Monday October 17 2011

Comet Garrard This is currently visible comet. It is not bright enuf to see with naked eye, but might be visible with binoculars or s moderate sized telescope.

***************************************************************************************

The Celestial Sphere. The sky can be thought of as the inside of a sphere of very large radius with us in the middle. The rotation of the Earth makes the celestial sphere appear to rotate every 23hr and 56min on an axis from the north celestial pole to the south celestial pole. These poles are the points on the celestial sphere where an extension of the Earth's rotational axis would intersect the celestial sphere.

Horizon coordinate system We can specify a a spot on the sky (direction in space relative to where we are on Earth as present moment) by giving its altitude (angle from horizon) and its azimuth (angle from north through east). The north celestial pole has an azimuth of 0 degrees and an altitude equal to the observers latitude (35 degrees for Norman). In this diagram, the observer is at 40 degrees latitude - Denver or Philadelphia, for example.

The horizon system is important as it is the natural system for pointing telescopes- gravity prvides a convenient reference for straight up (altitude = 90 degrees). HOWEVER, the horizon system coordinates of all stars are constantly changing with time, so we need a coordinate system FIXED WITH THE STARS also. A modern telescope has a computer that transforms between the star coordinate system and the horizon coordinate system second-by-second as the stars changes its horizon coordinates due to the rotation of the Earth.

Latitude and longitude on Earth. The surface of the Earth can be thought of as a 2 dimensional surface and any point can be specified with 2 coordinates- latitude and longitude. Latitude is the angle between a point and the the equator as seen from the center of the Earth. Longitude is the angle east west from the point to the meridian passing through Grenwich, England.

Example of a star atlas This is a page from a simple star atlas. (There are many different ones, at different levels of detail.) This shows the coordinate system that is "fixed with the stars". This is analogous to latitude and longitude on the surface of the Earth. Note the coordiate system: the "y axis" is measured in degrees declination (DEC) north or south of the celestial equator; the "x axis" is measured in units of hours, minutes and seconds of right ascension (RA). The zero point of the RA scale is set where the ecliptic (dashed line) crosses the equator in the fall (the autumnal equinox). This chart contains the point where the ecliptic crosses the equation at RA = 0, DEC = 0. The angle between equator and ecliptic is 23.5 degrees, as shown.

Any point on the celestial sphere can be specified by giving its RA and DEC, just like any point on the earth can be specified with its latitude and longitude. For example, the exact coordiantes of M31, a nearby galaxy shown on the chart, are: RA = 0 hr 42 min 44.32 sec ; DEC = 41 deg 16 arcmin 8.5 arcsec.

As the Earth turns, the RA on the merdian continuously changes. The RA on the meridan at any instant is the Local Sideral Time (LST). The LST at midnite (wall clock time) for each night at a particular place can be found on the sky calendar (see below- column 3).

(1) Celestial sphere _(2) RA and DEC Two diagrams that will help visualize celestial coordinate system.

Meridian and celestial sphere. The zenith is the point directly overhead from your location. The meridian is a cicle passing from straight north, through the zenith, and on to straight south. As the Earth turns, objects (except those near the poles) appear to rise, reach maximum altitude as the pass the merdian (transit) and then set. The celestial equator is a great circle 90 degrees away from the celestial poles- it can also be thought of as an extension of the plane that coincides with the equator of the Earth.

(1) Star paths as seen from northern mid-latitudes (2) Another viewgraph of same idea From mid-northern latitudes, the celestial sphere can be divided into 3 regions. First, stars within a certain angle (equal to the observers latitude) of the north celestial pole are always above the horizon. We call these circumpolar stars. A mirror-image region around the southern celestial pole contains stars that are never seen by the observer. Stars between these two circumpolar caps rise and set as the Earth turns. We can only see the half of the celestial sphere above our horizon, of course (unlike the 8000 mile tall woman in the diagram who can see "around" the Earth!). The dashed lines are the (unseen to us) paths of stars below our horizon.

Star paths. Paths of stars in the sky as seen looking towards the north, east, and south as seen from mid-northern latitude. See the preceeding figure to help understand what the star paths look like.

***********The next few slides are photpgraphs of star trails. These are made by taking a camera and doing a time exposure hours long. The stars "trail" as the Earth rotates. First, lets look at Orion , one of the easiest to find constellations.*********

Constellation of Orion (stick figure)

Constellation of Orion (19th art)

Constellation of Orion (sky photograph) Constellations are mythical people or creatures seen in patterns of stars. One of the most famous and easily visible is Orion the Hunter. This constellation is easily visible in winter skies. The 3 bright "belt stars" are a very prominent grouping of stars, while bright reddish Betelgeuse (one of "shoulder stars") and whiteish Rigel (one of "knee stars") are also easily seen by your naked eye, even if you are viewing from an area with lots of city lights brightening the sky. The photograph is a long time exposure (the camera was tracked to follow the motion of the stars, unlike the "star trails" below). It shows many maore stars than can be seen by the naked eye. The red glowing patches are clouds of glowing gas. These are not visible to the naked eye.

Orion rising . Here, somewhere in Colorado, the photographer left the shutter open for 20 minutes to catch the trailed stars of Orion rising, closed the shutter for a minute, then made a short exposure to catch the stars as points. Orion always rises "on its side". Here the belt stars form a line perpendicular to the eastern horizon.

Star trails over Oregon . You can see Polaris (North Star) as the shortest star trail.

Star trails from Mount Kilimanjaro. Star trails from a camp high on slopes of Mount Kilimanjaro in Africa. This is taken looking south. Note that the stars circle a point very near the horizon. This is because Kilimanjaro is near the equator (3 degrees south latitude).

Star trails over Andes peak. Again, looking south from near a big mountain in Chile.

"Full sky" star trails. A complicated but educational photo montage attempting to show star trails over the entire sky. This was made from near a town called Mudgee, in New South Wales, Australia, at 32 degrees south latitude. (As I am sure you know, the Mudgee district is known for its fine wines.)

To try to understand what is going on, imagine taking this image on a piece of paper, grasping the left and right edges, and forming the image into a cylinder around you head. If you look above the telescope dome to the left of center, you would be looking south. You can see the star trails around the south celestial pole. If you to the right of the right hand dome, you are looking due North. The north celestial pole is not visible, as it is below the horizon from this southern hemisphere location. In between the two dome you are looking east and see the stars around the celestial equator rising above the horizon.

************ seasons *************

Seasons. The Earth experiences seasons because of the tilt of the Earth's rotational axis by 23.5 degrees from the perpendicular to the plane of the Earth's orbit around the Sun.

Celestial Equator and Ecliptic. The ecliptic is the great circle on the celestial sphere that the Sun appears to follow as the Earth revolves around the Sun. The ecliptic is tilted by 23.5 degrees with respect to the celestial equator. The solstices mark the points where the Sun is farthest north or south of the equator, and the equinoxs mark the two points when the Sun is exactly on the equator.

Path of Sun in sky. As the Earth revolves around the Sun, it appears to us that the Sun moves in a great circle.

Constellations of the Zodiac. If you could see the stars in the daytime, the Sun would appear in different constellations as it moves around the ecliptic. We say the Sun is "in" the constellation it appears in front of.

Constellations of the Zodiac visible at night At night, of course, we see best the constellations that are 180 degrees away from the constellation the sun is "in".

Sun at soltices. At the time of summer solstice (around June 21 for us in northern hemisphere) the Sun is farthest north of the equator, sunlight is hitting us most directly, and the time the Sun is above the horizon is greatest. At winter solstice, the Sun is farthest south of the equator, Sunlight hits us at a large angle from the vertical, and the Sun is above the horizon the least amount of time possible. Note the lengths of the shadow of the figure. At local noon at the summer solstice (from Norman at latitude 35 degrees) you would have a short shadow extending to the north. At local noon at the winter solstice, your shadow would be much longer, as the Sun is much lower in the sky. Only if you in the Tropics (zone with latitude between -23.5 and +23.5 latitudes) can the sun ever be at the zenith.

Sun at different seasons This image shows the motion of the Sun across the sky on 3 different dates. The bottom curve of solar images are hourly images taken on 22 December, at the winter solstice. By counting the images, you can see that the Sun is above the horizon for about 8 hours. The middle line of images is taken at one of the equinoxes (spring or autumn). At these two times of the year, the sun is on the clestial equator (the ecliptic crosses the equator on the equinoxes) and so it is above the horizon for 12 hours and below the horizon for 12 hours. The top curve of images are for summer solstice (~22 June) when the Sun is at its most northern declination, so it appears above the horizon for the longest time (about 15 hours). The dates and times are for a mid-northern latitude. (Not sure the exact latitude of the phtograph site.)

Sun farthest from Earth in January These photos show the size of the Sun at perihelion (Earth closest to Sun) and aphelion (Sun farthest from Sun). The difference in distance (and apparent size of Sun) is about 3%. Note that the SUN LOOKS LARGEST AND IS HENCE CLOSEST TO EARTH IN JANUARY, when it is WINTER (at least in the northern hemsiphere). So, clearly, the earth-Sun distance plays NO ROLE in the seasons, as some people think.