(Originally just a copy of brief notes posted in my astronomy lab class; to be considerably expanded in its next iteration)
The Motion of the Sun
When the Sun is up, the sky is too bright to see any stars, so we can't actually "see" it moving among the stars from day to day; but it is easy to tell that it is doing so, in two ways:
(1) Just as for the stars, the Sun rises on the eastern horizon, crosses the sky, and sets in the west; but whereas a given star always rises and sets at the same points on the horizon every day, the Sun's rising and setting positions gradually move northward from late December to late June, then just as gradually move southward from late June to late December. In fact, a careful examination of its position can show that the angle that it sets north or south of west is usually a little different from the angle that it rose north or south of east, even on the same day; whereas for a star, the two angles are exactly the same.
(2) If we set up a clock to follow the motion of the stars, so that a given star rises, crosses the sky and sets at the same time every day, we'd find that the Sun crosses the sky at a different time each day, approximately 4 minutes later than the previous day, half an hour later than the previous week, and two hours later than the previous month.
Relative to the stellar background, the north-south motion of the Sun (along the horizon as it rises or sets, or along the Meridian as it passes due South) can be used to calculate its "declination", and the time at which it crosses the Meridian can be used to calculate its "right ascension"; and through such measurements it has been known for thousands of years that the Sun seems to move along a path in the sky called the Ecliptic once each year. In fact, all the "planetes", or "wanderers" move eastward in the sky over a period of time, along paths that are very close to the Ecliptic.
(much more to follow)