Mad Teddy's astronomy pages: distances in space

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Distances in space

In space, distances can get very large.

It's common to measure distances between astronomical objects in terms of the speed of light in a vacuum. This is very fast - just a whisker under 300,000 kilometres per second - but not so fast that it can't be noticed under certain conditions; and the fact that it's not even faster can actually be a bit of a nuisance!

During the Apollo program, conversations between Earth and astronauts on the moon sounded somewhat stilted, as if the participants were slow-witted and finding it difficult to think of anything to say. Obviously, this was not the case; the illusion was caused by the fact that the moon is far enough away (384,400 kilometres) so that light (and radio-waves, which travel at the same speed) takes a perceptible time to make the journey (about 1.28 seconds).

So if a person on Earth speaks to an astronaut on the moon, and the astronaut replies immediately, the person on earth will notice an apparent hesitation of about two and a half seconds. Of course, the astronaut will notice a similar delay.

Even at the geostationary orbit, in which a satellite travelling from west to east over the equator will stay at the same position above the Earth, the time-delay can be noticeable. This orbit is about 36,000 kilometres above the Earth, so that light (or a radio signal) will take about 0.12 second (about an eighth of a second) to cover the distance. If a reply is sent immediately, the round trip thus takes about a quarter of a second. This is not enough to be a real problem for speech, but for communication between electronic signalling systems, which communicate by "hand-shaking" (several back-and-forth messages to ensure that a signal arrives correctly), it's a real drag.

The distance from the Earth to the sun is about 150 million kilometres. Thus light from the sun takes (150 million / 300 thousand) seconds, i.e. 500 seconds, or eight and a third minutes, to reach the Earth. So we can say that this distance (also known as an "astronomical unit", AU) is eight and a third light-minutes.

- Which brings us to the idea of a light-year. One year is

365.25 24 60 60 = 31,557,600 seconds

so that a light-year is 31,557,500 / 500 = approximately 63,115 AU, or 9.467 trillion (million million) kilometres.

In the Southern Hemisphere, we can see a very striking constellation called Crux, or the Southern Cross. It consists of four stars arranged somewhat like a kite. Close by are two stars known as the "pointers", Alpha Centauri and Beta Centauri (both part of another constellation, Centaurus).

The following graphic of the Southern Cross and its pointers was obtained using the planetarium program Home Planet :


(This gives you a chance to see the weird colour scheme I like on my computer! )

The Cross is at lower right. The pointers are to its left. The further pointer from Crux, Alpha Centauri, is the bright star at the lower left corner of the graphic. It is the closest star to the Earth (other than the sun, of course - duh). Alpha Centauri is also known, by navigators, as Rigel Kentaurus - or simply Rigel Kent (labelled as Rigilkent on the graphic).

So, if Alpha Centauri is the closest star to us, just how far away is it?

It's not "close", in any sense of the term that we can easily relate to! It's 4.35 light years away. A quick check with a calculator shows that this is a distance of well over a quarter of a million AU!

Actually, Alpha Centauri is not a single star. In fact, it's a three-star system. Click here to see an interesting web page which goes into some detail. Also, this page is well worth a look.

Two of the Alpha Centauri stars are of comparable size and brightness to our sun, and orbit their common centre of mass. The third star, a red dwarf, is quite a lot further out. Presently, it's the closest of the three to Earth - which is why it's called "Proxima Centauri".

Just before moving on - see that funny-looking white thing called NGC5139 in the above graphic near top-centre? That's a globular cluster - one of a number of such more-or-less spherical aggregations of stars around the rim of the Milky Way. It's also known as Omega Centauri, and is about 16 thousand light years away. Click here to read more about it and see a photograph.

Other pages, with photos, about this interesting object are here , here , and here . (That last page has lots of other interesting pictures too - have a good look around.)

A different unit, the parsec, is another useful way to measure astronomical distances; and this one doesn't require any mention of the speed of light. Apparently, astronomers prefer this unit. If you're a science-fiction buff, chances are you may have seen it mentioned, possibly without knowing exactly what it means.

The term is a short form of "parallax second". The "second" here is not a unit of time, but a second of arc - a small angle.

To get an idea of how small this angle is, think of it in terms of latitude. The Earth has a radius of about 6,400 kilometres, and a diameter of twice that - 12,800 kilometres. Then the circumference is that figure times pi (approximately 3.1416), or 40,212 kilometres. So one quarter of this - 10,053 kilometres - is the distance from the equator to either pole. This is a latitude shift of 90 degrees, i.e. 90 60 60 = 324,000 seconds of arc. So one second of arc corresponds to a distance of 10,053 / 324,000 = 0.031 kilometres, or 31 metres - quite literally, a stone's throw.

Now, consider what a second of arc means on an astronomical scale. Imagine a vastly bigger sphere in which one second of latitude corrsponds to a distance, on its surface, of 1 AU. So we're scaling up by a factor of 150 million divided by 0.031, i.e. about 4.84 billion (thousand million).

If we scale up the radius of the Earth (6,400 kilometres) by the same factor, we get about 31 trillion (million million) kilometres for the radius of our big sphere. That distance is one parsec.

Now, recall that a light-year is about 9.467 trillion kilometres. Dividing 31 by 9.467 gives a figure of about 3.27, which is thus the number of light-years in one parsec.

Admittedly, we've been approximating perhaps more than we should have been, in reaching this figure. Still, the result is not bad: the accepted figure is 3.259 light-years.

Finally, also recall that Alpha Centauri is 4.35 light-years away. Dividing this by 3.259 gives 1.335. So our nearest stellar neighbour is about one and a third parsecs away.

The discussion just given involves one way of visualizing a parsec (which I hope has been helpful, in reducing it to things we can more easily get our heads around).

There are other, equivalent, ways to understand what a parsec is, and to calculate its size (although, of course, any such calculations end up simply being "variations on a theme", and giving the same result). Here are some links which deal with these:

http://www.physics.hku.hk/~tboyce/sfseti/A6parsec.html

http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/m0005746.html

http://www.astronomynotes.com/starprop/s2.htm

http://ourworld.compuserve.com/homepages/bmoler/litetime.htm

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