Health Warning! This is not necessarily everything you need to know from this lecture! I maintain exactly what you need to
know through the first few lectures as some people add the course late. But these questions are to help with just the most difficult concepts in
some lectures. If you want to discuss any of these concepts more, come see me during office hours.
Some questions to think about regarding understanding coordinates on the Celestial Sphere
What is zenith?
Say you are standing at the North Pole (latitude of 90°N). What is the declination of a star directly at zenith?
Say you are standing at the Equator (latitude of 0°N). What is the declination of a star directly at zenith?
Say you are standing in Laramie (latitude of about 40°N). What is the declination of a star directly at zenith?
Say you walk from the Equator to the North Pole. How does the declination of a star at zenith change as you walk north?
Think about the exact same set of questions for someone in the Southern Hemisphere of the Earth (e.g., South Pole, 40°S, etc.)
What is the horizon?
Say you are standing at the North Pole (latitude of 90°N). What is the declination of a star directly on the horizon?
Say you are standing at the Equator (latitude of 0°N). What is the declination of a star directly on the horizon?
Say you are standing in Laramie (latitude of about 40°N). What is the declination of a star directly on the horizon?
This one is subtle! Remember that you can see over the North Pole as well as down into the Southern Hemisphere
Say you walk from the Equator to the North Pole. How does the declination of a star on the horizon change as you walk north?
Think about the exact same set of questions for someone in the Southern Hemisphere of the Earth (e.g., South Pole, 40°S, etc.)
It will be helpful if you can learn to draw a diagram to always answer these sorts of questions.
The Right Ascension of stars changes with longitude but also with time of day and time of year
Why is Right Ascension ("Right", if you're interested, because it increases as you look east ... "Left" would be west) trickier than declination?
Right ascension is often measured in hours (strictly speaking in "hours of arc"), not degrees. 360° is a full circuit. 24 hours is a full circuit. Therefore, how many degrees are in one hour?
There are 360° in a circle (all the way around the Earth east-to-west), let's say you have a friend who lives 1° west of Laramie. How would a star that was at zenith in Laramie look to your friend at the same time of night, i.e., how far from zenith would it be?
I will continue to say "zenith" in the next few questions. But, the critical concept for Right Ascension isn't really your zenith, because of the
stars' East-West motion and the fact that stars rarely get directly overhead...it's your meridian (the north-south line that passes through zenith)
Let's say you have a friend who lives 15° west of Laramie. How would a star that was at zenith in Laramie look to your friend at the same time of night, i.e. how far from zenith would it be?
Let's say you have a friend who lives 90° west of Laramie. How would a star that was at zenith in Laramie look to your friend at the same time of night, i.e. how far from zenith would it be? How close to the horizon would it be?
Right Ascension is tricky because the Earth is turning. The Earth turns 360° in 24 hours (1 day) from west to east (which is why the stars, and Sun, seem to move east to west). How many degrees does the Earth turn in an hour? Remember your friend who lives 15° west of Laramie, how does the star that was at zenith in Laramie look to your friend one hour after you see it, i.e. how far from zenith is it?
Remember your friend who lives 90° due west of Laramie. How many hours does that friend have to wait before your star is at zenith for them (directly over their heads)? The fact that the Right Ascension of stars changes with time as well as position is why you can't use the stars to measure your longitude, like you can use them to measure your latitude, unless you have an accurate timepiece to keep track of the hours. John Harrison became a multi-millionaire in the 1760s by building such a timepiece.
Unfortunately, it's worse than this. Draw a diagram of the Earth orbiting the Sun in 4 equal positions over the period of a year. Consider what "day" and "night" mean in this diagram (when is the Sun in the sky as viewed from Earth)? How do the stars that are visible at night change over the course of a year?
It will be helpful if you can learn to draw diagrams to always answer these sorts of questions.
Harder but still helpful for real understanding of stars in the sky
Stars (just as is true for the Sun) appear to rise in the east (towards, say, Japan, "the land of the rising sun") and set in the west. If you stand at the North Pole, however, stars appear to just skim around the horizon (because the Earth turns around an axis through the poles). These stars are "circumpolar". If you stand at the equator, stars appear to rise due east, go right over your head, and set due west (again, because the Earth turns around an axis through the poles).
Say you are at the North Pole. Stars apear to orbit on the horizon. If you walk 90° south to the equator, stars orbit directly overhead (through zenith). The stars have tilted by 90° from horizon to zenith as you walked 90° to the south.
Say you are at the North Pole. Pick a star that is right on the horizon. You walk 1° to the south so you are at a latitude of 89°N. How does your star look over the course of the night? Where does it rise? Where does it set? How many degrees above the horizon does it get? Does it get higher above the horizon to the north or south (remember, if you walked 90° to the south the star would go all the way over your head)?
Say you are at the North Pole. You walk 10° to the south so you are at a latitude of 80°N. How does the same star look over the course of the night? Where does it rise? Where does it set? How many degrees above the horizon does it get? Does it get higher above the southern or northern horizon?
Say you live at 40°N (close to Laramie). How does the same star look over the course of the night? Where does it rise? Where does it set? How many degrees above the horizon does it get? Does it get higher above the southern or northern horizon?
Armed with the last 3 examples, how would you use your star of choice to determine your latitude on Earth (this, by the way is how people used to determine their latitude before Global Positioning Systems)?
Zero hours (or 0°) Right Ascension is the point in the sky where the Sun crosses the equator (specifically, where the ecliptic intersects the celestial equator) on the first day of spring...the spring equinox (~March 21)
Why is 12 hours (180°) Right Ascension where the Sun is in the sky near September 21?
Where are 6 hours and 18 hours of Right Ascension? Can you picture the Earth going around the Sun and draw the directions that correspond to different Right Ascensions?
What is the rough Right Ascension of a star that is in the night sky on March 21? (Remember: The Right Ascension of the Sun on March 21 is 0 hours or 0°)
