Peter Alway's Intro to Astronomy Lecture Notes
Part 1: The Sky vs. Space, Lunar Motions, Solar Motions, and Celestial Coordinates
Unit 1C: Celestial Coordinate, Motions, and time
What are altitude, azimuth, right ascension, and declination? What are the north celestial pole, zenith, celestial equator, and ecliptic? What is diurnal motion? What does it look like, and what causes it? What is annual motion? What does it look like, and what causes it? How do you plot objects on a star chart? What is sidereal time? What is solar time? Why do we have time zones?
Before digging in further, it is worth mentioning a few things about the celestial sphere. The celestial sphere is an imaginary spherical surface surrounding us. You are always at the center of the celestial sphere. A point on the celestial sphere corresponds to a direction in the real, three-dimensional world. For instance, the zenith, the point directly above you on the imaginary celestial sphere describes the direction "straight up." Distances between points on the celestial sphere are really angles between lines of sight, or "angular distances." A star chart is just a portion of this celestial sphere that has been squished flat onto a piece of paper. Remember that star charts show the view from the inside.
Horizon Coordinate System
There two coordinate systems for locating points on the celestial sphere. The first is the Horizon system, using "altitude" and "Azimuth." This system is fixed with respect to your local horizon and your local compas directions. It is useful because you can easily measure with this system, and it tells you in a very simple way where to look for something in the sky. "Look for the Moon low in the Northeast," is a simple set of directions in altitude and azimuth. But altitude and azimuth are given more precisely in degrees, as we shall see.
Altitude
Altitude is precisely defined as the angle between your lines of sight to the horizon and to a celestial object. More informally, it is the angle of an object above the horizon. The altitude of any object as it rises or sets is 0 degrees. The altitude of the zenith, the point directly overhead, is 90 degrees. A point halfway between the horixon and zenith has an altitude of 45 degrees. In southern lower Michigan, the altitude of the north celestial pole is about 42 degrees. (In the norther hemisphere, the altitude of the north celestial pole is equal to the observer's lattitude.
You can measure altitude using "nature's cross staff," your fist at arm's length as described in unit 1A.
Just measure up from the horizon to the object of interest. For instance, if you are looking at the rising moon, and it looks like this:
you can estimate that the moon is about 2 1/2 fists--25 degrees--above the horizon. That's an altitude of 25 degrees.
Azimuth
Azimuth is precisely defined as the angle measured eastward from the north point on the horizon to the point on the horizon below an object. An object that is due north has an azimuth of 0 degrees. An object to the east has azimuth 90 degrees, due south is 180 degrees azimuth, and due west is 270 degrees azimuth. An object that is straight up has an undefined azimuth.
It's easiest to keep track of north, south, east, and west, and then measure from those points with your fist at arm's length. For instance, the rising Moon below is one fist south of east:
Since each fist is about 10 degrees, and due east is 90 degrees azimuth, just add 10 degrees to 90 degrees for an azimuth of 100 degrees. Another example might be the sun setting 20 degrees south of west. That would have an azimuth of 270 - 20 = 250 degrees.
A good way to track celestial motions for yourself is to record altitudes and azimuths of celestial bodies, and see how they change. Try observing the Sun, Moon, a star, or a planet several hours, or observe the Moon at the same time for several nights, sunrise or sunset over the course of a few months, or the position of a star at the same time of night over the course of several months. You can record your observations on a form such as this one.
If you plotted the altitudes and azimuths of stars visible at midnight on December 21 (the first day of winter, if might look like this.
If you'd like to plot the altitude and azimuth you measure, you can download some special graph paper to plot motions of stars, planets, the Sun, and the Moon.
An objects altitude and azimuth change with time, and also with location. Altitude and azimuth of most stars changes visibly in an hour, and they are also visibly different at different locations. While Altitude and azimuth are handy for describing where an observer at a given location and a given time should look fo something, astronomers need a more stable coordinate system to communicate precise locations for people around the globe. But before we can understand these coordinates, right ascension and declination, we need to look at one sort of celestial motion.
Diurnal Motion
Diurnal motion is also called daily motion. If you watch the Sun, Moon, planets, or stars for several hours, you will notice that they move. Most objects rise in the east and set in the west. Stars close to the north celestial pole turn around the pole without ever hitting the horizon (this is true for northern hemisphere observers, anyway). If you look at the whole sky, you see that everything--the entire celestial sphere seems to turn around the north celestial pole. This motion takes 23 hours, 56 minutes to complete one cycle (the Sun lags a bit, so it takes all of 24 hours to make the trip). You can use a planisphere, sometimes called a star finder (my Omnibus Phy 104 students should have the "Edmund Scientific Star and Planet finder." Unit 1 D will have instructions for making yor own) to simulate daily motion just by turning the horizon clockwise or the chart counterclockwise. (My Omnibus Phy 104 students will also find some nice time-lapsed video of daily motion on their second videotape)
While diurnal motion looks like the celestial sphere slowly spinning around us, in reality it is a reflection of our own motion. The Earth spins (rotates) on its axis every 23 hours, 56 minutes, and we percieve sunrise, sunset, moonrise, moonset, and the stars turning overhead. (Ok Beatles fans, which song refers to daily motion and its cause).
Equatorial Coordinate System
The equatorial coordinate system--right ascension and declination--is very similar to the system of lattitude and longitude for the Earth. In fact, they share some of the smae framework. You will see a grid of right ascension and declination on better star charts.
Declination
The north celestial pole is directly above the Earth's north pole. The celestial equator is directly above the Earth's equator, and the south celestial pole is directly above the Earth's south pole. Just as latitude on Earth is measured in degrees nort or south of the equator, declination in te sky is measured in degrees north and south of the celestial equator. One difference is that in the sky, we call a north declination positive, and a south declination negative. Just as the north pole is at 90 degrees north latitude, the north celestial pole is at +90 degrees declination. The south celestial pole is at -90 degrees declination. the celestial equator, of course is at 0 degrees declination. This celestial sphere shows how declination is measured.
Right Ascension
Right ascension is similar to longitude, but with some twists. Longitude is measured in degrees east and west of Greenwich Observatory in England. Right ascension is measured eastward in hours from the position of the sun on first day of spring.
An east-west coordinate has to be based on some arbitrary point. On Earth it is at Greenwich Observatory simply because England was the largest imperial power when it bcame useful to select a worldwide standard for longitude. Astronomers could have chosen any number of points in the sky for theri zero point in right ascension. The vernal equinox point, where the sun appears on the first day of spring appealed to the sense of symmetry of astronomers centuries ago, and, since it's as good a point as any, we've kept it. The system of hours is tied in with daily motion. The sky seems to revolve about us 360 degrees in 24 hours, or at a rate of 15 degrees per hour. It was easier for astronomers to measure positions by timing objects as they passed overhead, so hours were convenient. If you start a clock when the zero-hour point passes overhead, you can read the right ascension of objects directly overhead right off the clock dial (the clock has to be 4 minutes fast per day, though). This celestial sphere shows how right ascension is measured.
You can get a better feel for right ascension and declination from a star chart:
Annual Motion
Annual motion is more subtle than diurnal motion. Both are caused by Earth's motion, which is reflected (figuratively) in the sky, but we can't even see the reflection in the sky clearly because we can't see the sun and the stars at the same time. As a result, there are two layers of appearances to peel back before we get to the real cause in space. The observable effects of annual motion are:
a change of stars we see in the evening
and the changing seasons
There are certain stars and constellations commonly called "Winter" stars. These include the constellation Orion and others nearbly. These are the obvious stars in a winter's evening, but as the season passes, these stars work their way west (if you look at the same time of night), and in spring, an new set of canstellations, dominated by Leo, comes into view in the evening. In Summer, we Sagitarius in the evening, and in the fall, it's the great square of Pegasus. Of course, these constellations aren't really moving. Peeling back the first layer of appearance, and looking at star charts, we see that the sun seems to be moving around the sky, outshining stars as it passes through a series of constellations called the zodiac. The exact path of the sun through the sky is called the ecliptic Stars close to the sun in the sky are invisible at night, stars to the east of the sun are visible in the evening, and stars to the west of the sun are visible before dawn.
In space, it's not the sun's motion, but our motion that causes the effect. As we travel (revolve) around the sun, the direction to the sun changes, moving around the sky. To see the effect clearly, walk around any object, and you will see that the objects you see in the background behind that object are constantly changing.
Over the course of a year, the sun also moves north and south. On December 21 (for Michigan observers) the sun rises an hour and a half late, gets only a quarter of the way up in the sky, and sets an hour and a half early. This is all because the sun's declination is -23 degrees. It is at its southernmost point in the sky. This day (plus or minus a day) is called the Winter Solstice, and marks the first day of winter. It's so dark and dreary many northern hemisphere cultures have created holidays close to the Solstice involving lots of candles to perk people up, and celebrate the fact that the sun won't be getting any lower. On or about March 21, we have the Vernal (spring) Equinox, the first day of spring. The sun's declination increases to zero, on the celestial equator, giving us equal nights (meanimg of equinox) and days. On June 21 (plus or minus a day) get the Summer Solstice marking the first day of summer. The sun is at +23 degrees declination, rises an hour and a half early, reaches 3/4 of the way to the zentith (in Michigan) and sets an hour and a half late. It's not the hottest day of the year, but it's the day we get the most solar energy. It takes a month or two for the temperature to peak out. On or about September 21, we have the Autumnal Equinox, the first day of Fall. The sun follows the sam path as on the spring equinox.
These changes are visible on the celestial sphere as a tilt between the celestial equator and the ecliptic. But the root cause is that the earth's daily rotation is tilted 23 1/2 degrees from the revolution of the Earth around the sun. The Earth axis stays pointed in about the same direction, toward the star polaris. When we are on the Polaris side of the sun, the north pole points away from the sun, and we have the cooler seasons of Fall and Winter. When we are on the sun away from Polaris, the north pole tilts toward the sun, and we get the warmer seasons of Spring and Summer.
Time
Before we can describe time, we need one more celestial sphere. This one shows the meridian, a line in the sly running from the due south point of the horizon, straight up to the zenith, and back to the north point on the horizon. As daily motion carries celestial bodies across the sky, they are at their highest, halfway betwen rising and setting, as they cross the meridian.
Solar Time:
When the sun crosses the meridian, it is noon solar time. Long ago, this was good enough for most people. When the sun crossed the meridian at a city hall, someon would lower a large "time ball" so that people around town could set their clocks, or just know it was lunch time. This is where New York's tradition of lowering a ball at Times Square on New Year's Eve comes from. Sundials read Solar time.
Mean Solar Time:
But solar time has a couple problems. The solar day, while on average is exactly 24 hours, is not exactly constant. The Earth's speed on its orbit around the sun is not exactly constant, and the tilt of the Earth axis confounds tings subtly as well. The sun can run 15 minutes fast or 15 minutes slow. In a world where mechanical, and ultimately electric clocks have replaced the sundial, we need a day with exactly 24 hours, no matter what the sun does. Mean solar time has exactly 24 hours. Solar noon is not at the same time every day, but who notices the sun anymore?
Standard Time:
Noon in Australia is about 12 hours earlier than noon in Maine. Noon in Detroit happens about half an hour after noon in Philadelphia. Before telephones and railroads, this was not a problem. But when railrads became important in the 1800's, it became a nuisance trying to juggle schedules if every town in the country was on its own time. Of course, if every city in the world were on a single time, such as Greenwich Mean time, the time based on the location of Greenwich observatory in England, the sun would rise in Michigan at 1:00 AM, and set around 1 PM. A compromise that minimizes the number of times and keeps clocks reasonably in tune with the sun is Standard time. The earth is sliced into 24 zones, each spanning 15 degrees of longitude, each with its clocks set one hour apart. The borders of these zones have been distorted for politics (to avoid splitting countries, states, and provinces) and convenience (putting Michigan in the Eastern Standard Time instead of Central Standard Time to keep in in synch with the east coast). There are even a few places with their own time zones--Newfoundland in Canada is half an hour off from its neigboring provinces.
Standard time can be nearly a half hour off from the sun, and "daylight time" adds another hour difference, forcing workers to rise an hour early during the summer months, so that there is more daylight after work for recreation (I personally think it's a conspiracy to keep golf courses in business). In western Michigan, where I grew up, solar noon may not come until nearly 2:00 clock time during the Summer.
Sidereal Time:
Siderial time is "star time," and is based on the Earth's actual rotation, not the sun's apparent postion. The sidereal day is 23 hours, 56 minutes long. Sidereal time uses slightly shorter sidereal hours and minutes, so that there are 24 sidereal hours in a sidereal day. The sidereal day starts when the point of zero hours Right Ascension crosses the meridian. This is noon on the first day of spring, and midnight on the first day of fall.
Part 1 B The Greeks work out the Earth, Moon, and Sun in 3-D
Part 1 B of the course is a craft project--we build a scale model of the Solar System!
Part 1C (you are here)
Part 1D of the course is Arts and Crafts again--we make a planisphere (star finder)