Units used in Astronomy
It is difficult to measure distances from far away. Suppose you are looking at a utility pole some distance from you. To the naked eye it looks quite small - it is hard for you to gauge how tall the pole is. However, if a person happens to pass by that pole, you might have a chance. How? Well, by comparing the height of that person to the height of the pole; knowing that a person is approximately 6 feet tall, one can estimate the height of the pole. If we are looking at the sky, we are confronted with a similar problem: gauging the distance of stars.
As I said, the brightest and apparently largest objects in the sky are
the sun and the moon. They look to us to have approximately the same dimensions. But they don't. The moon has a diameter of 3,400 Km while the Sun has a diameter of 1.4 million Km.
The Moon is much closer to the Earth (384,000 Km) than the Sun (150 million Km). In the picture below, the angle subtended by M (Moon) and S (Sun) is the same, but M and S have different distances from the observer A. (Please note that M, S, and their distances to A are not drawn to scale; D1 and D2 are the Moon's and Sun's diameters, respectively).
Click on the figure to make it bigger.
It is important to understand "angular size" since so much in astronomy depends on it; angular size is the fraction of a complete circle that a celestial body appears to cover when seen from our observation point. A complete circle is traditionally divided in 360 parts, or "degrees". Each degree is in turn subdivided into 60 minutes of arc, and each minute into 60 seconds of arc.
An angle can sometimes be more easily measured by taking the ratio of lengths, see the figure above. In this case, the unit of angle is the radian; to obtain an angle in degrees, multiply the value in radians by 180/3.1415. For example, if D1=3,400 Km and L1=384,00, the angle is 3,400/384,00=0.009 radians or 0.009 x 180/3.14 = 0.51 degree.
Once we have determined the angular size of an object, then we can estimate the distance from us. In the example above, if we know the diameter of the Sun and its angular size as seen from the Earth (0.5 deg.) then we can calculate the distance to Sun. Thus,
0.5 deg. x 3.14/180 = 0.009 rad.
1.4 106Km / 0.009 rad. = 1.55 108 Km (155 million Km).
In reality the average distance of the Earth from the Sun, when more accurate numbers are used, is 1.496 108Km. This is the average distance between the Earth and the Sun, and it has a name: Astronomical Unit, or AU. Thus, 1 AU = 1.496 108.
But this unit of distance is too small for astronomy, except when we deal with the Solar system (Mercury is 0.39 AU from the Sun, while Pluto is 39.44 AU from the Sun - these are actually the lengths of the semimajor axis of their orbits). If you consider that the our closest star besides the Sun, alpha-Centauri, is at about 2.7 105 AU, then you realize that the AU is too small a unit of distance.
Introducing the light-year. The light-year, or ly, is the distance travelled by light, in empty space, in one year. Alpha-Centaury is about 4.3 ly away. To get this distance in Km we proceed as folllows.
speed of light = 300,000 Km/sec
seconds in one minute = 60
seconds in one hour = 60 x 60 = 3,600
seconds in one day = 3,600 x 24 = 86,400
seconds in one year = 86,400 x 365 = 3.15 107
So, in one year, the light travels = spees x time = 300,000 Km/sec x 3.15 107 = 9.46 10 12 Km. To convert this number in AU, recall that 1 AU is 1.496 108 Km; thus:
9.46 1012 / 1.496 108 = 6.32 104.
It is clear that AU is not a useful unit to measure distances to stars.
To summarize, the units of distance and angle used in astronomy are:
AU, light-year, parsec (to be defined in the next section) and radian. Parsec is the unit that will be introduced next.
The following table is given to provide a more complete picture of units and constants used in astronomy. Other useful tables are located in the Topics Section. Click here to open the tables in a separate window.