates on the sky in terms of angles, or time.

Rotating System: Equatorial Coordinates

Define coordinates by the projection of the Earth's pole and equator onto the celestial sphere.

North celestial pole: projection of Earth's north pole
Celestial equator: projection of Earth's equator

Declination (delta): angular distance from the celestial equator (+=north, -=south)

Right Ascension (alpha): angular distance along circles parallel to the equator. Define zero point to be the vernal equinox, the point where the Sun's position crosses the celestial equator as it moves north. Right ascension increases going eastward.

Dec is measured in degrees, minutes of arc, seconds of arc, or decimal degrees.

RA is measured in either time (hr, min of time, sec of time), or in decimal degrees.

So, the coordinates for M87 can be written as

(a,d) = 12:30:49, +12:23:07
(a,d) = 187.705, +12.39619

Measuring in Time: 24hrs=360 degrees, so 1hr=15 deg.

Making your way around an astronomical image

Orientation: unless specified otherwise, standard orientation is north up and east to the left. This is flipped from terrestrial maps.

Scale: you are looking at a curved surface projected onto a plane. Distortions abound!

Common system: gnomic or tangent plane projection

One big, common clanger: coordinate distances are not angular separations!

For small separations (where tan(theta)~theta), we can say

dDec(deg)=(Dec1 - Dec2)


dRA(deg)=(RA1-RA2)*cos(Dec) (if RA is measured in degrees)
dRA(deg)=15*(RA1-RA2)*cos(Dec) (if RA is measured in hours)


d=sqrt(dDec^2 + dRA^2).

But for larger separations this won't work.

Finally, solid angle is a measure of area on the sky, and has units of steradians (for big areas; 4pi=sphere) or square degrees or square arcseconds (for small areas).


The system is tied to the Earth's rotational axis. But the Earth's axis shifts with time, due to precession, over a periodic cycle of 25,800 years. This means coordinates are constantly changing!

Rate of change:  360o/25800yr = 0.14o/yr = 50"/yr. Over 50 yrs, this is about 42', > half a degree!

So every coordinate must include an epoch. "B1950" refers to coordinates based on the 1950 pole position; "J2000" refers to coordinates based on the 2000 pole position. And for precise coordinate, you must correct your coordinates to be accurate to the present.

Local Sky

Think about

Observing run prep: Skycalendar/Skycalc by John Thorstensen

The Galactic Coordinate System

The equatorial system is very useful for the mechanics of observing. But its physical meaning is tied to the Earth. What about a galactic coordinate system?

l: galactic longitude
b: galactic latitude

Galactic center: l=0, b=0

Direction of motion: l=90, b=0

The Earth's axis is tipped from the galactic plane by about 80 degrees or so, so the equatorial and galactic coordinate systems are nearly at right angles to one another.

A handy-dandy visual calculator to transform coordinates, courtesy of level 5.

And NED's Coordinate Converter

Time: Sidereal vs Solar

The Earth is spinning on its axis and orbiting the Sun. This means that a solar day (defined as noon-to-noon) is different from a sidereal day (defined as one Earth rotation).

Mean Solar day: 24hrs
Sidereal day: 23hrs, 56min

This means that a fixed star rises 4 mins earlier each successive night, or two hours earlier each month.

We define the Local Sidereal Time to be the RA which is currently transiting.

Now see how LST, RA, and HA fit together:


Julian Dates

We want a date system which just counts days (not day/month/year/leapdays, etc). The Julian Date system does this.