Horizon Diagrams & The Celestial Sphere From geometry, it is easy to see that angle p, the elevation of the celestial pole from the horizon, is equal to angle l, the latitude. This is very important in navigation, as it allowed ancient sailors to tell their latitude by measuring the elevation of the celestial pole (in the Northern Hemisphere, this is easy because Polaris, a bright star lies near enough to the pole.) So if you're ever lost, you know how to find your latitude- the elevation of the celestial pole. Note also that the celestial equator always intersects the horizon exactly at East and West, wherever you are. To find the celestial equator, find the pole first. Look 90° one way, then the other, these are East and West. Then turn round through 180° so you're facing the opposite way. At this point (opposite the pole) the equator is at an elevation from the horizon of (90° - your latitude), and it runs from East, through this point, then down to meet the horizon again at West. It will help you if you learn where the celestial pole and equator are where you live. Now you can see how the stars appear to move: following the line of the celestial equator, rotating around the pole. Yearly Motion As I mentioned earlier, the stars daily rotation is just over a full circle, about 1° over- because the Earth has moved about 1° round the sun. This means that over the course of a year, the stars appear to complete one whole turn. If you went out and looked at a particular constellation over a period of months at the same time, it would appear to slowly move around the pole in the same direction as the daily motion- about 30° (or 2 hours of Right Ascension) a month. This also means that the constellations obscured by daylight slowly come round to be visible at night as the year progresses. So do I get to see all the stars on the celestial sphere at some point? Well, not usually, unless you live exactly on the equator. The pole is inclined at an angle equal to your latitude, so the equator is below the horizon at an angle of (90° - your latitude). Stars above the declination of 90° - your latitude never set. For instance, I live at 51° latitude, so the pole is at an elevation of 51°. Stars at 39° declination at their lowest point just touch the horizon, and all the stars at a declination above 39° never set: (Note the diagram is drawn illustrating the Northern Hemisphere, but it applies equally in the Southern Hemisphere, if you reverse the directions.) Angle l is your latitude. The stars inside the white line never set, either daily or yearly. Outside this line the stars rise and set at different times of the day and year. Conversely, looking opposite the pole: The stars below the white line, those with a declination greater than 90° - your latitude below the equator at their highest point still are below the horizon, so they never rise, either daily or yearly. This means you only ever see stars in your Hemisphere (declination greater than 0° in the Northern hemisphere and declination less than 0° in the Southern hemisphere), and the stars in the other hemisphere with a declination of 90° minus your latitude. Assignment: On the horizon diagram below, add the NCP, the observer’s Zenith and the Celestial Equator for our location at approximately 49 degrees North latitude. Identify the observer’s north and south horizon lines: Make horizon diagrams for the following four locations. Identify the cardinal directions (N,S,E,W), the NCP and/or SCP, the CE, the observer’s Zenith and the horizon lines on each diagram (ie: what areas of the celestial sphere are visible to an observer at each location?) Los Angeles, CA (latitude 34N) North Pole (latitude 90N) Equator (latitude 0 degrees) Sydney, Australia (latitude 34S) Using your horizon diagrams, answer the following questions: 1. Would the star Agena (dec -60.22”) be visible to an observer located in Los Angeles? Explain. 2. Add in the rotation of the celestial sphere around the axis of the NCP for each of your four horizon diagrams. 3. Add in the star track of Vega (dec +38.47”) on each of your horizon diagrams. Is Vega circumpolar at any location or not visible from any location? Explain.
