Introduction to Astronomy
February 2016
Chapter 1
The scale of the universe
The Earth has a radius of about 6000km. Its mass is about 6 × 1027 grams. The Moon is about
4×105 km from the Earth. It takes about one second for light to travel from the Moon to the Earth.
The Sun is 1.5 × 108 km from the Earth. Light takes over 8 min to get here from the Sun, we call
this distance the Astronomical Unit (AU). Its mass is 2 × 1033 g. The Sun’s radius is 6 × 105 km.
We measure big distances in light years or parsecs (1 parsec is 3.26ly)
Chapter 2
Brightness of starlight
Let b1 and b2 be the observed brightnesses of two stars, and let m1 and m2 be the corresponding
magnitudes. The statement that a five-magnitude difference gives a flux ratio of 100 corresponds
to
b1 /b2 = 100(m2 −m1 )/5 → b1 /b2 = 10(m2 −m1 )/2.5
Increasing the brightness decreases the magnitude. So m=0 is the brightest stars and m=6 is the
faintest star.
If we want to calculate the magnitude difference for a given ratio, we take the logarithm (base 10)
of both sides, giving
m2 − m1 = 2.5log(b1 /b2 )
The electromagnetic spectrum
The wavelength is the distance between the corresponding points of a wave in successive cycles.
For example, from peak to peak. The product of the wavelength and the frequency gives the speed
of the wave. That is: c = λv. The higher the frequency, the shorter the wavelength.
We can see that the visible spectrum goes from 400nm to 700nm.
1
, Colors of stars
The color of a star depends on its temperature. We know that as we heat an object, first it
glows in the red, the it turns yellow/green and then it turns blue as it becomes even hotter.
We can understand the relationship between color and temperate by considering objects called
blackbodies. A blackbody is an object that absorbs all of the radiation that strikes it and also
emits radiation. If it radiates less energy than it absorbs, it will heat up. If it radiates more
energy than it absorbs, than it will cool. If we look at the blackbody spectra, as the temperature
increases the peak of the spectrum shifts to shorter wavelengths. The relationship between the
wavelength at which the peak occurs, λmax , and the temperature T, is very simple. It’s given by
Wien’s displacement law:
λmax T = 2.90 × 10−1 cmK = 2.90 × 106 nmK
The total energy per unit time, per unit surface area, E, given off by a blackbody is proportional
to the fourth power of the temperature. That is
E = σT 4
This relationship is called the Stefan-Boltzmann law. The constant of proportionalty, σ, is called
the Stefan-Boltzmann constant and its equal to 5.7 × 10−5 erg/(cm2 K 4 s.
The luminosity of a star is the total energy per second (power) given off by the star.
L = 4πR2 σT 4
where 4πR2 is the surface area.
Page 2
February 2016
Chapter 1
The scale of the universe
The Earth has a radius of about 6000km. Its mass is about 6 × 1027 grams. The Moon is about
4×105 km from the Earth. It takes about one second for light to travel from the Moon to the Earth.
The Sun is 1.5 × 108 km from the Earth. Light takes over 8 min to get here from the Sun, we call
this distance the Astronomical Unit (AU). Its mass is 2 × 1033 g. The Sun’s radius is 6 × 105 km.
We measure big distances in light years or parsecs (1 parsec is 3.26ly)
Chapter 2
Brightness of starlight
Let b1 and b2 be the observed brightnesses of two stars, and let m1 and m2 be the corresponding
magnitudes. The statement that a five-magnitude difference gives a flux ratio of 100 corresponds
to
b1 /b2 = 100(m2 −m1 )/5 → b1 /b2 = 10(m2 −m1 )/2.5
Increasing the brightness decreases the magnitude. So m=0 is the brightest stars and m=6 is the
faintest star.
If we want to calculate the magnitude difference for a given ratio, we take the logarithm (base 10)
of both sides, giving
m2 − m1 = 2.5log(b1 /b2 )
The electromagnetic spectrum
The wavelength is the distance between the corresponding points of a wave in successive cycles.
For example, from peak to peak. The product of the wavelength and the frequency gives the speed
of the wave. That is: c = λv. The higher the frequency, the shorter the wavelength.
We can see that the visible spectrum goes from 400nm to 700nm.
1
, Colors of stars
The color of a star depends on its temperature. We know that as we heat an object, first it
glows in the red, the it turns yellow/green and then it turns blue as it becomes even hotter.
We can understand the relationship between color and temperate by considering objects called
blackbodies. A blackbody is an object that absorbs all of the radiation that strikes it and also
emits radiation. If it radiates less energy than it absorbs, it will heat up. If it radiates more
energy than it absorbs, than it will cool. If we look at the blackbody spectra, as the temperature
increases the peak of the spectrum shifts to shorter wavelengths. The relationship between the
wavelength at which the peak occurs, λmax , and the temperature T, is very simple. It’s given by
Wien’s displacement law:
λmax T = 2.90 × 10−1 cmK = 2.90 × 106 nmK
The total energy per unit time, per unit surface area, E, given off by a blackbody is proportional
to the fourth power of the temperature. That is
E = σT 4
This relationship is called the Stefan-Boltzmann law. The constant of proportionalty, σ, is called
the Stefan-Boltzmann constant and its equal to 5.7 × 10−5 erg/(cm2 K 4 s.
The luminosity of a star is the total energy per second (power) given off by the star.
L = 4πR2 σT 4
where 4πR2 is the surface area.
Page 2
