How Are Astronomical Distances Measured?

How is astronomical distance determined? Just cannot get my head around cepheid variables, parallax, etc. How is it possible to tell how far away something is when you cannot bounce a radar beam off the object and time its return?
RS Puppis rhythmically brightens and dims over a six-week cycle. It is one of the most luminous in the class of so-called Cepheid variable stars. Its average intrinsic brightness is 15,000 times greater than our Sun’s luminosity. Image Credit: NASA, ESA, and the Hubble Heritage Team (STScI/AURA)-Hubble/Europe Collaboration

RS Puppis rhythmically brightens and dims over a six-week cycle. It is one of the most luminous in the class of so-called Cepheid variable stars. Its average intrinsic brightness is 15,000 times greater than our Sun’s luminosity. Image Credit: NASA, ESA, and the Hubble Heritage Team (STScI/AURA)-Hubble/Europe Collaboration

Originally posted at Forbes!

Well, you’re absolutely right that radar is an ideal way of measuring distances to objects; with radar you bounce a radio or microwave pulse off of the other object (a planet, for instance) and wait for it to come back. The Arecibo Observatory in Puerto Rico is one of the best observatories for doing this kind of work, and it’s not limited to planets, though objects that are large and nearby are easiest. Asteroids and comets are also good targets for radar observations, and the radar allows us to not only get great distances but a general idea of the shape of the object.

But radar has limited usefulness once the object you’re interested in gets too far away, and when we need to get a distance from an object in the outer regions of our solar system, or for the nearest stars, we have to find another option. That option is parallax, which is also pretty straightforward as astronomy distance measurements go, because it’s mostly just geometry.

Parallax illustration. Image credit wikimedia user Abeshenkov, public domain.

Parallax illustration. Image credit wikimedia user Abeshenkov, public domain.

We’re well familiar with parallax as a phenomenon, even if we’ve never had the name to apply to it. Parallax is simply that objects which are close to you will appear to move, relative to some distant object, if you move. It’s why, when you take a picture out of a moving car’s window, the scenery along the roadside will be blurred out, whereas the distant scenery is captured without any motions. The roadside has a large parallax effect relative to the background. You can do this at home, too – close one eye and hold a finger out at arm’s length. Get your finger to cover up some object on your wall – a light switch or something. Now close that eye and open the other one. Your finger will appear to jump sideways away from the object it was covering. That’s parallax.

With a little math you can figure out how far away that apparently moving object is. All you need to know is how far apart your vantage points were (in the finger example, the distance between your eyes), and how far the object (your finger) appeared to move. With that information, you can work out how far away the object must have been in order for the angles to work out. If the object were closer, it would appear to have moved more. If it were farther, it would move less.

The other thing you can change is how far apart your viewing positions are. The farther apart, the more obvious the effect. For astronomical distances, we can make use of this by measuring the positions of stars when our planet is at opposite ends of our orbit around the Sun. Six months apart gives us viewing positions which are 186 million miles apart, instead of the few inches between your eyes. That allows you to see even the tiniest changes in a star’s position, relative to even more distant stars.

However, once you get beyond a few hundred parsecs, this kind of measurement gets really hard to do, and even with the best telescopes, parallax is only measurable out to about 1000 parsecs. Considering that we’re sitting 8,000 parsecs from the center of our galaxy, that doesn’t get very far. We’re going to need another method to get even farther away.

The NASA/ESA Hubble Space Telescope quashed the possibility that what was previously believed to be a toddler galaxy in the nearby universe may actually be considered an adult. Called I Zwicky 18, this galaxy has a youthful appearance that resembles galaxies typically found only in the early universe. Hubble has now found faint, older stars within this galaxy, suggesting that the galaxy may have formed at the same time as most other galaxies. Hubble data also allowed astronomers for the first time to identify Cepheid variable stars in I Zwicky 18, marked by the red circles. These flashing stellar mile-markers were used to determine that I Zwicky 18 is 59 million light-years from Earth, almost 10 million light-years more distant than previously believed. Image Credit: NASA/ ESA/ STScI (A. Aloisi)

The NASA/ESA Hubble Space Telescope quashed the possibility that what was previously believed to be a toddler galaxy in the nearby universe may actually be considered an adult. Called I Zwicky 18, this galaxy has a youthful appearance that resembles galaxies typically found only in the early universe. Hubble has now found faint, older stars within this galaxy, suggesting that the galaxy may have formed at the same time as most other galaxies. Hubble data also allowed astronomers for the first time to identify Cepheid variable stars in I Zwicky 18, marked by the red circles. These flashing stellar mile-markers were used to determine that I Zwicky 18 is 59 million light-years from Earth, almost 10 million light-years more distant than previously believed. Image Credit: NASA/ ESA/ STScI (A. Aloisi)

This is where Cepheid Variables come in. Cepheids are an interesting class of star which change their brightness over time in a predictable, repeating pattern. And, very usefully for distance measurements, that repeating pattern changes depending on how intrinsically bright the star is, a discovery made by Henrietta Swan Leavitt in 1902. We can therefore use the speed of the Cepheid’s pulse to tell if it’s faint in our skies because it’s intrinsically dim, or because it’s faint because it’s far away.

We know how bright the Cepheid should be, because of its pulse, so any fainter means it’s farther away. We know how brightness fades with distance – twice as far away means eight times as faint. The mismatch between how bright the Cepheid appears in the sky, and how bright it should be gives us this distance. This method works well throughout our galaxy and out to the nearest galaxies beyond us. To go even farther out in the universe, we need an even brighter tracer – supernovae.

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What is a kiloparsec?

Kiloparsec
(What is a kiloparsec, and what do we use it for?)



(Note: I am assuming this submission means “What is a kiloparsec, and what do we use it for?”. If that was not your question, please feel free to ask again!)

Kiloparsecs are another unit used to measure huge distances between objects in space, and if the ‘kilo’ part seems familiar from having seen words like kilogram and kilometer, you’d be exactly right - the prefix here just means 1000 of the part that follows. In this case, the base unit is a parsec, instead of a gram or a meter.

The parsec (regardless of what you remember from Star Wars’ infamous line re: the Kessel Run) is a unit of distance that’s equivalent to 3.26 light years. A light year, as we’ve talked about before, is quite a long distance, but once you get away from the immediate group of stars surrounding our solar system, it’s less useful as a ruler, since everything is so far away. The distance from us to the center of our galaxy is measured in tens of thousands of light years.

Unlike the light year, which is based in the physics of light, a parsec was determined geometrically using the size of the orbit of the Earth around the sun, and the apparent motion of nearby stars. The actual term “parsec” has a somewhat fun origin - it’s actually a mashup of the words “parallax” (the apparent motion of the stars) and “arcsecond” (how far they move). Arcseconds are frequently abbreviated as “arcsec”, so parallax-arcsec got shortened into parsec.

Parallax, as we just mentioned, is describing the apparent motion of a star. But more generally, parallax is the term for the relative motions of any two objects at different distances. The most common example is looking out the window of a moving vehicle - the shrubs, trees, and telephone poles near the road move very quickly past your window, but things further away - any mountains or distant buildings will appear to move at a much slower pace from your perspective. Applying this idea to the stars, stars which are quite close to us will appear to shift ever so slightly relative to other stars in the sky which are at much greater distances, which will appear fixed.

Arcseconds tell us how far these stars appear to move. They are a unit of size on the sky - sixty arcseconds go into an arcminute, sixty arcminutes go into a degree, and 360 degrees makes a full circle (no one has ever said that astronomers use sensible units). To give you some scale, the full moon is half a degree across - thirty arcminutes. Venus, the bright morning or evening star, tends to be a few tens of arcseconds in the sky.

One parsec is defined geometrically as the distance from the Sun where the motion of the earth around the Sun causes a parallax of one arcsecond. (The image at the top shows a diagram of this.) As our planet moves from one extreme in our orbit to the other extreme, it has moved by 2 astronomical units side to side - 186 million miles. And after moving 186 million miles, we are looking for a star which has moved by less than one tenth the size of Venus in the sky. If the star moved by exactly 1 arcsecond, it was defined to be at a distance of precisely one parsec from the sun. Most of the stars in the sky are too distant to make these measurements directly, but we can still use this geometric definition as a ruler.

This unit was useful back in the day when the speed of light was not so precisely known. Since the distance from the earth to the Sun was well known, and the rest of the calculation is just geometry, the parsec could be used as a distance measurement without depending on the speed of light. Nowadays, we have the speed of light measured to phenomenal precision, so we can use either unit of distance, depending on which one is more convenient.

Kiloparsecs (1000 parsecs, or 3260 light years) are the unit of choice for measuring distances when galaxies are involved. Rather than saying that the Earth is about 30,000 light years from the center of our galaxy, it’s easier to say that it’s a little over 8 kiloparsecs. The distances between galaxies can also be given in kiloparsecs, although unless something exciting is happening, or they’re in a very particular region of space, the distances between galaxies are often several hundred kiloparsecs or more. Andromeda, our galactic neighbor, is 780 kiloparsecs away. That’s about 2.5 million light years.

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