Determining Distances in Space There are several techniques

Determining Distances in Space

There are several techniques for measuring distances in space: • Geometric Methods (today) – For close stars • Spectroscopic Measurements (this week) – Close to medium distance stars (most of the stars in our galaxy) • Use of “Standard Candles” (this week) – Uses very bright objects in distant galaxies • Using Redshifts – (To be discussed at a later date. )

Geometric Methods 1) Parallax: -the apparent difference in position of an object view along 2 different lines of sight

Parallax • A triangle can be created, and if we know the length of the baseline, and angles x and y, we can calculate (using trigonometry) the distance to the object • Notice that… – The further away the object is, the closer the angles x and y are to each other – The larger the baseline is, the further apart the angles will be • Fortunately, we can use a very large baseline in astronomy: Earth’s orbit!

• Since the objects in space are very far away, the angles x and y will be VERY close to each other • In fact, the difference in angles is usually measure in units called arcseconds – A degree is divided into 60 minutes, and a minute into 60 seconds, so an arcsecond is 1/3600 th of a degree! – …and no stars have differences even that large! • This gives rise to a new unit: the parsec (pc) (short for “parallax arcsecond”) • By definition, this is the distance that would be measured if (y – x)/2 was exactly 1 arcsecond (/2 because the baseline is twice the Earth-Sun distance) • 1 pc = 3. 08568025 × 1016 m or 3. 26156 light years Example: The first star to be measured this way was a star in the constellation of Cygnus. The angular difference was found to be 0. 292 arcseconds. This gives a distance of 3. 48 pc, or 11. 36 light years

• Since measuring such small differences in angles is very difficult, using this method on more distant stars is not possible. • Nevertheless, it was a good starting point, that turns out to be invaluable in setting a standard for other measurement techniques.

Geometric Methods 2) Angular Size If we know how large an object really is, and we know what angle it takes up in the sky, then we can calculate how far it must be. Pro: Can be used for even distant galaxies and quasars Con: Requires an assumption about the actual size of the object. (Sometimes this is not a problem, but other times it definitely can be!) This method was used determine the distance to the centre of our galaxy.

Spectroscopic Measurements and Standard Candles • We know that brightness decreases as an object moves further away. (1/d 2) • So, if we know an object’s apparent magnitude, and its absolute magnitude, we can calculate how far away it is. • We can get its apparent magnitude through direct observation, but… • how do we know what its absolute magnitude is if we don’t know how far away it is? – A: 2 methods, depending on the object

Spectroscopic Method • If we look at the light spectrum from the star, we can determine… – its composition, and therefore… – what type of star it is, which give us… – its absolute brightness (among other things) • For example, the stars that are close enough to have their distance measured with parallax will have their spectrum analyzed. • From this, we can determine how bright a certain class of stars is supposed to be (absolute brightness) • Now, when we see stars in this category further in space, we know what there absolute brightness is. • Now we compare the absolute brightness to the stars apparent brightness to determine its distance.

Stellar “Candles” • There are certain very bright objects that have unique properties that allow us to determine distances to far away galaxies. We call these stellar candles • One of these candles is a type of variable star called a cepheid variable. • Variable stars are stars that pulsate, changing their size and temperature (and therefore their brightness) in a predictable way: – There is a mathematical relationship between the period of their oscillation (pulses) and their average brightness – (Again, this was determined by observing cepheids close to us so both their absolute brightness and their periods could be determined. ) • Now that we know their absolute brightness, we can use their apparent brightness to determine their distance.