Distances in Space
Kessel Run in 12
Parsecs will be famous!
No one will ever think it
is 14.
Astronomical unit (1 AU)
An astronomical unit (AU) is the average distance of the earth
from the sun which is 150 million km
1 AU = 1.5 x 1011 metres
Light Year
Defined as the distance
travelled by light in one year
1 ly = 3 x 108 x 365 x 24 x 60 x 60 = 9.46 x 1015 m
Distance between stars in a galaxy
About one parsec (defined later)
One parsec is 3.26 light years
Stars (more later!)
Stars (more later!)
• At the core, hydrogen is being fused to form helium, realeasing
LOTS of energy, pushing the gases outward.
• This is balanced by gravity trying to pull the gas together.
• The sun is equivalent to 10 000 hydrogen bombs exploding
every second!
Equilibrium between radiation pressure and
gravity
Parallax
Parallax angle
Parallax angle
P (in rads)
R (=1 AU)
d
tan p = R/d
» Tan p
for small p, tan p ≈ p
so d = R/p
Parsec
• If the parallax angle is one arcsecond (1 “) the distance to the
star is called a parsec
Parsec
• If the parallax angle is one arcsecond (1 “) the distance to the
star is called a parsec
• d (parsecs) = 1
p (in arcsecs)
Parsec
• 1 pc = 3.26 ly
Simulation
Example
• A star has a parallax angle of 0.34 arcsecs. How far is the star
away from earth in light years?
d (parsecs) = 1
=1
= 2.9pc
p (in arcsecs)
0.34
Distance in light years = 2.9 x 3.26 = 9.5 ly
Converting degrees to arcsecs in radians
• Multiply by
• Multiply by
2π to convert to radians
360
1
to convert to arcsecs
3600
Parallax method
• Only useful for close stars (up to 300 ly (100 pc) as further than
that the parallax angle is too small (space based telescopes can
use this method to measure stars up to distances of 500 pc).
D.1 Parallax questions
‘Parallax angle and parsec worksheet’
Luminosity (symbol L)
Luminosity is defined as the amount of energy radiated by the
star per second (The power radiated by the star)
Measured in Watts (J.s-1)
Black-body radiation
Black-body radiation
Need to “learn” this!
Black-body radiation
• Black Body - any object that is a perfect emitter and a perfect
absorber of radiation
• object does not have to appear "black"
• Stars behave approximately as black bodies
Black-body radiation
The amount of energy per second (power) radiated from a star
(its luminosity) depends on its surface area and absolute
temperature according to
L = σAT4
where σ is the Stefan-Boltzmann constant (5.67 x 10-8 W.m-2.K4)
Example
• The sun (radius R = 7.0 x 108 m) has a luminosity of 3.9 x 1026
W. Find its surface temperature.
• From L = σAT4 and A = 4πR2 we find
T = (L/σ 4πR2)¼ = 5800 K
Wien’s law – Finding the temp of a star
• λmaxT = constant (2.9 x 10-3 K)
Example
• The sun has an approximate black-body spectrum and most of
its energy is radiated at a wavelength of 5.0 x 10-7 m. Find the
surface temperature of the sun.
• From Wien’s law
5.0 x 10-7 x T = 2.9 x 10-3
T = 5800 K
Spectral Class
Colour
Temperature/K
O
Blue
25 000 – 50 000
B
Blue - white
12 000 – 25 000
A
White
7 500 – 12 000
F
Yellow - white
6 000 – 7 500
G
Yellow
4 500 – 6 000
K
Yellow - red
3 000 – 4 500
M
Red
2 000 – 3 000
You need to remember the classes and their order
and approximate temperatures.
How will you do this?
Spectral classes
Oh be a fine girl….k--- me!
Oh Boy, a fat guy kicked Me!
Make your own up!
Thought
experiment
Apparent brightness (symbol b)
Apparent brightness is defined as the amount of energy per
second per unit area of detector
b=
where
2
L/4πd
d is the distance from the star (in m)
L is the luminosity (in W)
Intensity at a distance from a light source
(Apparent brightness)
b = L/4πd2
d
Apparent brightness - CCD
Apparent brightness is measured using a charge-coupled
device (used also in digital cameras).
Apparent brightness and Luminosity
Note that the apparent brightness b and luminosity L are
proportional
b=
2
L/4πd
bαL α
4
T
Apparent brightness and Luminosity
b=
d=
2
L/4πd
½
(L/4πb)
D.1 Brightness and luminosity questions
Bummer.