# How does the luminosity equation work?

• IDK10
In summary: Pi is the square of the radius, so it helps to understand how the brightness (b) decreases with distance.
IDK10
I've read that L = 4 x Pi x b x d2
Where L = Luminosity (W)
d = distance (m)
b = brightness (W m-2)

But in a real life applied situation, how does it work, how does one measure the distance and its brightness? And what does the 4Pi do?

IDK10 said:
I've read that L = 4 x Pi x b x d2
Where L = Luminosity (W)
d = distance (m)
b = brightness (W m-2)

But in a real life applied situation, how does it work, how does one measure the distance and its brightness? And what does the 4Pi do?
Hint -- what is the surface area of a sphere in terms of its radius?

IDK10 said:
But in a real life applied situation, how does it work, how does one measure the distance and its brightness?

The distance can be measured with a variety of range finding devices. You can probably do a google search and find plenty. The brightness can be measured using a camera, photo-diode, or other device.

Also, notice that if you move everything on the right over to the left except for brightness, you then get the well known inverse square law.

4/3 x πr3.

(I really wish you could easily do fractions)

berkeman said:
No, the surface area increases as r^2. Try again?

And you can use LaTeX to do fractions... https://www.physicsforums.com/help/latexhelp/
Oh, thought you meant volume, I saw you said surface area, then thought of volume for some reason. Don't ask why, the brain is weird. So, its the same as that, but instead of r2, its bd2.

IDK10 said:
b = brightness (W m-2)
So how does the brightness fall off with distance, and why?

berkeman said:
So how does the brightness fall off with distance, and why?
What do you mean by fall off with distance?

IDK10 said:
What do you mean by fall off with distance?
As you get farther and farther from the light source, it appears dimmer and dimmer, right?

Maybe do a search on the hint that Drakkith gave you... (actually he even gave you a link to the inverse square law)...

berkeman said:
As you get farther and farther from the light source, it appears dimmer and dimmer, right?

Maybe do a search on the hint that Drakkith gave you... (actually he even gave you a link to the inverse square law)...
Oh, I meant a rephrasing, but I get what you mean.

IDK10 said:
Oh, thought you meant volume, I saw you said surface area, then thought of volume for some reason. Don't ask why, the brain is weird. So, its the same as that, but instead of r2, its bd2.

The distance (d) is the same thing as the radius (r) since the object is considered to be at the center of a sphere and the observer (you or an instrument) is some distance from the center. You can write bd2 or br2.

## 1. What is the luminosity equation?

The luminosity equation is a mathematical formula that calculates the total amount of energy that a star emits per unit time, also known as its luminosity. It takes into account the star's surface temperature and radius, and is often used in astrophysics to determine the properties of stars.

## 2. How is the luminosity equation calculated?

The luminosity equation is calculated by multiplying the star's surface area by its surface temperature to the fourth power. This is known as the Stefan-Boltzmann law. The equation can then be simplified by substituting the star's radius for its surface area, resulting in L = 4πR²σT⁴, where L is luminosity, R is radius, T is temperature, and σ is the Stefan-Boltzmann constant.

## 3. What units are used in the luminosity equation?

The units of the luminosity equation depend on the units used for the star's radius, temperature, and the Stefan-Boltzmann constant. However, in most cases, luminosity is expressed in watts (W) or solar luminosities (L☉), radius in meters (m), temperature in Kelvin (K), and the Stefan-Boltzmann constant in watts per square meter per Kelvin to the fourth power (W/m²K⁴).

## 4. Can the luminosity equation be used for all types of stars?

No, the luminosity equation is primarily used for stars that are in thermal equilibrium, meaning their energy output is primarily a result of their surface temperature. This equation would not accurately represent the luminosity of other types of stars such as pulsating or exploding stars.

## 5. What other factors can affect a star's luminosity?

Aside from surface temperature and radius, a star's composition, age, and mass can also affect its luminosity. For example, more massive stars tend to have higher luminosities. Additionally, the presence of companions or surrounding material can also impact a star's luminosity.

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