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

baseline

Angle 1

Angle 2

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

baseline

Angle 1

Angle 2

The longer the baseline, the greater difference in angles…

baseline

Angle 1

Angle 2

So parallax only works for relatively close things, like

planets & nearby stars.As an object is farther away, the angles get soso 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 BEMeasure the actual brightness, and

you can tell how far away it is.

There are several species and sub-species 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.