Akarsh Simha

# Cosmic Distance Ladder

The cosmic distance ladder refers to the succession of different methods that astronomers use to measure distances to objects in the sky. Some methods, like parallax, work well for only nearby objects. Other methods, like using the cosmological redshift, work only for very distance galaxies. Thus, there are several methods, each with its own limited validity, and hence the name.

## Direct measurements

The bottom of the ladder consists of objects whose distances can be directly measured, like the moon (see Lunar Laser Ranging). The same technique, using radio waves, is applied to find distances to planets as well.

For nearby stars, measuring the parallax is possible and yields the distance to the star.

## Standard candles

"Standard candles" are objects whose intrinsic brightnesses we can know for sure. The apparent magnitude, which is easy to measure, tells us how bright an object appears, not how bright it actually is. Distant objects appear less brighter, because their light gets spread out over a larger area.

In accordance with the inverse square law for light intensities, the amount of light we receive from an object drops with the distance squared. Thus, we may compute the distance to an object if we know both how bright it actually is (absolute magnitude; 'M') and how bright it appears to us on earth (apparent magnitude; 'm'). We may define the distance modulus as follows:

Distance Modulus = M - m = 5 log10 d - 5

Here 'd' is the distance measured in parsecs.

For these special standard candle objects, we have some other way of knowing their intrinsic brightness, and thereby can calculate their distance.

Common "standard candles" used in astronomy are:

- Cepheid Variables: A kind of periodic variable star, whose variation period is related to the luminosity

- RR Lyrae Variables: Another such periodic variable star with a well-known period-luminosity relationship

- Type-Ia supernovae: These supernovae have a very well-defined luminosity as a result of the physics that governs them and hence serve as standard-candles

## Other methods

There are many other methods. Some of them rely on the physics of stars, such as the relationship between luminosity and color for various types of stars (this is usually represented on a Hertzsprung-Russel Diagram). Some of them work for star clusters, such as the Moving cluster method and the main-sequence fitting method. The Tully-Fisher relation that relates the brightness of a spiral galaxy to its rotation can be used to find the distance modulus, since the rotation of a galaxy is easy to measure using Doppler shift. Distances to distant galaxies may be found by measuring the Cosmological redshift, which is the redshift of light from distance galaxies that results from the expansion of the universe.

For further information, consult Wikipedia on Cosmic Distance Ladder