Astronomical distances
The SI unit for length, the meter, is a very small unit to
measure astronomical distances. There units usually used is
astronomy:
The Astronomical Unit (AU) – this is the average distance between
the Earth and the Sun. This unit is more used within the Solar System.
1 AU = 1.5x1011 m
Astronomical distances
The light year (ly) – this is the distance travelled by the
light in one year.
c = 3x108 m/s
t = 1 year = 365.25 x 24 x 60 x 60= 3.16 x 107 s
Speed =Distance / Time
Distance = Speed x Time
= 3x108 x 3.16 x 107 = 9.46 x 1015 m
1 ly = 9.46x1015 m
Astronomical distances
The parsec (pc) – this is the
distance at which 1 AU subtends an
angle of 1 arcsencond.
“Parsec” is short for
parallax arcsecond
1 pc = 3.086x1016 m
or
1 pc = 3.26 ly
1 parsec = 3.086 X 1016 metres
 Nearest Star
1.3 pc
(206,000 times
further than
the Earth is
from the Sun)
Parallax
Where star/ball
appears relative
to background
Angle star/ball
appears to
shift
Distance to
star/ball
“Baseline”
Space
Parallax
Parallax is the change of
angular position of two
observations of a single
object relative to each other
as seen by an observer,
caused by the motion of the
observer.
Parallax
We know how big the Earth’s orbit is, we measure the shift
(parallax), and then we get the distance…
Distance to
Star - d
Parallax - p
(Angle)
Baseline – R
(Earth’s orbit)
Parallax
R (Baseline)
tan p (Parallax) 
d (Distance)
For very small angles tan p ≈ p
R
p
d
In conventional units it means that
1.5 x 1011
1 pc 
m  3.986 x 1016 m
 2   1 



 360   3600 
Parallax
1.5 x 1011
1 pc 
m  3.986 x 1016 m
 2   1 



 360   3600 
R
p
d
R
d
p
1
d (parsec) 
p ( arcsecond)
Parallax has its limits
The farther away
an object gets,
the smaller its
shift.
Eventually, the shift
is too small to see.
Quick Reference
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0.5 degree
The width of a full Moon, as viewed from the Earth's surface, is about 0.5
degree.
The width of the Sun, as viewed from the Earth's surface, is also about 0.5
degree.
1.5 degrees
Hold your hand at arm's length, and extend your pinky finger. The width of your
pinky finger is about 1.5 degrees.
5 degrees
Hold your hand at arm's length, and extend your middle, ring, and pinky fingers,
with the three fingers touching. The width of your three fingers is about 5
degrees.
10 degrees
Hold your hand at arm's length, and make a fist with your thumb tucked over
(or under) your other fingers. The width of your fist is about 10 degrees.
20 degrees
Hold your hand at arm's length, and extend your thumb and pinky finger. The
distance between the tip of your thumb and the tip of your pinky finger is about
20 degrees.
Parallax Experiment
 Using the quick reference angles that I
gave you determine how far something
is away near your house based on the
parallax method. Include a schematic
to show the placement of all objects.
Your schematic should include relevant
distances and calculations.
Usually, what we know is how
bright the star looks to us here
on Earth…
We call this its
Apparent Magnitude
“What you see is
what you get…”
The Magnitude Scale
 Magnitudes are a way of
assigning a number to a star so
we know how bright it is
 Similar to how the Richter scale
assigns a number to the
strength of an earthquake
Betelgeuse and Rigel,
stars in Orion with
apparent magnitudes
0.3 and 0.9
This is the “8.9”
earthquake off
of Sumatra
The historical magnitude scale…
 Greeks ordered the
stars in the sky
from brightest to
faintest…
…so brighter stars
have smaller
magnitudes.
Magnitude
Description
1st
The 20 brightest
stars
2nd
stars less bright
than the 20
brightest
3rd
and so on...
4th
getting dimmer
each time
5th
and more in each
group, until
6th
the dimmest stars
(depending on your
eyesight)
Later, astronomers quantified
this system.
 Because stars have such a wide range in
brightness, magnitudes are on a “log scale”
 Every one magnitude corresponds to a factor
of 2.5 change in brightness
 Every 5 magnitudes is a factor of 100 change
in brightness
(because (2.5)5 = 2.5 x 2.5 x 2.5 x 2.5 x 2.5 = 100)
Brighter = Smaller magnitudes
Fainter = Bigger magnitudes
 Magnitudes can even be negative for
really bright stuff!
Object
Apparent Magnitude
The Sun
-26.8
Full Moon
-12.6
Venus (at brightest)
-4.4
Sirius (brightest star)
-1.5
Faintest naked eye stars
6 to 7
Faintest star visible from
Earth telescopes
~25
However:
knowing how bright a star looks
doesn’t really tell us anything
about the star itself!
We’d really like to know things that are
intrinsic properties of the star like:
Luminosity (energy output)
and
Temperature
In order to get from how
bright something looks…
to how much energy
it’s putting out…
…we need to know its distance!
The whole point of knowing the
distance using the parallax method is
to figure out luminosity…
It is often helpful to put
luminosity on the magnitude
scale…
Once we have both
brightness and distance,
we can do that!
Absolute Magnitude:
The magnitude an object would have if
we put it 10 parsecs away from Earth
Absolute Magnitude (M)
removes the effect of distance
and
puts stars on a common scale
 The Sun is -26.5 in
apparent magnitude,
but would be 4.4 if we
moved it far away
 Aldebaran is farther
than 10pc, so it’s
absolute magnitude is
brighter than its
apparent magnitude
Remember magnitude scale is “backwards”
Absolute Magnitude (M)
Knowing the apparent magnitude (m) and the
distance in pc (d) of a star its absolute magnitude (M)
can be found using the following equation:
m  M  5 log d  5
Example: Find the absolute magnitude of the Sun.
The apparent magnitude is -26.7
The distance of the Sun from the Earth is 1 AU = 4.9x10-6 pc
Therefore,
M= -26.7 – log (4.9x10-6) + 5 =
= +4.8
So we have three ways of
talking about brightness:
 Apparent Magnitude - How bright a star
looks from Earth
 Luminosity - How much energy a star
puts out per second
 Absolute Magnitude - How bright a star
would look if it was 10 parsecs away