Download Measuring Distances

Measuring Distances
Taking the Measure of the Universe
The Importance of Distance
We talked about how the brightness of a star can
be due to 2 effects: distance or luminosity.
Without a direct measurement of a star’s distance,
we can’t determine the star’s luminosity or where
it is in space!
This is not only true of individual stars, but of
star clusters and galaxies themselves.
The Importance of Distance
Ultimately, knowing distances across the Universe
also allow us to determine the Universe’s age.
While distance is so critical in astronomy, it is also
one of the most difficult things to measure.
Fortunately, Greek astronomers imagined a
method 2000 years ago that is still in use today.
Measuring Distances
Hold your finger out in front of your
face at arm’s length.
Look at your finger through each
eye separately.
What do you notice?
This change in perspective is known as parallax.
Ancient Greek astronomers expected to see a
similar change in the positions of nearby stars if
Earth actually moved around the Sun.
Measuring Distances
This apparent shift in position is called parallax.
Because we are riding on Earth as it orbits the
Sun we see the same effect for faraway objects
like planets or stars.
To the ancient astronomers of Greece, their
failure to see stellar parallax meant that Earth
must not be moving!
Parallax
The problem was ancient astronomers could not
conceive of the vast distances between stars.
In reality, even the stars closest to the Sun have
very small parallaxes that require powerful
telescopes to measure.
The first stellar parallax was
not measured until 1838 by
Friedrich Bessel at the
Berlin Observatory.
Parallax
How small a parallax are we talking about?
Imagine someone standing at the top of the MCC
football stadium holding a dime.
Now imagine standing on the roof of the Physical
Science Building (about 1 kilometer away) looking
at the face of the dime.
The largest parallaxes (of the nearest stars) are
equivalent to the apparent size of that dime!
Parallax
Astronomers use a set of special units for angles:
There are 60 arcseconds in 1 arcminute,
and 60 arcminutes in 1 degree.
(Just like units of time: hours, minutes, seconds.)
An object that shows a parallax of 1 arcsecond lies
at a distance of 1 parsec (parallax arcsecond).
The parsec is abbreviated “pc”.
Parallax
More distant objects have smaller parallax; closer
objects have larger parallax. We can relate this
through an equation:
1
distance in parsecs =
parallax in arcseconds
1
or d =
p
Bessel found that the star 61 Cygni shifted by a
tiny angle of 0.3 arcsecond.
1
=
3
.
33
parsecs
So the star 61 Cygni: 0.3 arcseconds
The Parsec
It takes a little trigonometry to determine, but:
• one parsec is equal to 206,265 Astronomical Units
• one parsec is equal to 3.26 light-years
Astronomers also use:
• the kiloparsec (1,000 parsecs = 1 kpc)
• the megaparsec (1 million parsecs = 1 Mpc)
The modern standard
Modern parallax measurements come from the
HIPPARCOS satellite (1989-1993), capable of
measuring parallax angles as small as 1/500th of
an arcsecond (0.002 arcsecond).
1
What distance does this correspond to? d =
p
A distance of 500 pc
Distances derived from a parallax shift are known
as trigonometric distances or trigonometric
parallaxes. This is the fundamental method for
measuring the distances to nearby stars.
Star Alpheratz has a parallax of 0.1 arcsecond.
How far away is this star?
A. 0.1 light-year
B. 0.1 parsec
C. 10 light-years
D. 10 parsecs
Star Kappa has an apparent magnitude of +3.6
and a parallax of 0.08 arcsecond.
Which of the following is closest to the absolute
magnitude of Star Kappa?
A. +6.6
B. +3.2
C. +0.8
D. -0.2
Which star is the most luminous?
• Star A has an apparent magnitude of +0.2 and a
parallax of 0.1 arcsecond.
• Star B has an apparent magnitude of +0.2 and a
parallax of 0.001 arcsecond.
A. Star A
B. Star B
C. The two stars have equal luminosities.
D. Information is not sufficient.
Astronomers discover a previously-unseen object
with a parallax of 4.5 arcseconds.
What is the distance to this object?
A. About 4.5 light-years
B. About 4.5 parsecs
C. About 0.2 light-years
D. About 0.2 parsecs
What could we say about the object from the
previous question (the one with a parallax of
4.5 arcseconds)?
A. It must have a very high luminosity to be
visible at all at that distance from the Sun.
B. It must have a very low luminosity to have
gone undiscovered that far from the Sun.
C. It must be one of the most distant stars ever
discovered.
D. It is likely the first individual star ever
detected outside of the Milky Way.