There are a variety of methods used to measure distance, each one building on the one before and forming a cosmic distance ladder.
The first, which is actually only usable inside the solar system, is basic Radar and LIDAR. LIDAR is really only used to measure distance to the moon. This is done by flashing a bright laser through a big telescope (such as the 3.5 m on Apache Point in New Mexico (USA), see the Apollo Project) and then measuring the faint return pulse with that telescope from the various corner reflectors placed there by the Apollo moon missions.
This allows us to measure the distance to the Moon very accurately (down to centimeters I believe). Radar has been used at least out to Saturn by using the 305 m Arecibo
radio dish as both a transmitter and receiver to bounce radio waves off of Saturn's moons. Round trip radio time is on the order of almost 3 hours.
If you want to get distances to things beyond our solar system, the first rung on the distance ladder is, as Wedge described in his answer, triangulation, or as it is called in astronomy, parallax. To measure distance in this manner, you take two images of a star field, one on each side of the Earth's orbit so you effectively have a baseline of 300 million kilometers. The closer stars will shift relative to the more distant background stars and by measuring the size of the shift, you can determine the distance to the stars. This method only works for the closest stars for which you can measure the shift. However, given today's technology, that is actually quite a few stars. The current best parallax catalog is the Tycho-2 catalog made from data observed by the ESA Hipparcos satellite in the late 1980s and early 1990s.
Parallax is the only direct distance measurement we have on astronomical scales. Beyond that everything else is based on data calibrated using stars for which we can determine parallax. And they all rely on some application of the distance-luminosity relationship
$m - M = 5log_{10}\left(\frac{d}{10pc}\right)$
where
- m = apparent magnitude (brightness) of the object
- M = Absolute magnitude of the object (brightness at 10 parsecs)
- d = distance in parsecs
Given two of the three you can find the third. For the closer objects, for which we know the distance, we can measure the apparent magnitude and thus compute the absolute magnitude. Once we know the absolute magnitude for a given type of object, we can measure the apparent magnitudes of these objects in more distant locations, and since we now have the apparent and absolute magnitudes, we can compute the distance to these objects.
It is this relationship that allows us to define a series of "standard candles" that serve as ever more distant rungs on our distance ladder stretching back to the edge of the visible universe.
The closest of these standard candles are the Cepheid variable stars. For these stars, the period of their variability is directly related to the absolute magnitude. The longer the period, the brighter the star. These stars can be seen in both our galaxy and in many of the closer galaxies as well. In fact, observing Cepheid variable stars in distant galaxies, was one of the original primary mission of the Hubble Space Telescope (named after Edwin Hubble who measured Cepheids in M31, the Andromeda Galaxy, thus proving that it was an “island universe” itself and not part of the Milky Way).
Beyond the Cepheid variables, other standard candles, such as planetary nebula, the Tully-Fisher relation and especially Type 1a supernova allow us to measure the distance to even more distant galaxies and out to the edge of the visible universe. All of these later methods are based on calibrations of distances made using Cepheid variable stars (hence the importance of the Hubble mission to really nail down those observations.
This post imported from StackExchange Physics at 2014-03-24 04:41 (UCT), posted by SE-user dagorym
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