# Relationship Between a Star's Mass, Luminosity, & Density

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• 0:02 The Masses of Stars
• 0:53 Mass-Luminosity Relation
• 1:54 Mass-Density Relationship
• 3:09 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov
In this lesson, you will learn the important relationship between a main sequence star's mass and its luminosity as well as the relationship between a star's density and volume.

## The Masses of Stars

I remember in elementary school when we would be told to get in line at gym class. But not just any line. We'd be told to get in line from tallest to shortest so that teams could be selected with about an equal average of height to play a game against one another. As you surely understand, most of the time the taller kids were also the heavier ones.

A similar kind of line, or band, exists on an H-R diagram, a diagram that plots a star's luminosity vs. surface temperature. It's called the main sequence band. Here, stars aren't in a line from tallest to shortest. Instead, they are grouped from least massive, all the way down at the bottom right, to most massive, all the way at the top left. You'll soon learn how a star's mass is related to its luminosity and density.

## Mass-Luminosity Relation

Luminosity is a rate of the total radiant energy output of a star. In more familiar terms, it's the intrinsic brightness of a star stretched over the entire electromagnetic spectrum, not just the portion that includes visible light. You can approximate the luminosity of a main-sequence star, a star lying on the main-sequence band of the H-R diagram, based on its mass with a simple equation as shown on your screen.

I don't want you to get bogged down with it even though it is really easy. What I need you to understand is what you can probably already see for yourself. The more massive the star, the more luminous it is going to be because luminosity and mass are directly proportional to one another.

This is roughly saying that the bigger the flashlight, the more likely it is to be brighter than the smaller flashlight or that a big log burning in a fireplace will emit more heat than a matchstick ever would.

## Mass-Density Relationship

Any star's mass can be related to its density as well. The average density of a star is its mass divided by volume. I use the term 'average density' because stars are anything but uniformly dense throughout their diameter. They are more like a fluffy ball of cotton candy around a center made of a jawbreaker. That is to say, their centers are much denser than their outer layers. And this changes things a bit. You'd think that if a star's mass were to go up, then average density would go up, too. This need not be the case, however!

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