# Is the distance relative

## cosmology

The Cepheids are variable stars that follow the star δ Cephei; are named in the constellation Cepheus, a subclass of the pulsation variables. Cepheids change their luminosity strictly periodically, while their spectral class and thus their surface temperature also change.

In 1912 Henrietta Swan LEAVITT (1868 - 1921) examined photographic plates at the Harvard College Observatory with images of the very bright, pulsating stars in the small magellanic cloud (Fig. 1). She found out that the brightnesses of a group of 25 stars in the small Magellanic Cloud, which resemble the star δ Cephei, are related to their period.

#### Straight lines on a double logarithmic scale

On a double logarithmic scale (the relative brightness plotted upwards) to the right, the logarithm of the period, parallel straight lines resulted for both the radiation maximum and the radiation minimum, as shown in the graph on the right, published by Pickering in 1912.
This results in the following law for the mean relative brightness m and period p of equally distant Cepheids:
\ [\ frac {{{p_1}}} {{{p_2}}} = {10 ^ {\ frac {{{m_2} - {m_1}}} {{2,54}}}} \ Rightarrow \ lg \ frac {{{p_1}}} {{{p_2}}} = \ frac {{{m_2} - {m_1}}} {{2.54}} \ Rightarrow {m_1} = {m_2} - 2.54 \ cdot \ lg \ frac {{{p_1}}} {{{p_2}}} \]

On the right the apparent brightnesses of four different Cepheids roughly equidistant.

Lighter Cepheids (smaller m) have a larger period.

#### Conclusion about the absolute brightness

Since all the stars of the small Magellanic Cloud are the same distance from us, this formula naturally also applies in the same way to absolute brightnesses. In order to "calibrate" the formula to absolute brightness, one needed a Cepheid whose distance and thus its absolute brightness was known. In 1919 Harlow Shapley succeeded in doing this with Cepheids from globular clusters of our galaxy.

The pulsation variable page shows what causes the pulsation change.

#### Distance determination with Cepheids

Cepheids are quite common giant stars and very bright objects that can be observed from Earth up to a distance of a few megaparsecs, with the Hubble space telescope even up to a distance of around 20 megaparsecs. This makes Cepheids a useful means for determining astronomical distance: From the period of a Cepheid, which can be observed directly, one can infer its absolute brightness. By comparison with the observed relative brightness, the distance of the Cepheid from the earth can then be calculated purely from the so-called distance module \ (mM = 5 \ cdot \ lg \ left ({\ frac {r} {{10 \, \ rm { pc}}}} \ right) \).

#### Standard candles

In astronomy, a standard candle is a luminous object with a known or simply calculable absolute brightness. With standard candles one can deduce the distance of objects accordingly. In a range up to 20 Mpc, Cepheids are suitable standard candles. Other standard candles are the RR Lyrae stars, the W Virginis stars and, for very distant objects, type 1a supernovae.