# measuring stellar distance for the intellectually challenged

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Can some one explain in simple terms how stellar distance is measured please. I've got high school maths and have got my head around parallax however I'm lost once things move on to cephid variables and beyond. Anyone care to simplify things a bit? Be gentle please

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Cephid variables have a period that is related to it's brightness. If you know the period, you know how bright it actually is. You can compare how bright it actually is with how bright it appears giving you an estimate of the distance. Essentially we need to know how bright an object actually is, whether it is a cephid variable, supernova, quasar or whatever and compare this with how bright it appears.

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Once beyond parallax we often rely on the idea that there is a difference between how bright something really is and how bright it appears to us at the distance it is from us.

If we have a 100 watt lightbulb its hundred watts will be radiated out in all directions (ignoring the brass bit that sticks in the holder!) If we are a metre away we can imagine a spherical shell with a 1 metre radius. That 1 metre shell has, in total, 100 watts worth of light at its imaginary surface. If we move to a distance of 2 metres and imagine a spherical shell around the bulb, the surface of that shell is now 4x larger and the 100 watts are now spread 4x thinner over that surface. So the apparent brightness of the bulb goes down as the inverse square of its distance. Now say we are 100 metes away and we have a photometer with a 1 square metre detector and this measures a certain (small) amount of  light flux from the new shell. From this we can calculate the total surface area of the shell and so its radius, which is the distance we were looking for.

How do we know the true wattage of a star or a galaxy? Partly from measuremnt of known examples, partly from astrophysics and a knowledge of nuclear energy. Certain types of object are considered 'standard candles.' They should give off a pretty standard wattage so how bright they appear gives an idea of how far away they are.

An amateur's answer while waiting for the pros.

Olly

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Thanks Olly, I'm getting there now. Regarding the methods of determining the true brightness of a star (wattage in your analogy) I take it there are a limited number of different types of stars out there in the first place which make comparison and assessment of brightness less of a guess ?

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Yes. (By the way, stars are measured in Watts with a lot of zeros begind the first digit!)

Do you know the HR diagram? It Googles. Stars can be placed on the diagram using thier spectra to identify them and then an absolute magnitude (true intrinsic brightness) can be read off on the left hand side. When compared with the distance-affected apparent magnitude this yields an approximate distance.

Type 1a supernovae are good bright candles. They should all be similar because they go Pop when the accreting star reaches 1.6 solar masses.

Olly

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Got it now ( or enough for my wee brain anyway) thanks

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The Cepheid variable relationship was worked out by Henrietta Swan Leavitt  observing Cepheids in the Magellanic Clouds. This is a smallish (astronomically speaking) cluster of stars a ways outside our galaxy, so to all intents and purposes are more or less all at the same distance. A bit like observing the lights of Manchester from London, they're all about the same distance away.

So if there is a relationship between their brightening and dimming and their luminosity, you can tell that the relationship is pretty much fixed.

It turned out there is a little more to it in the case of Cepheids, but that's mostly what it is.

So once you have calibrated this and worked out how this equates with distance, you have a convenient yardstick

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Julian, do you know how Shapely calibrated the Cepheid distance, though? This bit seems to be glossed over in most of the histories.

Olly

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Both Hertzsprung and Shapley tried to calibrate based on nearby Cepheids for which there were known parallax measurements. There were a lot of issues to solve about extinction and so on before a firm equation for the distance was worked out, and of course there was then the issue of Cepheid II's!

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• 6 years later...

Hello everyone,

I am now in the process of completing the write up for a science project on parallax and I came across a question which I need an answer in order to explain my project. (google was no help cuz already tried that and couldnt find a correct answer

How do astronomers actually measure the parallax angle of a star? do they use any special equipment or do they calculate it mathematically? and can someone explain the equation d = 1/p which is used to calculate stellar distances in parsecs and how  it relates to the earth-sun distance(if it does) and parallax angle?

May the Force be with you.

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Parallax is measured by observing the position of a star against its background. Traditional terrestrial based astrometry you'd then make another observation 6 months later and measure the position again. You can now use simple trigonometry to work it out. You have the base of the triangle - the diameter of the Earth's orbit, you now have the angle that it seems to have moved so you can now work out the 'height' of the triangle. You need to look up 'astrometry'.

A 'parsec' is the distance represented by a parallax of one second of arc. It's about 3.2 light years I think.

Edited by Tenor Viol
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