Transcript Measuring large distances

How Far is far ?
Measuring the size of the
Universe.
The easiest way to measure the
distance to a planet or star is
through a method called parallax.
• The parallax method (or triangulation, as
it’s sometimes known) depends on having a
baseline of known length.
• A distant object is sighted accurately from
both ends of the baseline. The angles to the
object from each starting point are different.
• A little trigonometry shows how far out
each line of sight meets the other.
Parallax at work
Angle 2
baseline
Angle 1
The astronomer’s favorite
distance unit is the PARSEC
(not a light-year)
1 parsec = 3.26 light years
= 3.1 E13 km
= 1.9 E13 miles
1 parsec:
when angle 1 is only different by
1 arcsecond from angle 2
Angle 2
baseline
Angle 1
The longer the baseline, the
greater difference in angles…
Angle 2
baseline
Angle 1
So parallax only works for
relatively close things, like
planets & nearby stars.
As an object is farther away, the angles get so close to the same
that parallax doesn’t work.
Make the baseline longer ! But eventually, even using a baseline
formed by the earth travelling to the opposite side of the sun isn’t
long enough….
In practice, the longest baseline we can
use is the 6 month change in position as
the Earth orbits the Sun. Unless we
launch a satellite on an even bigger
orbit…
Ground-based telescopes: .01 arcseconds
(= reciprocal = 100 pc)
Hipparcos satellite (ESA): .00097 arcsec
(= 1000 pc = 100,000 stars)
Gaia satellite (ESA): .000002 arcsec
(8,000 pc = center of Milky Way)
How else?
The “Standard Candle”
We assumed all
the headlights
were the same:
a “STANDARD
CANDLE”
So the brighter it
is, the closer it is.
You don’t have the same luxury
with stars, or groups of stars…
they’re not all the same. Oh, no.
You just can’t be very certain of
INTRINSIC brightness.
But still, progress can be made,
especially if compare less
definite methods against the stars
you have PARALLAX for.
Intrinsic Brightness
Stars that start out larger are brighter
and bluer
Stars that start out with
less fuel are colder and
redder (& last longer)
So based on the color of a star, and how bright it is, it’s possible to
make a guess about how far away the star is.
This provides a rough estimate
• But it’s very hard (impossible) to see
normal, individual stars in any galaxy but
our own.
• And, anyway, the correspondence between
color and star luminosity is only
approximate
A special type of star, called a
variable, pulses. Tick-tock.
• They grow brighter and dimmer regularly
over a period of days or weeks.
• These pulses are very closely related to the
size and therefore the brightness of the
stars.
Time the Pulse,
& you know how bright it
SHOULD BE
Measure the actual brightness, and
you can tell how far away it is.
There are several species and subspecies of regular variables.
Even Cepheids are hard to see in distant galaxies.
• Supernovas, exploding stars, are
easier to spot in distant galaxies
• Some types of Supernova have an intrinsic
brightness which can be compared to their
actual brightness observed on Earth to judge
distance.
• But Supernova are not all the same...
Another method relates the brightness of spiral
galaxies to their rotational speed, which can be
measured by Doppler shifting.
As one side of the galaxy swings toward the
earth, its light is slightly blue-shifted.
As the other side turns away, its light is slightly
red-shifted.
The more shifting, the faster the rotational speed,
the brighter the galaxy.
Again, compare the brightness it should have
with what is observed.
Gravitational lensing is an effect predicted by General Relativity
As light travels to Earth from a distant galaxy, it may be bent
around an intervening galaxy by the curvature of space, and
follow 2 distinct paths to the Earth.
By tracking both paths exactly, an estimate can be made of the
distance of the “lensing” galaxy.
The famous “Einstein Cross” Gravitational Lens : a distant galaxy’s light
is bent by gravity around a closer intervening galaxy. The four light
sources are actually images of only one light source – like when you see
the sun in a lot of raindrops on the window.
Yet another method results from the fact that as we look out
farther, we look back in time : light takes billions of years to reach
us from the edges of the universe.
Since clusters of galaxies were denser and hotter in the early
universe, the farther away a galaxy cluster is, the hotter it should
be.
Very very precise temperature measurements of far away galaxy
clusters can indicate how far away they are.
A final method of distance measurement
involves brightness fluctuations.
As a telescope gathers light from a nearby
galaxy, there are small regions of the galaxy that
appear brighter or darker.
But the light from galaxies farther away will be
more diffused, and the galaxy will lose its
lighter or darker regions as seen by Earth-based
telescopes.
All galaxies are Red -Shifted
• Their light is shifted lower in frequency,
meaning they are moving away from us.
• The farther away they are, the more they’re
red-shifted, the faster they’re moving.
• This was the first strong piece of evidence
that the universe is expanding.
How fast is the universe
expanding ?
• If you know this, you can determine the age
of the universe and the time of the BIG
BANG !
• You can account for all kinds of
observations : the structure of galaxy
clusters, old & new stars.
• You can even speculate on the origin of life.
This ultimately depends
on relating speed
(measured by red-shift)
to distance (measured
by a variety of
techniques, which don’t
always agree and are
constantly being
refined.