|MadSci Network: Astronomy|
The distances to the planets can be computed and refined using Kepler's laws. The orbital period of the planets is proportional to the length of the semi-major axis of their orbits. Since we know this value for Earth, we can compute it for the other planets based on their orbital periods. In recent decades, more accurate values have been obtained by powerful radar signals and spacecraft flybys.
There are several methods used to measure interstellar distances. For nearer stars, we can use direct triangulation: The position of a star relative to more distant background stars is measured, and then is measured again six months later. Since the Earth is at the opposite side of its orbit than it was six months before, the minute shift in the star's apparant position (know as its "parallax") is a direct measure of its distance from our Solar System. This is where the term "parsec" comes from. It means "PARallax of one SECond"; in other words the distance at which a start will have a parallax of one second of arc (which is about 3.26 Light Years).
For more distant stars, the properties of their spectra can be used. Different spectral classes of stars have different known brightness ranges, so by comparing their apparent brightness with the known brightness range the distance can be estimated.
Certain types of stars have other properties that allow their distances to be measured very accurately. A type of star called a "Cepheid variable" gets brighter and dimmer in a fixed cycle. The maximum brightness correlates with the rate of the cycle. Thus, if you can see a Cepheid variable at all, you can know its distance just by measuring the cycle time of its brightness. This method has been used to measure the distance to nearby star clusters outside our galaxy.
Certain type of supernovae also have known brightness properties. They are so bright they can be seen when they flare up in nearby galaxies--and allow us to measure the distance to those galaxies.
For more distant galaxies we can determine their distance by their "redshift". Since the universe is expanding more or less uniformly on a large scale the farther away a galaxy is, the faster it appears to be receding from us. The light from these galaxies is doppler-shifted into the red by this apparent motion. This redshift can be measured on a spectrograph and, using the Hubble constant, this redshift can be converted into a distance.
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