## Cepheid variables: Stars, black holes and galaxies

Cepheid variables are a subgroup of a class of stars called variable stars. Other classes include RR Lyrae variables, Mira variables, W. Virginis stars etc. Variable stars are those stars whose brightness oscillates with a definite periodicity. The variation is caused because of the star puffing out and contracting back again. Cepheid variable stars have masses between five and twenty times the mass of the sun.

The period of oscillation has a relation to its luminosity (thus there is a period-luminosity relation for these stars), which is why they are so useful. If you have a method of determining the luminosity of stars, then you can calculate the distance to these stars easily.

It was the observations of Cepheid variable stars which enabled astronomer Hubble (after whom the Hubble Space Telescope is named) to determine that spiral nebulae like the one in Andromeda were galaxies separate from the Milky Way.

The gravitation is hugely more powerful. What is the fundamental reason why this happened ?? Yes it is the massive density that will be there giving it the huge mass, but in a hugely shrunken volume, which has decreased the distance from the surface to the center of the mass immensely also. That is the main reason ; The great decrease in the distance to the center of the mass that will greatly amplify the effects of the curvature of space, by causing greater gravitational field effects, as space around it is much more affected by the same mass but at a hugely more proximate distance, with much greater effect of the same mass at a far closer distance !

The simplest way to mathematically understand it is Newton’s equation of universal gravitation, which is F = Gm1m2/d^2, which immediately tells you that the force of gravitation is inversely proportional to the square of the distance, and directly to the product of the masses. With markedly decreased radius, the inverse relationship noted above will hugely amplify the gravitational force field, even if the product of two masses remains the same (hypothetically, say you or I in the gravitational field of a star vs a black hole of the same mass, but with much decreased radius).

In situations where there are two equal volumes but greater density or mass of one over the other, then it is the mass that will predominantly have effects on the space around it as the distance factor will remain the same. Please note that Einstein’s gravitational field equation simplifies to Newton’s equation on gravitational force brilliantly in nonrelativistic situations(non-accelerating situations) showing you the great connection between the curvature of space and gravitational force field, relating back to Einstein and Newton both beautifully