How are cepheid and rr lyrae variables used in determining distances?
The absolute magnitude of a Cepheid variable can be deduced from its period (the interval between times maximum brightness), which is easily measured. Once you know the absolute brightness (how much power is emitted) of a star, its distance can easily be inferred from the apparent magnitude.
The mechanism whereby the period of Cepheid variables is related to the absolute brightness (and mass) was first explained by Robert Christy, a Caltech physics professor who worked on the Manhattan (atomic bomb) Project. Prof. Christy passed away last year. He was one of my physics profs there.
RR Lyrae variables have a similar period-luminosity correlation, as do Cepheids, but the starts are smaller and cooler, and the mechanism of both involves pulsation (periodic radius and temperture variation).
You can read more about this type varable at
http://en.wikipedia.org/wiki/RR_Lyrae_variable
Again, once you know how bright a star really is, its apparent brightness can be used to determine the distance. Both types are sometimes referred to as "standard candles"
Cepheid and RR Lyrae variables are important tools for measuring distances to celestial objects. They have a specific relationship between their periods and luminosities, which allows astronomers to determine their distances based on their observed properties.
Cepheid variables are pulsating stars that expand and contract in a regular and predictable manner. They have a well-defined period-luminosity relationship, meaning that the period of their brightness changes is directly related to their intrinsic brightness (or luminosity). By measuring the period of a Cepheid variable, astronomers can determine its luminosity. By comparing the observed brightness of a Cepheid with its known luminosity, they can then calculate its distance using the inverse square law of light. This method is known as the "period-luminosity relationship" and is commonly used in determining distances to nearby galaxies.
On the other hand, RR Lyrae variables are another type of pulsating star, but they have a different period-luminosity relationship compared to Cepheids. RR Lyrae variables have shorter periods and lower luminosities compared to Cepheids. They are often found in ancient stellar populations like globular clusters and the halo of galaxies. By measuring the period of an RR Lyrae variable, astronomers can estimate its intrinsic luminosity and calculate its distance by comparing it to the observed brightness.
To summarize, Cepheid and RR Lyrae variables are used to determine distances by relying on their periods and the established relationships between their periods and luminosities. By measuring the period and observing the brightness of these variables, astronomers can calculate their distances and gain insights into the vastness of the universe.