# Brightness and luminosity relationship

### Luminosity and Apparent Brightness | Astronomy Planets, Stars, Galaxies, and the Universe

Some extremely large and hot stars blaze away with the luminosity of a star's luminosity – relative to the sun's – with the following equation. Brightness, luminosity and the magnitude scale. In about B.C., Hipparchus devised the system of quantifying the brightness of stars still in use today. But from a distance of yards, the searchlight is the brighter of the two. Why? Because We call the total energy output per second of an object its luminosity. It depends This is expressed mathematically using the inverse-square relation: .

In practice bolometric magnitudes are measured by taking measurements at certain wavelengths and constructing a model of the total spectrum that is most likely to match those measurements.

• How Stars Work
• Luminosity and how far away things are
• Brightness, luminosity and the magnitude scale

Bolometric luminosities can also be calculated using a bolometric correction to a luminosity in a particular passband. These are not generally luminosities in the strict sense of an absolute measure of radiated power, but absolute magnitudes defined for a given filter in a photometric system.

Several different photometric systems exist. Some such as the UBV or Johnson system are defined against photometric standard stars, while others such as the AB system are defined in terms of a spectral flux density. To determine a star's radius, two other metrics are needed: Both can be measured with great accuracy in certain cases, with cool supergiants often having large angular diameters, and some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI.

## Mass–luminosity relation

However, for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is merely a number that represents the temperature of a black body that would reproduce the luminosity, it obviously cannot be measured directly, but it can be estimated from the spectrum.

An alternative way to measure stellar luminosity is to measure the star's apparent brightness and distance. A third component needed to derive the luminosity is the degree of interstellar extinction that is present, a condition that usually arises because of gas and dust present in the interstellar medium ISMthe Earth's atmosphereand circumstellar matter.

Consequently, one of astronomy's central challenges in determining a star's luminosity is to derive accurate measurements for each of these components, without which an accurate luminosity figure remains elusive.

### Luminosity and Distance

Because luminosity is proportional to temperature to the fourth power, the large variation in stellar temperatures produces an even vaster variation in stellar luminosity. However, not all light bulbs are the same luminosity. If you put an automobile headlight 10 feet away and a flashlight 10 feet away, the flashlight will appear fainter because its luminosity is smaller.

Stars have a wide range of apparent brightness measured here on Earth. The variation in their brightness is caused by both variations in their luminosity and variations in their distance.

An intrinsically faint, nearby star can appear to be just as bright to us on Earth as an intrinsically luminous, distant star. There is a mathematical relationship that relates these three quantities—apparent brightness, luminosity, and distance for all light sources, including stars.

Why do light sources appear fainter as a function of distance? The reason is that as light travels towards you, it is spreading out and covering a larger area.

## Luminosity

This idea is illustrated in this figure: The Inverse Square Law Credit: Wikimedia Commons Again, think of the luminosity—the energy emitted per second by the star—as an intrinsic property of the star. As that energy gets emitted, you can picture it passing through spherical shells centered on the star.

In the above image, the entire spherical shell isn't illustrated, just a small section.