which is also the angular resolution of the Solar Optical Telescope on the Hinodemission. The size of a telescope required to give this angular resolution at a yellow wavelength ofk=580 nm isDT=k=h&0.5 m. TheHinode mission also has an x-ray instrument, operating at a wavelength of k=1.24910-10m, corresponding to 10 keV in photon energy (seeSect. 2.6 for definition of photon energy). The size of the x-ray telescope for the same angular resolution isDT=k=h&0.0001 m. A ground-based radio telescope is not limited in angular resolution by the atmosphere, but to achieve an angular resolution of 0.2500at a radio wavelength ofk=1 m, the telescope diameter would have to beDT=k=h&106m or a million meters, comparable in size to a large country and about one sixth the radius of the Earth.
The smallest linear size,L, that can be resolved on the Sun with any tele- scope with this angular resolution is L=D9h, where the mean distance between the Earth and the Sun isD=1 AU=1.49691011 m, and therefore
L&181 km for an angular resolution of 0.2500 =1.212910-6rad. By
way of comparison, the angular resolution of the human eye is about 6000so the smallest sunspot that the eye can resolve has a size of L =AU 9 6000 94.848910-6&4.359107m&6.8RE where the radius of the EarthRE=6,378 km. The tallest mountain that can be observed at the limb, or edge, of the Moon with the unaided human eye will have a height H=D9hwhere the mean distance of the Moon is 3.8449108m and for h=6000we have a mountain height ofH=1.12 9105m, much taller than Mount Everest, whose elevation is 8.8489103m. In other words, we could not see mountains on the Moon until telescopes were used.
galaxy often contains even more mass in invisible dark matter that lies beyond the visible stars.
The rate at which radiation carries energy away from a cosmic object is known as its luminosity, designated by L. Luminosity has the units of energy per unit time, which is also the unit of power. The SI unit of luminosity is a joule per second (J s-1), where joule is the unit of energy, and one watt of power is equal to one joule per second, or 1 J s-1=1 W.
The unit of luminosity used by astronomers is often the Sun’s luminosity, denotedL. Its value is:
L¼3:828 1026J s1;
where J s-1denotes joule per second. Stars vary by many orders of magnitude in their luminosity, from 0.001L to a millionLor from 10-3L to 106L. The luminosity of a galaxy is roughly 1011L.
In astronomy and astrophysics, temperatures are measured on the kelvin scale, named after Lord Kelvin (1824-1907) who proposed it (Kelvin 1848). This temperature unit is written kelvin, with a lower case k, and assigned the unit symbol capital K. The freezing temperature of water is 273.15 K and the boiling temperature of water at sea level on Earth is 373.15 K. The kelvin scale is an absolute, thermodynamic temperature scale where absolute zero is the temperature at which all thermal motion ceases. Nothing can move at a temperature of 0 K. For conversion to the degrees Centigrade, denoted by C, and degrees Fahrenheit, abbreviated by F, we have K=C?273.15=(5F=9) ?255.22, with C=K- 273.15 and F=(9 K=5)-459.67=(9C=5)?32.
Astronomers use the astronomical unit (AU) as the unit of distance within the solar system. It is the mean distance between the Earth and the Sun, with a value of
1 AU¼149597870691 m 1:496 1011m:
To be exact, astronomers now use the speed of light, denoted by the lower case letterc, as a defining constant for distance, with
Speed of light¼c¼299792458 m s1 2:9979 108m s1; with the derived value of the light travel time,sA, for 1 AU
sA¼499:0047863852 s 499 s:
This is the time it takes for radiation to travel from the Sun to the Earth.
The unit of stellar size is the radius of the Sun, denotedR, given by R¼6:955108m:
The supergiant stars can be as large as 1,000Rin radius, giant stars are about 10 times smaller, and the smallest stars that shine by nuclear reactions are about 0.1Rin radius. Collapsed white dwarf stars are about as big as the Earth, whose radius is 6.3789106m and about 0.01R.
28 1 Observing the Universe
The distances between stars are expressed in a unit called the parsec, or pc for short, where
1pc¼3:08567758128 1016m¼206265 AU3:086 1016m;
which is also equivalent to
1pc¼3:261564 light-year3:26 light-year;
where a light-year is the distance light travels in one year at the speed of light,c, or 1 light-year¼9:4607304726 1015m9:461 1015m:
As we shall subsequently see, the term parsec is derived from the parallax method of determining distance, where one parsec is a parallax of one second of arc.
Example: How far away and long ago was starlight emitted?
The Sun is located at a mean distance of 1 AU=1.49691011m. Traveling at the speed of light c=2.99799108m s-1, it takes a time s=AU=c=499 s for radiation to travel from the Sun to the Earth, so the sunlight we see this very moment was emitted 499 s ago. The nearest star other than the Sun is Proxima Centauri, and it takes 4.286 light-years for starlight to travel from this star to the Earth. Since 1 year=3.1569107s, the ratio of the distance to Proxima Centauri and the distance to the Sun is about 4.28693.1569107=499&271,000. The first stars were formed shortly after the big bang, which occurred about 13.7 billion years ago. So these first stars are located at a distance of about 13.7 billion light-years.
Using the conversion of 1 parsec=1 pc=3.26 light-years and l light-year
=9.46191015m, these first stars are located at a distance of about 4.29109pc and 1.391026 m, almost 1 million billion times further away than the Sun.
The extent of a galaxy is measured in units of kiloparsec, or kpc for short, where 1 kpc=103pc. The distance between the Sun and the center of our Galaxy is, for example, about 8.5 kpc. Nearby galaxies are separated by about a million parsecs, denoted as a megaparsec and abbreviated Mpc, where 1 Mpc=106 pc= 3.085791022m. The nearest large spiral galaxy, Andromeda or M 31, is located at a distance of 0.78 Mpc, while a very remote galaxy might be at a distance of a billion parsec, denoted as a gigaparsec and abbreviated as Gpc, where 1 Gpc=109pc.
Astronomers use the second, abbreviated by the lower case letter s, for small time scales and the year, or yr for short, for large ones. The orbital period of the Earth around the Sun is one year, with a value of
1 yr¼3:156 107s¼365:25 d;
1.10 Units Used by Astronomers and Astrophysicists 29
and 1 day=1 d=86,400 s. A pulsar might rotate with a period of 1 s, the Earth is 4.6 billion years, or 4.6 Gyr, old and the expanding universe originated about 14 billion years ago. The International System of Units (Système International, abbreviated SI, is used in this book. It includes the length unit of meter (m), the mass unit of kilogram (kg), and the time unit of second (s). The SI units of energy, luminosity, temperature, and magnetic field strength, are joule (J), watt (W, or J s-1), kelvin (K), and tesla (T), respectively.
Many astronomers and astrophysicists have often used, and still use, the c.g.s.
units of centimeter (cm), gram (g), second (s) in their professional papers.
Conversions from the SI units to the c.g.s. units are given in Table1.2.