# Relationship between size and brightness of a star

### Brightest Stars: Luminosity & Magnitude

For two stars of identical size and temperature, the closer one to us will What is the relationship between distance to a star and its brightness (that is the. Likewise, if two stars are the same temperature but different sizes, then the large This is the relationship between luminosity (L), radius(R) and temperature (T). In this lesson, you will learn the important relationship between a main sequence star's mass and its luminosity as well as the relationship.

What Determines a Star's Luminosity? As we have seen in the section on spectroscopy, we can approximate the behaviour of stars as black body radiators.

What properties determine the intrinsic power output or luminosity of a star? Temperature and size of the star.

Fundamentally there are just two key properties - the effective temperature, Teff and the size of the star, its radius, R. Let us look briefly at each of these: A black body radiates power at a rate related to its temperature - the hotter the black body, the greater its power output per unit surface area.

## Luminosity and the Distance to Stars

An incandescent or filament light bulb is an everyday example. As it gets hotter it gets brighter and emits more energy from its surface.

The relationship between power and temperature is not a simple linear one though. The power radiated by a black body per unit surface area is given varies with the fourth power of the black body's effective temperature, Teff.

As a star is not a perfect black body we can approximate this relationship as: A small increase in effective temperature can significantly increase the energy emitted per second from each square metre of a star's surface.

How Do We Measure the Distance of Stars?

If two stars have the same effective temperature but one is larger than the other it has more surface area. The power output per unit surface area is fixed by equation 4.

This becomes apparent when we plot stars on an HR diagram. Assuming stars are spherical then surface area is given by: The star appears so big just because of the scattering of light by the telescope's optics as well as in the photographic emulsion. Alpha Centauri is the closest star system to the Solar System. However, the brightness of a star depends on its composition and how far it is from the planet. Astronomers define star brightness in terms of apparent magnitude — how bright the star appears from Earth — and absolute magnitude — how bright the star appears at a standard distance of A light-year is the distance light travels in one year — about 6 trillion miles, or 10 trillion kilometers.

Astronomers also measure luminosity — the amount of energy light that a star emits from its surface. Measuring star brightness is an ancient idea, but today astronomers use more precise tools to obtain the calculation.

From Greek to modern times More than 2, years ago, the Greek astronomer Hipparchus was the first to make a catalog of stars according to their brightness, according to Dave Rothstein, who participated in Cornell University's " Ask An Astronomer " website in Human eyes, however, are not very discerning. Large differences in brightness actually appear much smaller using this scale, Rothstein said. Light-sensitive charged-coupled devices CCDs inside digital cameras measure the amount of light coming from stars, and can provide a more precise definition of brightness.

Using this scale, astronomers now define five magnitudes' difference as having a brightness ratio of Vega was used as the reference star for the scale.

### Luminosity and the Distance to Stars

Initially it had a magnitude of 0, but more precise instrumentation changed that to 0. Orion is the brightest and most beautiful of the winter constellations. Some of its stars, including Betelgeuse and Rigel, are among the brightest stars. Starry Night Software Apparent magnitude vs.

The apparent brightness, or apparent magnitude, depends on the location of the observer.