Relating a Star's Brightness to Luminosity

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  • 0:01 Wattage and Luminosity
  • 1:08 The Inverse Square Law
  • 3:55 Using Luminosity for…
  • 4:37 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov
This lesson will explore how luminosity, apparent brightness, and distance are related to one another using the inverse square law. You'll also learn how luminosity can be gauged based on distance and apparent brightness.

Wattage and Luminosity

At home, probably in your garage or basement, you keep a bunch of light bulbs in stock. If you were to go look at them, you'd see they're labeled as something like 60 W, or 14 W, or 100 W. The W stands for a watt, a unit of energy equal to one joule per second. One joule is approximately equal to the energy released when an apple falls to the ground from a table one meter high.

Now, what if you entered your basement and found an object that emits 3.8 * 10^26 W? Actually, that would be kind of impossible as that wouldn't fit in your basement because that object would be our sun. 3.8 * 10^26 W, our sun's luminosity, the total energy a star radiates in one second, is equal to one solar luminosity, abbreviated as shown on screen. This means that a star that is labeled as five solar luminosities emits five times more energy than our sun every single second.

Luminosity is the energy a star emits in one second

The Inverse Square Law

A star's luminosity is very important for something. The closer a luminous object is to you, the brighter it appears to be. How bright something appears to be is related to how close it is to you.

This is nothing new for you to grasp. Just think of a light bulb you find in your basement. If you turn it on and hold it a foot away from you, it will make you squint. If you place the light bulb a mile away, it may be so faint you won't even see it. Such a relationship can be put into something known as the inverse square law, a law that relates apparent brightness and luminosity.

To put this law into perspective for you, imagine that a star is in the center of a sphere with a radius of d. The amount of energy that moves every second through one square meter of the sphere's surface area is the luminosity of the star (L, measured in W) divided by the entire surface area of the sphere itself, which is calculated as 4 * Pi * d^2. The number you come up with by performing this calculation is known as the apparent brightness of a star (b, in W/m^2).

The apparent brightness of a star becomes smaller and smaller with increasing distances away from the star because the light emitted by the star has to spread over larger and larger areas of space. There's only so much light to go around! To demonstrate this for yourself, take a flashlight and shine it at a white wall about an inch or so from the wall. Note how the brightness of the circle formed by the flashlight is very intense. Now move further and further away from the wall with the flashlight. You'll notice that the area the light covers becomes greater and greater, but the light becomes fainter and fainter.

The inverse square law
Inverse Square Law

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