Lecture 2: The Stars



Last lecture we saw what happens with the rotation of the Earth (day/night). Now lets do what happens as the Earth orbits around the Sun (year).

The most dramatic effect of course are the effect this has on the apparent motion of the sun, giving rise to the seasons. The orbit of the Earth then gets projected on the sky as the circular path of the Sun across the celestial sphere - called the ecliptic. The ecliptic is then at an angle of 23.5 degrees to the celestial equator since the earths rotation axis is tilted by 23.5 degrees with respect to the orbital axis.

At the summer solstice (sun standing still) the pole of the earths rotation axis points towards the Sun, and we see the sun at its maximum height above the celestial equator so it has dec of 23.5 degrees. so the sun rises N of E, sets N of W, is above the horizon for more than 12 hours and has a maximum altitude of 90 - lat + 23.5 = 58.5 degress. At the winter solstice the pole of the earths rotation axis still points in the same direction, but we are now on the other side of the sun so it points away from the sun. The sun is at its maximum distance below the celestial equator, ie at dec of -23.5 so it rises S of E, sets S of W, is visible for less than 12 hours, and has maximum height above the horizon of 90 - lat - 23.5 = 11.5 degrees. This means that in winter the sunlight makes a larger angle with the surface of the earth, so is spread over a larger area, so its cooler as well as the shorter days meaning that the ground has less time to heat up. More on the seasons Equinoxes (equal nights) are where the sun crosses the celestial equator so dec=0 and its visible for 12 hours and rises in the E and sets in the W.

But theres also a difference in the stars that can be seen. The motion of the Earth around the Sun during the year then makes the Sun appear to move against the background of stars. Constellations (join the dots) which are on this projected path are the constellations of the zodiac. More on the apparent motion of the sun. The Earth goes round in its orbit once a year, so at the end of a year all the stars are back in the same places. A circle is 360 degrees, while the Earths orbit is 365 days. So the Earth moves by about 1 degree per day (the angular size of the disk of the sun is 0.5 degrees). So the time between the sun making 2 sucessive crossings (called transits) of the meridian is a solar day of 24 hours (by definition). But for the stars, the time taken for them to make 2 sucessive transits of the meridian is NOT 24 hours. The Earth moves around the sun by 1 degree per day - 1 earth rotation is 360 degrees in 24 hours. so 1 degree is 24/360 hours = 0.06666 hours = 4 minutes. Thus the stars rise 4 minutes earlier each night - a sidereal day is 23 hours and 56 minutes long. That means a given star or constellation will rise 2 hours earlier at the end of the month than at the beginning (12 months, and they have to rise at the same time of day a year later). More on solar and sidereal time.

RA of zero is defined as the point where the ecliptic and celestial equator cross - vernal equinox at march 21st. so RA of zero is on the meridian at noon on march 21st, so RA of 12 hours is on the meridian at midnight on march 21st. Then we get the second coordinate (longitude) by the time at which the star crosses the meridian relative to the vernal equinox. So at star which crosses the meridian 6 hours after the vernal equinox has RA of 6h and so is on the meridian at 18:00h on march 21st. It has maximum visibility when its on the meridian at midnight i.e. on December 21st.

So suppose you are headed back from the pub at 11pm on Oct 21st. You see a bright star due south, about 5 degrees above the horizon. What is its RA and dec ? Due south is the meridian so must be at its highest altitude for that star. So 90-lat + dec = 5 so dec=-30. On Oct 21st then the meridian at noon is RA of 12 hours. so meridian at 11pm is RA=12+11=23 hours. The star is Fomalhaut, in the constellation of Piscis Australis

There are two main things to remember. 0:0h RA is on the meridian at noon on march 21st. And then RA is time the object gets onto the meridian after this. So on the sky, looking south, things towards the east have larger RA (as they are not yet on the meridian) than things in the west. so on star maps where east and west are reversed, stars on the left have larger RA.