# How to Find the Size of a Star

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• 0:03 Finding the Size of Something
• 1:07 The…
• 3:37 The Stars on the Diagram
• 4:45 Why the Stars are…
• 6:42 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

This lesson will tell you how astronomers figure out the size of stars. You'll learn it has to do with a star's temperature, luminosity, and a cool thing known as the H-R diagram.

## Finding the Size of Something

To find the size of a shoe, you look at the label on the box or, in the worst case scenario, you take a ruler and just measure it. To find the circumference of your waist, you can use a waist tape measure. But finding the size of a star is hard to do. Yes, it's because they're far away, and we can't reach them directly. Yes, we don't have a ruler big enough to measure them. Yes, we'd be burned alive if we even tried to get too close even if we had a big enough ruler.

But there's another problem: no matter what telescope you use, stars look like a point of light, making it difficult to figure out their true size. This is why astronomers figured out a workaround for this problem, a workaround using a very famous, very important diagram, a workaround that can tell us the size of a distant star. This workaround includes things we'll cover in this lesson, including something called the H-R diagram, temperature, and luminosity.

## The Hertzsprung-Russell Diagram

To find out the size of a star, you first need to know its temperature and luminosity. Luminosity refers to the total energy a star radiates in one second. In simple terms, it is a star's intrinsic brightness. A separate lesson on luminosity and brightness exists for more information on this.

In the 20th Century, two astronomers independently discovered a very basic relationship between the temperatures and luminosities of stars. These astronomers were Henry N. Russell of the U.S. and Ejnar Hertzsprung of Denmark. Their work came to be known as the Hertzsprung-Russell (H-R) diagram. As you can tell below, it's a diagram that plots a star's luminosity vs. surface temperature. Carefully note how the temperature gets hotter as we move left along the horizontal axis and luminosity gets larger as we move up the vertical, or y-, axis. By the way, the luminosity of a star is measured relative to the sun.

Looking at the diagram, you can tell what the H-R diagram plots out and what important relationship was discovered: a star with a high temperature and luminosity is larger in size. A star with lower temperature and lower luminosity is smaller in size. To understand why this is the case, you must understand that surface area and temperature affect luminosity.

Think of a candle flame burning a couple of feet away from you. A small candle flame has a pretty small surface area. If you touch your finger to the flame, it would burn you because it's hot. But because the flame is small, it can't radiate a lot of heat outwards, towards you. Remember: luminosity is the total energy a star radiates in one second. This means you can comfortably sit there and not worry about the small flame making it uncomfortable for you to sit near it.

Now, think of another candle flame as hot to the touch as the small one but 20 feet tall! Its surface area is humongous, so huge that its luminosity would make it extremely uncomfortable for you to do anything but run away from the flame.

## The Stars on the Diagram

When several thousand stars are chosen at random and plotted on the H-R diagram, they will fall into specific regions. Such patterning shows us that there is a true connection between a star's temperature and luminosity. Had there been no meaningful connection between temperature and luminosity, our randomly chosen stars should have been scattered all over the graph in a random, rather than specific, fashion. But they weren't and they aren't. So there.

Approximately 90% of stars lie on a band that is called the main sequence. A star whose characteristics place it in the main sequence is also called a main-sequence star. Stars in the sequence include our sun and red dwarfs. The majority of the remaining ten percent of stars are found elsewhere. One percent are found in the upper right region of the H-R diagram, representing cool, bright giants and supergiants. Conversely, nine percent can be found in the lower left corner, where they are hot white dwarfs with low luminosity.

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