The Celestial Sphere
The Celestial Sphere is a concept which helps us think about the positions of objects in the sky. Looking up at the sky, you might imagine that it is a huge dome or top half of a sphere, and the stars are points of light on that sphere. Visualising the sky in such a manner, it appears that the sphere moves, taking all the stars with it — it seems to rotate. If watch the movement of the stars we can see that they seem to rotate around a static point about once a day. Stellarium is the perfect tool to demonstrate this!
- Open the configuration window, select the location tab. Set the location to be somewhere in mid-Northern latitudes. The United Kingdom is an ideal location for this demonstration.
- Turn off atmospheric rendering and ensure cardinal points are turned on. This will keep the sky dark so the Sun doesn't prevent us from seeing the motion of the stars when it is above the horizon.
- Pan round to point North, and make sure the field of view is about 90°.
- Pan up so the `N' cardinal point on the horizon is at the bottom of the screen.
- Now increase the time rate. Press k, l, l, l, l - this should set the time rate so the stars can be seen to rotate around a point in the sky about once every ten seconds If you watch Stellarium's clock you'll see this is the time it takes for one day to pass as this accelerated rate.
The point which the stars appear to move around is one of the Celestial Poles.
The apparent movement of the stars is due to the rotation of the Earth. The location of the observer on the surface of the Earth affects how she perceives the motion of the stars. To an observer standing at Earth's North Pole, the stars all seem to rotate around the zenith (the point directly upward). As the observer moves South towards the equator, the location of the celestial pole moves down towards the horizon. At the Earth's equator, the North celestial pole appears to be on the Northern horizon.
Similarly, observers in the Southern hemisphere see the Southern celestial pole at the zenith when they are at the South pole, and it moves to the horizon as the observer travels towards the equator.
- Leave time moving on nice and fast, and open the configuration window. Go to the location tab and click on the map right at the top - i.e. set your location to the North pole. See how the stars rotate around a point right at the top of the screen. With the field of view set to 90° and the horizon at the bottom of the screen, the top of the screen is the zenith.
- Now click on the map again, this time a little further South, You should see the positions of the stars jump, and the centre of rotation has moved a little further down the screen.
- Click on the map even further towards and equator. You should see the centre of rotation have moved down again.
To help with the visualisation of the celestial sphere, turn on the equatorial grid by clicking the button on the main tool-bar or pressing the on the e key. Now you can see grid lines drawn on the sky. These lines are like lines of longitude and latitude on the Earth, but drawn for the celestial sphere.
The Celestial Equator is the line around the celestial sphere that is half way between the celestial poles - just as the Earth's equator is the line half way between the Earth's poles.
The Altitude/Azimuth coordinate system can be used to describe a direction of view (the azimuth angle) and a height in the sky (the altitude angle). The azimuth angle is measured clockwise round from due North. Hence North itself is °, East 90°, Southwest is 225° and so on. The altitude angle is measured up from the horizon. Looking directly up (at the zenith) would be 90°, half way between the zenith and the horizon is 45° and so on. The point opposite the zenith is called the nadir.
However, the altitude/azimuth coordinate system is not suitable for describing the general position of stars and other objects in the sky - the altitude and azimuth values for an object in the sky change with time and the location of the observer.
Stellarium can draw grid lines for altitude/azimuth coordinates. Use the button on the main tool-bar to activate this grid, or press the z key.
Right Ascension/Declination Coordinates
Like the Altitude/Azimuth system, the Right Ascension/Declination (RA/Dec) coordinate system uses two angles to describe positions in the sky. These angles are measured from standard points on the celestial sphere. Right ascension and declination are to the celestial sphere what longitude and latitude are to terrestrial map makers.
The Northern celestial pole has a declination of 90°, the celestial equator has a declination of °, and the Southern celestial pole has a declination of -90°.
Right ascension is measured as an angle round from a point in the sky known as the first point of Aries, in the same way that longitude is measured around the Earth from Greenwich. Figure RA/Dec illustrates RA/Dec coordinates.
Unlike Altitude/Azimuth coordinates, RA/Dec coordinates of a star do not change if the observer changes latitude, and do not change over the course of the day due to the rotation of the Earth (the story is complicated a little by precession and parallax - see sections precession and parallax respectively for details). RA/Dec coordinates are frequently used in star catalogues such as the Hipparcos catalogue.
As Douglas Adams pointed out in the Hitchhiker's Guide to the Galaxy[hhg],
Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.[hhg]
Astronomers use a variety of units for distance that make sense in the context of the mind-boggling vastness of space.
Astronomical Unit (AU) This is the mean Earth-Sun distance. Roughly 150 million kilometres (1.49598x108km). The AU is used mainly when discussing the solar system - for example the distance of various planets from the Sun.
Light year A light year is not, as some people believe, a measure of time. It is the distance that light travels in a year. The speed of light being approximately 300,000 kilometres per second means a light year is a very large distance indeed, working out at about 9.5 trillion kilometres (9.46073x1012 km). Light years are most frequently used when describing the distance of stars and galaxies or the sizes of large-scale objects like galaxies, nebulae etc.
Parsec A parsec is defined as the distance of an object that has an annual parallax of 1 second of arc. This equates to 3.26156 light years (3.08568x1013 km). Parsecs are most frequently used when describing the distance of stars or the sizes of large-scale objects like galaxies, nebulae etc.
The length of a day is defined as the amount of time that it takes for the Sun to travel from the highest point in the sky at mid-day to the next high-point on the next day. In astronomy this is called a solar day. The apparent motion of the Sun is caused by the rotation of the Earth. However, in this time, the Earth not only spins, it also moves slightly round it's orbit. Thus in one solar day the Earth does not spin exactly 360° on it's axis. Another way to measure day length is to consider how long it takes for the Earth to rotate exactly 360°. This is known as one sidereal day.
Figure [fig:solarsiderealday] illustrates the motion of the Earth as seen looking down on the Earth orbiting the Sun. The red triangle on the Earth represents the location of an observer. The figure shows the Earth at four times:
- The Sun is directly overhead - it is mid-day.
- Twelve hours have passed since 1. The Earth has rotated round and the observer is on the opposite side of the Earth from the Sun. It is mid-night. The Earth has also moved round in it's orbit a little.
- The Earth has rotated exactly 360°. Exactly one sidereal day has passed since 1.
- It is mid-day again - exactly one solar day since 1. Note that the Earth has rotated more than 360° since 1.
It should be noted that in figure [fig:solarsiderealday] the sizes of the Sun and Earth and not to scale. More importantly, the distance the Earth moves around it's orbit is much exaggerated. In one real solar day, the Earth takes a year to travel round the Sun - 3651/4 solar days. The length of a sidereal day is about 23 hours, 56 minutes and 4 seconds.
It takes exactly one sidereal day for the celestial sphere to make one revolution in the sky. Astronomers find sidereal time useful when observing. When visiting observatories, look out for doctored alarm clocks that have been set to run in sidereal time!
Astronomers typically use degrees to measure angles. Since many observations require very precise measurement, the degree is subdivided into sixty minutes of arc also known as arc-minutes. Each minute of arc is further subdivided into sixty seconds of arc, or arc-seconds. Thus one degree is equal to 3600 seconds of arc. Finer grades of precision are usually expressed using the SI prefixes with arc-seconds, e.g. milli arc-seconds (one milli arc-second is one thousandth of an arc-second).
Degrees are denoted using the ° symbol after a number. Minutes of arc are denoted with a ′, and seconds of arc are denoted using ″. Angles are frequently given in two formats:
- DMS format — degrees, minutes and seconds. For example 90°15′12″. When more precision is required, the seconds component may include a decimal part, for example 90°15′12.432″.
- Decimal degrees, for example 90.2533°
The Magnitude Scale
|Sirius (the brightest star)||-1.5||1.4|
|Venus (at brightest)||-4.4||-|
|Full Moon (at brightest)||-12.6||-|
When astronomers talk about magnitude, they are referring to the brightness of an object. How bright an object appears to be depends on how much light it's giving out and how far it is from the observer. Astronomers separate these factors by using two measures: absolute magnitude (M) which is a measure of how much light is being given out by an object, and apparent magnitude (m) which is how bright something appears to be in the sky.
For example, consider two 100 watt lamps, one which is a few meters away, and one which is a kilometre away. Both give out the same amount of light - they have the same absolute magnitude. However the nearby lamp seems much brighter - it has a much greater apparent magnitude. When astronomers talk about magnitude without specifying whether they mean apparent or absolute magnitude, they are usually referring to apparent magnitude.
The magnitude scale has its roots in antiquity. The Greek astronomer Hipparchus defined the brightest stars in the sky to be first magnitude, and the dimmest visible to the naked eye to be sixth magnitude. In the 19th century British astronomer Norman Pogson quantified the scale more precisely, defining it as a logarithmic scale where a magnitude 1 object is 100 times as bright as a magnitude 6 object (a difference of five magnitudes). The zero-point of the modern scale was originally defined as the brightness of the star Vega, however this was re-defined more formally in 1982[landolt]. Objects brighter than Vega are given negative magnitudes.
Luminosity is an expression of the total energy radiated by a star. It may be measured in watts, however, astronomers tend to use another expression — solar luminosities where an object with twice the Sun's luminosity is considered to have two solar luminosities and so on. Luminosity is related to absolute magnitude.
As the Earth orbits the Sun throughout the year, the axis of rotation (the line running through the [rotational] poles of the Earth) seems to point towards the same position on the celestial sphere, as can be seen in figure [fig:obliquityecliptic]. The angle between the axis of rotation and the perpendicular of the orbital plane is called the obliquity of the ecliptic. It is 23° 27'.
Observed over very long periods of time the direction the axis of rotation points does actually change. The angle between the axis of rotation and the orbital plane stays constant, but the direction the axis points — the position of the celestial pole transcribes a circle on the stars in the celestial sphere. This process is called precession. The motion is similar to the way in which a gyroscope slowly twists as figure [fig:precession] illustrates.
Precession is a slow process. The axis of rotation twists through a full 360° about once every 28,000 years.
Precession has some important implications:
- RA/Dec coordinates change over time, albeit slowly. Measurements of the positions of stars recorded using RA/Dec coordinates must also include a date for those coordinates.
- Polaris, the pole star won't stay a good indicator of the location of the Northern celestial pole. In 14,000 years time Polaris will be nearly 47° away from the celestial pole!
Parallax is the change of angular position of two stationary points relative to each other as seen by an observer, due to the motion of said observer. Or more simply put, it is the apparent shift of an object against a background due to a change in observer position.
A similar thing happens due to the Earth's motion around the Sun. Nearby stars appear to move against more distant background stars, as illustrated in figure parallax. The movement of nearby stars against the background is called stellar parallax, or annual parallax.
In figure parallax the annual parallax p is half the angular distance between the apparent positions of the nearby star. The distance of the nearby object is d. Astronomers use a unit of distance called the parsec which is defined as the distance at which a nearby star has p = 1″.
Even the nearest stars exhibit very small movement due to parallax. The closest star to the Earth other than the Sun is Proxima Centuri. It has an annual parallax of 0.77199″, corresponding to a distance of 1.295 parsecs (4.22 light years).
Even with the most sensitive instruments for measuring the positions of the stars it is only possible to use parallax to determine the distance of stars up to about 1,600 light years from the Earth, after which the annual parallax is so small it cannot be measured accurately enough.
Proper motion is the change in the position of a star over time as a result of it's motion through space relative to the Sun. It does not include the apparent shift in position of star due to annular parallax. The star exhibiting the greatest proper motion is Barnard's Star which moves more then ten seconds of arc per year.