The next thing you may want to do is change the time and/or date. When KStars starts up, the time is set to your computer's system clock, and the KStars clock is running to keep up with the real time. If you want to stop the clock, select Stop Clock from the Time menu, or simply click on the Pause icon in the toolbar. You can make the clock run slower or faster (even backward) than normal using the time-step spinbox in the toolbar. This spinbox has two sets of up/down buttons. The first one will step through all 83 available time steps, one by one. The second one will skip to the next higher (or lower) unit of time, which allows you to make large timestep changes more quickly.

You can change to any time or date by selecting Set Time... from the Time menu, or by pressing the hourglass icon in the toolbar. The Set Time window uses a standard KDE Date Picker widget, coupled with three spinboxes for setting the hours, minutes and seconds. If you ever need to reset the clock back to the current time, just select Set Time to Now from the Time menu.

Now that we have the time and location set, let's have a look around. You can pan the display using the arrow keys. If you hold down the Shift key before panning, the scrolling speed is doubled. The display can also be panned by clicking and dragging with the mouse. Note that while the display is scrolling, not all objects are displayed. This is done to cut down on the CPU load of recomputing object positions, which makes the scrolling smoother (you can configure what gets hidden while scrolling in the Display Options window; this is covered in the next chapter). There are five ways to change the magnification of the display:

Notice that as you zoom in, you can see fainter stars than at lower zoom settings.

Zoom out until you can see a green curve; this represents your local horizon. If you haven't adjusted the KStars configuration, the display will be solid green below the horizon, representing the solid ground of the Earth. There is also a white curve, which represents the celestial equator (an imaginary line which divides the sky into northern and southern hemispheres). There is also a tan curve, which represents the Ecliptic, the path that the Sun appears to follow across the sky over the course of a year. Therefore, the Sun is always found somewhere along the Ecliptic, and the planets are never far from it.

KStars displays thousands of objects: stars, planets, clusters, nebulae and galaxies. By default, stars are drawn as white circles with a colored border that simulates the star's real color. Planets are drawn as colored dots at low zoom levels, but as an actual image of the planet as you zoom in. Deep-sky objects (clusters, nebulae and galaxies) are drawn with symbols color-coded to indicate the catalog to which they belong (Messier, NGC or IC). Most Messier objects are drawn as real images on the map at higher zoom levels. Deep-sky objects with extra image or information links available are drawn with a special color (red by default). Clicking on an object will identify it in the status bar. Double clicking will recenter the display on the object and begin tracking the object (so that it will remain centered as time passes). Right clicking an object opens a popup menu with more options.

The Popup Menu

Here is an example of the right click popup menu, for the Orion Nebula:

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The appearance of the popup menu depends somewhat on the kind of object you right click on, but the basic structure is the following:

The top section contains information labels, which are not selectable. The top one to three labels display the object's name(s) and object type. The next three labels show the object's rise, transit, and set times. The next section contains two selectable items. First, a Center and Track item, which will recenter the display on the object, and keep it centered as time passes (you can also center and track an object by simply double clicking on it). Next, a Details... item, which will show a window with more detailed information about the object. The bottom section contains links to images and/or informative webpages about the selected object.

If you know of an additional URL with information or an image of the object, you can add a custom link to the object's popup menu using the Add Link... item at the bottom of the menu. This opens a window in which you can enter the URL and the text that should appear in the popup menu. You can make sure the URL is correct with the Check URL button, which will test the URL in your web browser. Please specify whether the URL points to an Image, or to an HTML document! If you specify Image here, the new menu item will open the Image Viewer, not the web browser. You can also point to files on your local disk, so this feature could be used to attach observing logs or other custom information to objects in KStars. Your custom links are automatically loaded whenever KStars starts up, and they are stored in the directory ~/.kde/share/apps/kstars/, in files myimage_url.dat and myinfo_url.dat. If you build an extensive list of custom links, consider submitting them to us, we would like to include them in the next version of KStars!

There are several ways to modify the display to your liking. First of all, you can select a different color scheme in the Settings->Color Schemes menu. There are three predefined color schemes, and you can define your own in the View Options window (covered in the next chapter). You can hide the Toolbars in the Settings->Toolbars menu, and hide the Info Boxes in the Settings->Info Boxes menu. In addition, you can manipulate the Info Boxes with the mouse. Each box has additional lines of data that are hidden by default. You can toggle whether these additional lines are visible by double-clicking a box to “shade” it. Also, you can reposition a box by dragging it with the mouse. When a box hits a window edge, it will “stick” to the edge when the window is resized.

The remaining customizations are covered in the next chapter.

The current RA, Dec coordinates of the mouse cursor is always displayed in the status bar. Clicking the Mouse anywhere will identify the nearest object in the status bar. Double-clicking will center and track on the clicked location or object. Click and drag to pan the display. Right click to bring up the popup menu with detailed options for the clicked object. Holding the middle mouse button and moving the mouse vertically will change the zoom level (you can also use the mouse scroll wheel, if you have one).

You can also move the Info Boxes by dragging them with the mouse, and "shade" the Info Boxes by double-clicking on them.

A basic requirement for studying the heavens is determining where in the sky things are. To specify sky positions, astronomers have developed several coordinate systems. Each uses a coordinate grid projected on the Celestial Sphere, in analogy to the Geographic coordinate system used on the surface of the Earth. The coordinate systems differ only in their choice of the fundamental plane, which divides the sky into two equal hemispheres along a great circle. (the fundamental plane of the geographic system is the Earth's equator). Each coordinate system is named for its choice of fundamental plane.

The sky appears to drift overhead from east to west, completing a full circuit around the sky in 24 (Sidereal) hours. This phenomenon is due to the spinning of the Earth on its axis. The Earth's spin axis intersects the Celestial Sphere at two points. These points are the Celestial Poles. As the Earth spins; they remain fixed in the sky, and all other points seem to rotate around them. The celestial poles are also the poles of the Equatorial Coordinate System, meaning they have Declinations of +90 degrees and -90 degrees (for the North and South celestial poles, respectively).

The North Celestial Pole currently has nearly the same coordinates as the bright star Polaris (which is Latin for “Pole Star”). This makes Polaris useful for navigation: not only is it always above the North point of the horizon, but its Altitude angle is always (nearly) equal to the observer's Geographic Latitude (however, Polaris can only be seen from locations in the Northern hemisphere).

The fact that Polaris is near the pole is purely a coincidence. In fact, because of Precession, Polaris is only near the pole for a small fraction of the time.

The celestial sphere is an imaginary sphere of gigantic radius, centered on the Earth. All objects which can be seen in the sky can be thought of as lying on the surface of this sphere.

Of course, we know that the objects in the sky are not on the surface of a sphere centered on the Earth, so why bother with such a construct? Everything we see in the sky is so very far away, that their distances are impossible to gauge just by looking at them. Since their distances are indeterminate, you only need to know the direction toward the object to locate it in the sky. In this sense, the celestial sphere model is a very practical model for mapping the sky.

The directions toward various objects in the sky can be quantified by constructing a Celestial Coordinate System.

The ecliptic is an imaginary Great Circle on the Celestial Sphere along which the Sun appears to move over the course of a year. Of course, it is really the Earth's orbit around the Sun causing the change in the Sun's apparent direction. The ecliptic is inclined from the Celestial Equator by 23.5 degrees. The two points where the ecliptic crosses the celestial equator are known as the Equinoxes.

Since our solar system is relatively flat, the orbits of the planets are also close to the plane of the ecliptic. In addition, the constellations of the zodiac are located along the ecliptic. This makes the ecliptic a very useful line of reference to anyone attempting to locate the planets or the constellations of the zodiac, since they all literally “follow the Sun”.

The Altitude of the ecliptic above the Horizon changes over the course of the year, because of the 23.5 degree tilt of the Earth's spin axis. This causes the seasons. When the ecliptic (and therefore the Sun) is high above the horizon, the days are longer, and you have Summer. When the ecliptic is low in the sky, you have Winter.

Most people know the Vernal and Autumnal Equinoxes as calendar dates, signifying the beginning of the Northern hemisphere's Spring and Autumn, respectively. Did you know that the equinoxes are also positions in the sky?

The Celestial Equator and the Ecliptic are two Great Circles on the Celestial Sphere, set at an angle of 23.5 degrees. The two points where they intersect are called the Equinoxes. The Vernal Equinox has coordinates RA=0.0 hours, Dec=0.0 degrees. The Autumnal Equinox has coordinates RA=12.0 hours, Dec=0.0 degrees.

The Equinoxes are important for marking the seasons. Because they are on the Ecliptic, the Sun passes through each equinox every year. When the Sun passes through the Vernal Equinox (usually on March 21st), it crosses the Celestial Equator from South to North, signifying the end of Winter for the Northern hemisphere. Similarly, when the Sun passes through the Autumnal Equinox (usually on September 21st), it crosses the Celestial Equator from North to South, signifying the end of Winter for the Southern hemisphere.

Locations on Earth can be specified using a spherical coordinate system. The geographic (“earth-mapping”) coordinate system is aligned with the spin axis of the Earth. It defines two angles measured from the center of the Earth. One angle, called the Latitude, measures the angle between any point and the Equator. The other angle, called the Longitude, measures the angle along the Equator from an arbitrary point on the Earth (Greenwich, England is the accepted zero-longitude point in most modern societies).

By combining these two angles, any location on Earth can be specified. For example, Baltimore, Maryland (USA) has a latitude of 39.3 degrees North, and a longitude of 76.6 degrees West. So, a vector drawn from the center of the Earth to a point 39.3 degrees above the Equator and 76.6 degrees west of Greenwich, England will pass through Baltimore.

The Equator is obviously an important part of this coordinate system, it represents the zeropoint of the latitude angle, and the halfway point between the poles. The Equator is the Fundamental Plane of the geographic coordinate system. All Spherical Coordinate Systems define such a Fundamental Plane.

Lines of constant Latitude are called Parallels. They trace circles on the surface of the Earth, but the only parallel that is a Great Circle is the Equator (Latitude=0 degrees). Lines of constant Longitude are called Meridians. The Meridian passing through Greenwich is the Prime Meridian (longitude=0 degrees). Unlike Parallels, all Meridians are great cricles, and Meridians are not parallel: they intersect at the north and south poles.

Consider a sphere, such as the Earth, or the Celestial Sphere. The intersection of any plane with the sphere will result in a circle on the surface of the sphere. If the plane happens to contain the center of the sphere, the intersection circle is a Great Circle. Great circles are the largest circles that can be drawn on a sphere. Also, the shortest path between any two points on a sphere is always along a great circle.

Some examples of great circles on the celestial sphere include: the Horizon, the Celestial Equator, and the Ecliptic.

The Horizon is the line that separates Earth from Sky. More precisely, it is the line that divides all of the directions you can possibly look into two categories: those which intersect the Earth, and those which do not. At many locations, the Horizon is obscured by trees, buildings, mountains, etc. However, if you are on a ship at sea, the Horizon is strikingly apparent.

The horizon is the Fundamental Plane of the Horizontal Coordinate System. In other words, it is the locus of points which have an Altitude of zero degrees.

As explained in the Sidereal Time article, the Right Ascension of an object indicates the Sidereal Time at which it will transit across your Local Meridian. An object's Hour Angle is defined as the difference between the current Local Sidereal Time and the Right Ascension of the object:

HA_obj = LST - RA_obj

Thus, the object's Hour Angle indicates how much Sidereal Time has passed since the object was on the Local Meridian. It is also the angular distance between the object and the meridian, measured in hours (1 hour = 15 degrees). For example, if an object has an hour angle of 2.5 hours, it transited across the Local Meridian 2.5 hours ago, and is currently 37.5 degrees West of the Meridian. Negative Hour Angles indicate the time until the next transit across the Local Meridian. Of course, an Hour Angle of zero means the object is currently on the Local Meridian.

The Meridian is an imaginary Great Circle on the Celestial Sphere that is perpendicular to the local Horizon. It passes through the North point on the Horizon, through the Celestial Pole, up to the Zenith, and through the South point on the Horizon.

Because it is fixed to the local Horizon, stars will appear to drift past the Local Meridian as the Earth spins. You can use an object's Right Ascension and the Local Sidereal Time to determine when it will cross your Local Meridian (see Hour Angle).

Precession is the gradual change in the direction of the Earth's spin axis. The spin axis traces a cone, completing a full circuit in 26,000 years. If you've ever spun a top or a dreidel, the “wobbling” rotation of the top as it spins is precession.

Because the direction of the Earth's spin axis changes, so does the location of the Celestial Poles.

The reason for the Earth's precession is complicated. The Earth is not a perfect sphere, it is a bit flattened, meaning the Great Circle of the equator is longer than a “meridonal” great circle that passes through the poles. Also, the Moon and Sun lie outside the Earth's Equatorial plane. As a result, the gravitational pull of the Moon and Sun on the oblate Earth induces a slight torque in addition to a linear force. This torque on the spinning body of the Earth leads to the precessional motion.

The Zenith is the point in the sky where you are looking when you look “straight up” from the ground. More precisely, it is the point on the sky with an Altitude of +90 Degrees; it is the Pole of the Horizontal Coordinate System. Geometrically, it is the point on the Celestial Sphere intersected by a line drawn from the center of the Earth through your location on the Earth's surface.

The Zenith is, by definition, a point along the Local Meridian.

The Julian Calendar is a way of reckoning the current date by a simple count of the number of days that have passed since some remote, arbitrary date. This number of days is called the Julian Day, abbreviated as JD. The starting point, JD=0, is January 1, 4713 BC (or -4712 January 1, since there was no year '0'). Julian Days are very useful because they make it easy to determine the number of days between two events by simply subtracting their Julian Day numbers. Such a calculation is difficult for the standard (Gregorian) calendar, because days are grouped into months, which can contain a variable number of days, and there is the added complication of Leap Years.

Converting from the standard (Gregorian) calendar to Julian Days and vice versa is best left to a special program written to do this, and there are many to be found on the web (and KStars does this too, of course!). However, for those interested, here is a simple example of a Gregorian to Julian day converter:

JD = D - 32075 + 1461*( Y + 4800 * ( M - 14 ) / 12 ) / 4 + 367*( M - 2 - ( M - 14 ) / 12 * 12 ) / 12 - 3*( ( Y + 4900 + ( M - 14 ) / 12 ) / 100 ) / 4

where D is the day (1-31), M is the Month (1-12), and Y is the year (1801-2099). Note that this formula only works for dates between 1801 and 2099. More remote dates require a more complicated transformation.

An example Julian Day is: JD 2440588, which corresponds to 1 Jan, 1970.

Julian Days can also be used to tell time; the time of day is expressed as a fraction of a full day, with 12:00 noon (not midnight) as the zero point. So, 3:00 pm on 1 Jan 1970 is JD 2440588.125 (since 3:00 pm is 3 hours since noon, and 3/24 = 0.125 day). Note that the Julian Day is always determined from Universal Time, not Local Time.

Astronomers use certain Julian Day values as important reference points, called Epochs. One widely-used epoch is called J2000; it is the Julian Day for 1 Jan, 2000 at 12:00 noon = JD 2451545.0.

Much more information on Julian Days is availabel on the internet. A good starting point is the U.S. Naval Observatory. If that site is not available when you read this, try searching for “Julian Day” with your favorite search engine.

The Earth has two major components of motion. First, it spins on its rotational axis; a full spin rotation takes one Day to complete. Second, it orbits around the Sun; a full orbital rotation takes one Year to complete.

There are normally 365 days in one calendar year, but it turns out that a true year (i.e., a full orbit of the Earth around the Sun; also called a tropical year) is a little bit longer than 365 days. In other words, in the time it takes the Earth to complete one orbital circuit, it completes 365.24219 spin rotations. Don't be too suprised by this; there's no reason to expect the spin and orbital motions of the Earth to be synchronized in any way. However, it does make marking calendar time a bit awkward!

What would happen if we simply ignored the extra 0.24219 rotation at the end of the year, and simply defined a calendar year to always be 365.0 days long? The calendar is basically a charting of the Earth's progress around the Sun. If we ignore the extra bit at the end of each year, then with every passing year, the calendar date lags a little more behind the true position of Earth around the Sun. In a few centuries, Winter will begin in September!

In fact, it used to be that all years were defined to have 365.0 days, and the calendar “drifted” away from the true seasons as a result. In the year 46 BCE, Julius Caeser established the Julian Calendar, which implemented the world's first leap years: He decreed that every 4th year would be 366 days long, so that a year was 365.25 days long, on average. This basically solved the calendar drift problem.

However, the problem wasn't completely solved by the Julian calendar, because a tropical year isn't 365.25 days long; it's 365.24219 days long! You still have a calendar drift problem, it just takes many centuries to become noticeable. And so, in 1582, Pope Gregory XIII instituted the Gregorian calendar, which was largely the same as the Julian Calendar, with one more trick added for leap years: even Century years (those ending with the digits “00”) are only leap years if they are divisible by 400. So, the years 1700, 1800, and 1900 were not leap years (though they would have been under the Julian Calendar), whereas the year 2000 was a leap year. This change makes the average length of a year 365.2425 days. So, there is still a tiny calendar drift, but it amounts to an error of only 3 days in 10,000 years! The Gregorian calendar is still used as a standard calendar throughout most of the world.

Sidereal Time literally means “star time”. The time we are used to using in our everyday lives is Solar Time. The fundamental unit of Solar Time is a Day: the time it takes the Sun to travel 360 degrees around the sky, due to the rotation of the Earth. Smaller units of Solar Time are just divisions of a Day:

However, there is a problem with Solar Time. The Earth doesn't actually spin around 360 degrees in one Solar Day. The Earth is in orbit around the Sun, and over the course of one day, it moves about one Degree along its orbit (360 degrees/365.25 Days for a full orbit = about one Degree per Day). So, in 24 hours, the direction toward the Sun changes by about a Degree. Therefore, the Earth has to spin 361 degrees to make the Sun look like it has traveled 360 degrees around the Sky.

In astronomy, we are concerned with how long it takes the Earth to spin with respect to the “fixed” stars, not the Sun. So, we would like a timescale that removes the complication of Earth's orbit around the Sun, and just focuses on how long it takes the Earth to spin 360 degrees with respect to the stars. This rotational period is called a Sidereal Day. On average, it is 4 minutes shorter than a Solar Day, because of the extra 1 degree the Earth spins in a Solar Day. Rather than defining a Sidereal Day to be 23 hours, 56 minutes, we define Sidereal Hours, Minutes and Seconds that are the same fraction of a Day as their Solar counterparts. Therefore, one Solar Second = 1.00278 Sidereal Seconds.

The Sidereal Time is useful for determining where the stars are at any given time. Sidereal Time divides one full spin of the Earth into 24 Sidereal Hours; similarly, the map of the sky is divided into 24 Hours of Right Ascension. This is no coincidence; Local Sidereal Time (LST) indicates the Right Ascension on the sky that is currently crossing the Local Meridian. So, if a star has a Right Ascension of 05h 32m 24s, it will be on your meridian at LST=05:32:24. More generally, the difference between an object's RA and the Local Sidereal Time tells you how far from the Meridian the object is. For example, the same object at LST=06:32:24 (one Sidereal Hour later), will be one Hour of Right Ascension west of your meridian, which is 15 degrees. This angular distance from the meridian is called the object's Hour Angle.

The Earth is round, and it is always half-illuminated by the Sun. However, because the Earth is spinning, the half that is illuminated is always changing. We experience this as the passing of days wherever we are on the Earth's surface. At any given instant, there are places on the Earth passing from the dark half into the illuminated half (which is seen as dawn on the surface). At the same instant, on the opposite side of the Earth, points are passing from the illuminated half into darkness (which is seen as dusk at those locations). So, at any given time, different places on Earth are experiencing different parts of the day. Thus, Solar time is defined locally, so that the clock time at any location describes the part of the day consistently.

This localization of time is accomplished by dividing the globe into 24 vertical slices called Time Zones. The Local Time is the same within any given zone, but the time in each zone is one Hour earlier than the time in the neighboring Zone to the East. Actually, this is a idealized simplification; real Time Zone boundaries are not straight vertical lines, because they often follow national boundaries and other political considerations.

Note that because the Local Time always increases by an hour when moving between Zones to the East, by the time you move through all 24 Time Zones, you are a full day ahead of where you started! We deal with this paradox by defining the International Date Line, which is a Time Zone boundary in the Pacific Ocean, between Asia and North America. Points just to the East of this line are 24 hours behind the points just to the West of the line. This leads to some interesting phenomena. A direct flight from Australia to California arrives before it departs! Also, the islands of Fiji straddle the International Date Line, so if you have a bad day on the West side of Fiji, you can go over to the East side of Fiji and have a chance to live the same day all over again!

The time on our clocks is essentially a measurement of the current position of the Sun in the sky, which is different for places at different Longitudes because the Earth is round (see Time Zones).

However, it is sometimes necessary to define a global time, one that is the same for all places on Earth. One way to do this is to pick a place on the Earth, and adopt the Local Time at that place as the Universal Time, abbrteviated UT. (The name is a bit of a misnomer, since Universal Time has little to do with the Universe. It would perhaps be better to think of it as global time).

The geographic location chosen to represent Universal Time is Greenwich, England. The choice is arbitrary and historical. Universal Time became an important concept when European ships began to sail the wide open seas, far from any known landmarks. A navigator could reckon the ship's longitude by comparing the Local Time (as measured from the Sun's position) to the time back at the home port (as kept by an accurate clock on board the ship). Greenwich was home to England's Royal Observatory, which was charged with keeping time very accurately, so that ships in port could re-calibrate their clocks before setting sail.

A blackbody refers to an idealized concept of an object that emits thermal radiation perfectly. Since emission of light and absorption of light are inverse processes, a perfect emitter of light would also need to be a perfect absorber of light. Therefore, at room temperature, such an object would appear to be perfectly black. Hence the term blackbody.

All objects emit thermal radiation (as long as their temperature is above Absolute Zero, or -273.15 degrees Celsius), but no object is really a perfect emitter; rather, they are better at emitting/absorbing some wavelengths of light than others. These uneven efficiencies make it difficult to study the interaction of light, heat and matter using normal objects.

Fortunately, it is possible to construct a nearly-perfect blackbody. Construct a box made of a thermally conductive material, such as metal. The box should be completely closed on all sides, so that the inside forms a cavity that does not receive light from the surroundings. Then, make a very small hole somewhere on the box. The light coming out of this hole will almost perfectly resemble the light from an ideal blackbody, for the temperature of the air inside the box.

At the beginning of the 20th century, scientists Lord Rayleigh, Wilhelm Wein, and Max Planck (among others) studied the blackbody radiation using such a device. After much work, Planck was able to perfectly describe the intenisty of light emitted by a blackbody as a function of wavelength. Furthermore, he was able to describe how this spectrum would change as the temperature changed. Planck's work on blackbody radiation is one of the areas of physics that led to the foundation of the wonderful science of Quantum Mechanics, but that is unfortunately beyond the scope of this article.

What Planck and the others found was that as the temperature of a blackbody increases, the total amount of light emitted per second increases, and the wavelength of the spectrum's peak shifts to bluer colors (see Figure 1).

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The spectrum of three blackbodies at different temperatures.

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Wilhelm Wein quantified the relationship between blackbody temperature and the wavelength of the spectral peak with the following equation:

lamdba(max} * T = 0.29 cm K

where T is the temperature in Kelvin. Wein's law (also known as Wein's displacement law) can be stated in words as "the wavelength of maximum emission from a blackbody is inversely proportional to its temperature". This makes sense; shorter-wavelength (higher-frequency) light corresponds to higher-energy photons, which you would expect from a higher-temperature object.

For example, the sun has an average temperature of 5800 K with a wavelength of maximum emission equal to lambda(max) = 0.29 cm / 5800 = 500 nm. This wavelengths falls in the green region of the visible light spectrum, but the sun's continuum radiates photons both longer and shorter than lambda(max) and the human eyes perceives the sun's color as white.

In 1879, Austrian physicist Stephan Josef Stefan showed that the luminosity, L, of a black body is proportional to the 4th power of its temperature T.

L = A * alpha * T^4

where A is the surface area, alpha is a constant of proportionality, and T is the temperature in Kelvin. That is, if we double the temperature (e.g. 1000 K to 2000 K) then the total energy radiated from a blackbody increase by a factor of 2^4 or 16.

Five years later, Austrian physicist Ludwig Boltzman derived the same equation and is now known as he Stephan-Boltzman law. If we assume a spherical star with radius R, then the luminosity of such a star is

L = 4*PI*R^2 * Alpha * T^4

where R is the star radius in cm, and the alpha is the Stephan-Boltzman constant, which has the value: Alpha = 5.670 * 10^-5 erg/s/cm^2/K^-4.

Scientists are now quite comfortable with the idea that 90% of the mass is the universe is in a form of matter that cannot be seen.

Despite comprehensive maps of the nearby universe that cover the spectrum from radio to gamma rays, we are only able to account of 10% of the mass that must be out there. As Bruce H. Margon, an astronomer at the University of Washington, told the New York Times in 2001: [It's a fairly embarrassing situation to admit that we can't find 90 percent of the universe].

The term given this “missing mass” is Dark Matter, and those two words pretty well sum up everything we know about it at this point. We know there is “Matter”, because we can see the effects of its gravitational influence. However, the matter emits no detectable electromagnetic radiation at all, hence it is “Dark”. There exist several theories to account for the missing mass ranging from exotic subatomic particles, to a population of isolated black holes, to less exotic brown and white dwarfs. The term “missing mass” might be misleading, since the mass itself is not missing, just its light. But what is exactly dark matter and how do we really know it exists, if we can't see it?

The story began in 1933 when Astronomer Fritz Zwicky was studying the motions of distant and massive clusters of galaxies, specifically the Coma cluster and the Virgo cluster. Zwicky estimated the mass of each galaxy in the cluster based on their luminosity, and added up all of the galaxy masses to get a total cluster mass. He then made a second, independent estimate of the cluster mass, based on measuring the spread in velocities of the individual galaxies in the cluster. To his suprise, this second dynamical mass estimate was 400 times larger than the estimate based on the galaxy light.

Although the evidence was strong at Zwicky's time, it was not until the 1970s that scientists began to explore this discrepancy comprehensively. It was at this time that the existence of Dark Matter began to be taken seriously. The existence of such matter would not only resolve the mass deficit in galaxy clusters; it would also have far more reaching consequences for the evolution and fate of the universe itself.

Another phenomenon that suggested the need for dark matter is the rotational curves of Spiral Galaxies. Spiral Galaxies contain a large population of stars that orbit the Galactic center on nearly circular orbits, much like planets orbit a star. Like planetary orbits, stars with larger galactic orbits are expected to have slower orbital speeds (this is just a statement of Kepler's 3rd Law). Actually, Kepler's 3rd Law only applies to stars near the perimeter of a Spiral Galaxy, because it assumes the mass enclosed by the orbit to be constant.

However, astronomers have made observations of the orbital speeds of stars in the outer parts of a large number of spiral galaxies, and none of them follow Kepler's 3rd Law as expected. Instead of falling off at larger radii, the orbital speeds remain remarkably constant. The implication is that the mass enclosed by larger-radius orbits increases, even for stars that are apparently near the edge of the galaxy. While they are near the edge of the luminous part of the galaxy, the galaxy has a mass profile that apparently continues well beyond the regions occupied by stars.

Here is another way to think about it: Consider the stars near the perimeter of a spiral galaxy, with typical observed orbital velocities of 200 kilometers per second. If the galaxy consisted of only the matter that we can see, these stars would very quickly fly off from the galaxy, because their orbital speeds are four times larger than the galaxy's escape velocity. Since galaxies are not seen to be spinning apart, there must be mass in the galaxy that we are not accounting for when we add up all the parts we can see.

Several theories have surfaced in literature to account for the missing mass such as WIMPs (Weakly Interacting Massive Particles), MACHOs (MAssive Compact Halo Objects), primordial black holes, massive neutrinos, and others; each with their pros and cons. No single theory has yet been accepted by the astronomical community, because we so far lack the means to conclusively test one theory against the other.

Parallax is the apparent change of an observed object's position caused by a shift in the observer's position. As an example, hold your hand in front of you at arm's length, and observe an object on the other side of the room behind your hand. Now tilt your head to your right shoulder, and your hand will appear on the left side of the distant object. Tilt your head to your left shoulder, and your hand will appear to shift to the right side of the distant object.

Because the Earth is in orbit around the Sun, we observe the sky from a constantly moving position in space. Therefore, we should expect to see an annual parallax effect, in which the positions of nearby objects appear to “wobble” back and forth in response to our motion around the Sun. This does in fact happen, but the distances to even the nearest stars are so great that you need to make careful observations with a telescope to detect it^[2].

Modern telescopes allow astronomers to use the annual parallax to measure the distance to nearby stars, using triangulation. The astronomer carefully measures the position of the star on two dates, spaced six months apart. The nearer the star is to the Sun, the larger the apparent shift in its position will be between the two dates.

Over the six-month period, the Earth has moved through half its orbit around the Sun; in this time its position has changed by 2 Astronomical Units (abbreviated AU; 1 AU is the distance from the Earth to the Sun, or about 150 million kilometers). This sounds like a really long distance, but even the nearest star to the Sun (alpha Centauri) is about 40 trillion kilometers away! Therefore, the annual parallax is very small, typically smaller than one arcsecond, which is only 1/3600 of one degree. A convenient distance unit for nearby stars is the parsec, which is short for "parallax arcsecond". One parsec is the distance a star would have if its observed parallax angle was one arcsecond. It is equal to 3.26 light-years, or 31 trillion kilometers^[3].

Retrograde Motion is the orbital motion of a body in a direction opposite that which is normal to spatial bodies within a given system.

When we observe the sky, we expect most objects to appear to move in a particular direction with the passing of time. The apparent motion of most bodies in the sky is from east to west. However it is possible to observe a body moving west to east, such as an artificial satellite or space shuttle that is orbiting eastward. This orbit is considered Retrograde Motion.

Retrograde Motion is most often used in reference to the motion of the outer planets (Mars, Jupiter, Saturn, and so forth). Though these planets appear to move from east to west on a nightly basis in response to the spin of the Earth, they are actually drifting slowly eastward with respect to the stationary stars, which can be observed by noting the position of these planets for several nights in a row. This motion is normal for these planets, however, and not considered Retrograde Motion. However, since the Earth completes its orbit in a shorter period of time than these outer planets, we occassionally overtake an outer planet, like a faster car on a multiple-lane highway. When this occurs, the planet we are passing will first appear to stop its eastward drift, and it will then appear to drift back toward the west. This is Retrograde Motion, since it is in a direction opposite that which is typical for planets. Finally as the Earth swings past the the planet in its orbit, they appear to resume their normal west-to-east drift on succesive nights.

This Retrograde Motion of the planets puzzled ancient Greek astronomers, and was one reason why they named these bodies “planets” which in Greek means “wanderers”.

Elliptical galaxies are spheroidal concentrations of stars that resemble Globular Clusters on a grand scale. They have very little internal structure; the density of stars declines smoothly from the concentrated center to the diffuse edge, and they can have a broad range of ellipticities (or aspect ratios). They typically contain very little interstellar gas and dust, and no young stellar populations (although there are exceptions to these rules). Edwin Hubble referred to Elliptical galaxies as “early-type” galaxies, because he thought that they evolved to become Spiral Galaxies (which he called “late-type” galaxies). Astronomers actually now believe the opposite is the case (i.e., that Spiral galaxies can turn into Elliptical galaxies), but Hubble's early- and late-type labels are still used.

Once thought to be a simple galaxy type, ellipticals are now known to be quite complex objects. Part of this complexity is due to their amazing history: ellipticals are thought to be the end product of the merger of two Spiral galaxies. You can view a computer simulation MPEG movie of such a merger at this NASA HST webpage (warning: the file is 3.4 MB).

Elliptical galaxies span a very wide range of sizes and luminosities, from giant Ellipticals hundreds of thousands of light years across and nearly a trillion times brighter than the sun, to dwarf Ellipticals just a bit brighter than the average globular cluster. They are divided to several morphological classes:

2500 years ago, the ancient Greek astronomer Hipparchus classified the brightnesses of visible stars in the sky on a scale from 1 to 6. He called the very brightest stars in the sky “first magnitude”, and the very faintest stars he could see “sixth magnitude”. Amazingly, two and a half millenia later, Hipparchus's classification scheme is still widely used by astronomers, although it has since been modernized and quantified.

The modern magnitude scale is a quantitative measurement of the flux of light coming from a star, with a logarithmic scaling:

m = m_0 - 2.5 log (F / F_0)

If you don't understand the math, this just says that the magnitude of a given star (m) is different from that of some standard star (m_0) by 2.5 times the logarithm of their flux ratio. The 2.5 *log factor means that if the flux ratio is 100, the difference in magnitudes is 5 mag. So, a 6th magnitude star is 100 times fainter than a 1st magnitude star. The reason Hipparchus's simple classification translates to a relatively complex function is that the human eye responds logarithmically to light.

There are several different magnitude scales in use, each of which serves a different purpose. The most common is the apparent magnitude scale; this is just the measure of how bright stars (and other objects) look to the human eye. The apparent magnitude scale defines the star Vega to have magnitude 0.0, and assigns magnitudes to all other objects using the above equation, and a measure of the flux ratio of each object to Vega.

It is difficult to understand stars using just the apparent magnitudes. Imagine two stars in the sky with the same apparent magnitude, so they appear to be equally bright. You can't know just by looking if the two have the same intrinsic brightness; it is possible that one star is intrinsically brighter, but further away. If we knew the distances to the stars (see the parallax article), we could account for their distances and assign Absolute magnitudes which would reflect their true, intrinsic brightness. The absolute magnitude is defined as the apparent magnitude the star would have if observed from a distance of 10 parsecs (1 parsec is 3.26 light-years, or 3.1 x 10^18 cm). The absolute magnitude (M) can be determined from the apparent magnitude (m) and the distance in parsecs (d) using the formula (note that M=m when d=10):

M = m + 5 - 5 * log d

The modern magnitude scale is no longer based on the human eye; it is based on photographic plates and photoelectric photometers. With telescopes, we can see objects much fainter than Hipparchus could see with his unaided eyes, so the magnitude scale has been extended beyond 6th magnitude. In fact, the Hubble Space Telescope can image stars nearly as faint as 30th magnitude, which is one trillion times fainter than Vega!

A final note: the magnitude is usually measured through a color filter of some kind, and these magnitudes are denoted by a subscript describing the filter (i.e., m_V is the magnitude through a “visual” filter, which is greenish; m_B is the magnitude through a blue filter; m_pg is the photographic plate magnitude, etc.).

Stars appear to be exclusively white at first glance. But if we look carefully, we can notice a range of colors: blue, white, red, and even gold. In the winter constellation of Orion, a beautiful contrast is seen between the red Betelgeuse at Orion's "armpit" and the blue Bellatrix at the shoulder. What causes stars to exhibit different color remained a mystery until two centuries ago, when Physicists gained enough understanding of the nature of light and the properties of matter at immensely high temperatures.

Specifically, it was the physics of blackbody radiation that enabled us to understand the variation of stellar colors. Shortly after blackbody radiation was understood, it was noticed that the spectra of stars look extremely similar to blackbody radiation curves of various temperatures, ranging from a few thousand Kelvin to ~50,000 Kelvin. The obvious conclusion is that stars are similar to blackbodies, and that the color variation of stars is a direct consequence of their surface temperatures.

Cool stars (i.e., Spectral Type K and M) radiate most of their energy in the red and infrared region of the electromagnetic spectrum and thus appear red, while hot stars (i.e., Spectral Type O and B) emit mostly at blue and ultra-violet wavelengths, making them appear blue or white.

To estimate the surface temperature of a star, we can use the known relationship between the temperature of a blackbody, and the wavelength of light where its spectrum peaks. That is, as you increase the temperature of a blackbody, the peak of its spectrum moves to shorter (bluer) wavelengths of light. This is illustrated in Figure 1 where the intensity of three hypothetical stars is plotted against wavelength. The "rainbow" indicates the range of wavelengths that are visible to the human eye.

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The spectra of three hypothetical stars of different temperatures

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This simple method is conceptually correct, but it cannot be used to obtain stellar temperatures accurately, because stars are not perfect blackbodies. The presence of various elements in the star's atmosphere will cause certain wavelengths of light to be absorbed. Because these absorption lines are not uniformly distributed over the spectrum, they can skew the position of the spectral peak. Moreover, obtaining a usable spectrum of a star is a time-intensive process and is prohibitively difficult for large samples of stars.

An alternative method utilizes photometry to measure the intensity of light passing through different filters. Each filter allows only a specific part of the spectrum of light to pass through while rejecting all others. A widely used photometric system is called the Johnson UBV system. It employs three bandpass filters: U ("Ultra-violet"), B ("Blue"), and V ("Visible") regions of the electromagnatic spectrum.

The process of UBV photometry involves using light sensitive devices (such as film or CCD cameras) and aiming a telescope at a star to measure the intensity of light that passes through each of the filters individually. This procedure gives three apparent brightnesses or fluxes (amount of energy per cm^2 per second) designated by Fu, Fb, and Fv. The ratio of fluxes Fu/Fb and Fb/Fv is a quantitative measure of the star's "color", and these ratios can be used to establish a temperature scale for stars. Generally speakiing, the larger the Fu/Fb and Fb/Fv ratios of a star, the hotter is its surface temperature.

For example, the star Bellatrix in Orion has Fb/Fv = 1.22, indicating that it is brighter through the B filter than through the V filter. furthermore, its Fu/Fb ratio is 2.22, so it is brighest through the U filter. This indicates that the star must be very hot indeed, since the position of its spectral peak must be somewhere in the range of the U filter, or at an even shorter wavelength. The surface temperature of Bellatrix (as determined from comparing its spectrum to detailed models that account for its absorption lines) is about 25,000 Kelvin.

We can repeat this analysis for the star Betelgeuse. Its Fb/Fv and Fu/Fb ratios are 0.15 and 0.18, respectively, so it is brightest in V and dimmest in U. So, the spectral peak of Betelgeuse must be somewhere in the range of the V filter, or at an even longer wavelength. The surface temperature of Betelgeuse is only 2,400 Kelvin.

Astronomers prefer to express star colors in terms of a difference in magnitudes, rather than a ratio of fluxes. Therefore, going back to blue Bellatrix we have a color index equal to

B - V = -2.5 log (Fb/Fv) = -2.5 log (1.22) = -0.22,

Similarly, the color index for red Betelgeuse is

B - V = -2.5 log (Fb/Fv) = -2.5 log (0.18) = 1.85

The color indices, like the magnitude scale, run backward. Hot and blue stars have smaller and negative values of B-V than the cooler and redder stars as illustrated below.

An Astronomer can then use the color indices for a star, after correcting for reddening and interstellar extinction, to obtain an accurate temperature of that star. The relationship between B-V and temperature is illustrated in Figure 2.

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The relationship between a stars's B-V color index and its temperature.

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The Sun with surface temperature of 5,800 K has a B-V index of 0.62.