How do astronomers determine the distances between Earth and distant stars?

Question

do they aim a laser at the star and wait? how can they be accurate in distances over 100 light years?

Answer 1

We guess.

But we make very well educated guesses.

First, we begin with very near stars. We actually measure the "parallax", the angle by which their position changes depending on which side of its orbit Earth is at the time of the observation.

The latest measurments have been made from space, with HIPPARCOS.
http://en.wikipedia.org/wiki/Hipparcos

This gives us somewhat accurate distances for only the one million nearest stars (and even at that, there is still debate as to the accuracy of the furthest stars inside this list).

Within this list, there are many Main Sequence Stars (stars that are still young enough to be fusing hydrogen in their core as their source of energy -- like our Sun). The temperature, light colour, luminosity, etc, of a Main Sequence star is all related to its mass.

If all the Main Sequence Stars having the same mass were put at the same distance from us, they would all have the same brilliance. This is called Absolute Magnitude. When you see a table giving the Absolute Magnitude of a Star, this is how bright the star would appear if it were at exactly 10 parsecs (32.6 light-years).

For distant stars, we try to determine the spectral class (temperature, luminosity...) which gives us the mass; from that we calculate what the Absolute Magnitude would be. We can observe the apparent magnitude. The difference (used in an equation called "distance modulus") is caused by the star's real distance.

Some stars have been observed to behave strangely, in a way that is associated with their mass. These are not Main Sequence stars. For example, a class of variable stars called Cepheids will have a variability period (in days) that is directly related to its Absolute Magnitude.

If we find a Cepheid in another galaxy, we can find its variability period. This gives us its Absolute Magnitude. We can measure the apparent magnitude (by direct observation). Distance modulus calculation = distance to the galaxy.

Many stars explode in different ways (nova, supernova, different types of supernova).

One type of supernova is thought to occur when a very dense star is sucking the material from a companion star. When the mass of the dense star reaches a limit (called the Chandrasekhar limit), it can no longer support itself and explodes.

We can tell the type of supernova by analysing the light during the explosion (they last for weeks). If all the Type Ia supernova occur with stars at esactly the same mass, then the light of the explosion should all have the same Absolute Magnitude. We can observe the apparent magnitude. Distance modulus thing again.
http://en.wikipedia.org/wiki/Type_Ia_supernova

By looking at the closer galaxies (relatively speaking), we find trends that seem to fit: for example, all galaxies of a certain type (e.g., a spiral) appear to have "brightest stars" of the same Absolute Magnitude.

When we find a new galaxy of the same type, we seek its brightest stars and observe the apparent magnitude. Distance modulus equation gets used again.

There are other similar tricks.
http://en.wikipedia.org/wiki/Standard_candle

Hubble (the astronomer, not the telescope) found that the further a galaxy appeared to be, the faster it seemed to move away from us (he found that through the Doppler shift which changes the position of absoption lins in the light spectrum).

Today, we use Hubble (the telescope) to take detailed spectra of distant galaxies and calculate the Doppler shift of its light. Using Hubble's formula (from the astronomer), we estimate the distance to the distant galaxy based on the speed at which it appears to recede from us.

These methods always use other (smaller) methods so that the inaccuracies of each method is added to all the other ones.

Are we 100% sure of the distances, of course not. However, we are quite confident that if a method shows galaxy A to be twice as far as galaxy B, then A is not closer to us than B.

Most of the time (we have had a few surprises, so we are very careful with our affirmations).

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We only use radar on objects that are within our solar system (from Earth: Moon, Mercury, Venus, Mars, some asteroids...; from probes: Jupiter, Saturn)
http://en.wikipedia.org/wiki/Radar_astronomy

For laser, I'm only aware of it being used to measure the distance to the Moon.
http://en.wikipedia.org/wiki/Laser_applications#Lunar_laser_ranging

Answer 2

Well, Parallax is like this: Let's say the gas tank in your car is exactly half full, and it has a needle gauge, not a digital one.There's a needle that is in front of a graduated scale of some kind, and the needle is pointing straight up. If you look at the needle, from the DRIVER'S seat, you can see that that needle points to the half way mark on the scale. If however, you are sitting in the PASSENGER'S seat, and you look over, you will see a different result. In NZ (since you are sitting on the left as a passenger), you would think the tank read a bit more full than it really is, because you see the needle pointing straight up, but the scale behind it appears shifted a bit right. That shift is called Parallax. It is the difference in appearance of the same thing from two different observation points. To do that with stars, you think of the star you are targeting as the needle, and the rest of the stars you can see as the scale, then you look at the star from the same place on Earth, but six months apart, using the Earth's orbit around the Sun as to create your driver's seat and your passenger's seat. Dig it? We can also tell how far away some stars are by using their absolute magnitude, and comparing it to their apparent magnitude. That's a whole different process. It's best to try to use both when possible, but the truth is, that the farther away a star is, the harder and more inaccurate it is to use the parallax method.

Answer 3

Several ways.

One is to measure the brightness, the temparature and the luminosity as perceived here on earth.

Now hold on to yourself, this one is really interesting.

By measuring the paralax shift of a star against the background stars on either side of the earth's orbit, we can calculate the distance to fairly nearby stars fairly accurately. A parsec is defined as a paralax shift of 1 second of arc on each side of earth's orbit.

To see this effect for yourself, do the following.

Hold your thumb up in front of you and focus on a distant object behind your thumb. Close one eye and then the other looking back and forth from one eye to the other while keeping your thumb still. You will see your thumb "shift" position in relation to the background. This is because your eyes are separated by a few inches and "sees" the thumb in a slightly different position by each eye.

It's the same thing with a parsec, only instead of closing an eye, we are looking at the near star in relation to the more distant background stars on either side of the earth's orbit.

Google parsec for more information.

By the way, a parsec is 3.26 light-years.

Answer 4

I believe it is a proportionate calculation. Finding the angle and determining with reference to a known object. For closer ones just like you said they look at the travel time of light.