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Appendix A: Scientific Notation Appendix A: Scientific Notation Since in astronomy we often have to deal with large numbers, writing a lot of zeros is not only cumbersome, but also inefficient and difficult to count. Scientists use the system of scientific notation, where the number of zeros is short handed to a superscript. For example, 10 has one zero and is written as 101 in scientific notation. Similarly, 100 is 102, 100 is 103. So we have: 103 equals a thousand, 106 equals a million, 109 is called a billion (U.S. usage), and 1012 a trillion. Now the U.S. federal government budget is in the trillions of dollars, ordinary people really cannot grasp the magnitude of the number. In the metric system, the prefix kilo- stands for 1,000, e.g., a kilogram. For a million, the prefix mega- is used, e.g. megaton (1,000,000 or 106 ton). A billion hertz (a unit of frequency) is gigahertz, although I have not heard of the use of a giga-meter. More rarely still is the use of tera (1012). For small numbers, the practice is similar. 0.1 is 10À1, 0.01 is 10À2, and 0.001 is 10À3. The prefix of milli- refers to 10À3, e.g. as in millimeter, whereas a micro- second is 10À6 ¼ 0.000001 s. It is now trendy to talk about nano-technology, which refers to solid-state device with sizes on the scale of 10À9 m, or about 10 times the size of an atom. With this kind of shorthand convenience, one can really go overboard. Physicists now boldly talk about what is happening in the first 10À26 s of the Universe. Now that is a lot faster than a blink of an eye. S. Kwok, Stardust, Astronomers’ Universe, DOI 10.1007/978-3-642-32802-2, 215 # Springer-Verlag Berlin Heidelberg 2013 Appendix B: Units of Measurement Distance Because the scales in space and time that we study in astronomy are so different from our everyday lives, astronomers find it necessary to devise new, and some- times bizarre, units of measurements. Instead of kilometer (or miles in the United States), astronomers talk about light years (the distance traveled by light in one year), or even the obscured unit of a parsec (the distance of a star which will shift in position in the sky by 1 arc second in angle when the Earth moves from one side of the Sun to the other). The unit of parsec was first devised as a common unit to refer to distance of stars, as the nearest star Proxima Centauri is located at 1.3 pc (or 4.2 light years). The distance between the Sun and the center of the Milky Way Galaxy is about 8,000 parsecs, or 26,000 light years. The Andromeda Galaxy, the nearest galaxy similar to our Milky Way galaxy, is at 770,000 parsecs (or 2.5 million light years) away. For studies of the Solar System, and now increasingly the study of extra-solar planetary systems, the astronomical unit (A.U.) is commonly used. One A.U. is the distance between the Earth and the Sun, or about 150,000,000 km. There are 63,240 A.U.s in a light year, so the size of planetary systems is much smaller than the separation between stars. The unit light year is commonly used in popular astronomy writings, but almost never in professional literature, where the unit of parsec is almost exclusively used. Since a light year is only three times smaller than a parsec, there is no reason why light year cannot be adopted as standard unit of measurement for distance in astronomy. The practice of using parsec is more a habit and tradition than logic, as the unit light year is clearly much easier to understand. I sometimes cannot help but feel that the use of jargons in science (this is worse in social sciences) is more intended to confuse the outsiders than for clear communication. While the size of stars are huge and the size of the Universe is even larger, in astronomy we also have to deal with small objects, such as atoms, molecules, and S. Kwok, Stardust, Astronomers’ Universe, DOI 10.1007/978-3-642-32802-2, 217 # Springer-Verlag Berlin Heidelberg 2013 218 Appendix B: Units of Measurement the dust particles that we describe in this book. Here, more conventional systems of units are used. The size of an atom is about 0.1 nm (1 nm ¼ 10À9 m), and stardust that we talk about in this book has sizes of the order of a micrometer (micrometer, or μm, where 1 μm ¼ 10À6 m). The wavelengths of visible colors are measured in fraction of a micrometer, or hundreds of nanometer (nm). Time Fortunately, astronomers do not see fit to invent a new unit of time. The most commonly used units of time are the familiar units of seconds and years. However, the long lives of stars and the age of the Universe necessitate the need of using million (106) or billion (109) years to refer to long intervals of time. Angle The sky above us is two dimensional. We see a distribution of stars in the sky but we have no concept of depth. It is not easy to tell which star is farther away than the other. We are, however, able to measure the angular separation between two stars. Because the year is 365 days, which is close to the nice number of 360 which can be divided by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, etc., we have adopted 360 as a full circle. Again, since 60 is a good number, we divide a degree into 60 arc minute, and an arc minute into 60 arc second. A 1-cm coin placed at a distance of 1 km will have an angular size of 2 arc second, so 1 arc second is very small separation indeed. Color The visible light is made up of different colors ranging from red to violet. We now know that light is just part of the general phenomenon of electromagnetic waves, and there is no fundamental difference between visible light and radio waves. The only difference between the two is the wavelength (the distance between the repeating peaks of the waves), with radio waves having wavelengths of the order of meters and visible light with wavelengths of fractions of a micrometer. Within the range of visible light, different colors are characterized again by different wavelengths. The rainbow colors from red to violet correspond to a decreasing wavelength scale, with the red color having a wavelength of about 0.7 μm and the blue color about 0.4 μm. Just outside the visible range, on the long wavelengths side is the infrared, and on the short wavelength side is ultraviolet. X-rays have even shorter wavelengths than ultraviolet, with wavelengths of the order of nanometer. Appendix B: Units of Measurement 219 Alternatively, colors can be specified by frequency measured in units of cycles per second (Hz). Frequency and wavelengths are two ways to describe the same thing, but in a reciprocal way. The multiplication product of frequency (ν) and wavelengths (λ) is a constant (the speed of light) so one can easily derive one from the other. Mathematically, the relationship between the two is ν Á λ ¼ c; where c is the speed of light (3 Â 1010 cm/s). In other words, electromagnetic waves with a high frequency have short wavelengths. Frequency as a unit of color is more commonly used in radio waves, e.g., we refer to the FM radios having frequency coverage from 88 to 108 MHz (1 MHz ¼ 106 Hz). Usual cellular phone communication frequencies are 900 MHz and 1.8 GHz (1 GHz ¼ 109 Hz). Expressed in wavelengths, FM radio waves have wavelengths of the order of 3 m, whereas radio waves from cellular phones have wavelengths of 33 and 17 cm. Scientists rarely ever use frequency as a measure of color in the visible. Appendix C: Color and Temperature The precise formula governing the amount of radiation at any wavelength emitted by an object of a certain temperature was worked out by Max Planck (1858–1947) based on the quantum nature of light. The relationship between the peak of the radiation and the temperature is very simple: λmaxðÞÁcm TKðÞ¼0:3 which is known as the Wien’s law. For example, a star of 6,000 K will have its radiation peak at 0.00005 cm, or 0.5 μm, which is in the visible region. An object at room temperature (300 K) will radiate at 0.001 cm, or 10 μm, which in the infrared. S. Kwok, Stardust, Astronomers’ Universe, DOI 10.1007/978-3-642-32802-2, 221 # Springer-Verlag Berlin Heidelberg 2013 Appendix D: Naming Convention of Astronomical Objects Since there are billions of celestial objects in the sky, there is a need to devise a system for us to refer to them. The naming of celestial objects is diverse, although the International Astronomical Union has tried to regulate the practice in recent years. The Sun, the Moon, and the Earth all have names in each individual culture. Due to historical reasons, different classes of objects are named in a different manner. 1. Planets: names of the five brightest planets Mercury, Venus, Mars, Jupiter, and Saturn were named after mystic Greek or Roman gods. The later discovered planets Uranus and Neptune also followed this tradition. Outside of the western culture, all these planets have different names in different languages.
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