Chapter 5 part 1 — Star brightness
Introduction
Well well well… we’re at one of the best topics in Astrophysics in my opinion. Stars are absolutely fascinating, they look small specks in the sky, smaller than a thumbtack… yet they’re huge balls of plasma, often times having a radius of thousands of kilometers, yet our understanding of stars is very minute, we have a long way to go so buckle up.(Also I’m very sorry for not posting in quite a while, I’ve been extremely busy with schoolwork.) Stars are so cool that the logo of Project Bluestar is a Star!!!
“The Nitrogen in our DNA. The Calcium in our teeth. The Iron in our blood. The Carbon in our apple pies, were all made in the interior of collapsing stars. We are made of star stuff.”
- Carl Sagan
Before we go back to the quote, here are a few questions you can try and answer without the help of any resources, to see if you really know stars very well. If you don’t not to worry, this chapter will answer all these questions.
- What is a star?
- What are the properties of stars?
- Are there different types of stars?
- What are stars made of?
- Do we have a method of classifying stars?
- If we classify stars, on what properties do we classify them on?
A star is a big ball of plasma. What is plasma? Plasma is a separate state of matter, you’ve likely heard of the three states of matter: Solids, liquids and gases. There are two more states of matter: Plasma and Bose-Einstein condensate.
The Sun is a star, it might seem really special to us. It gives us light, it allows plants to photosynthesise and the daylight in horror movies makes us feel safe as ghosts can’t appear in the light. However it’s really not that special if you zoom out to the Universe. The Sun is actually quite average, there isn’t anything that really makes it unique apart from the fact that without the Sun, we’d die.
Now stars are really really really really really really really really really far away. Did I mention that stars are far away? The Sun is around 1.49 x 10¹¹ m away from the Earth (Check my post on the scale of the cosmos). The next closest star is Proxima Centauri which is about 4 ly away from us. The reason for this is because stars are really really really really really really really really really hot.
The temperature of the Sun is about 5778 K which is around 5504.85 degrees Celsius, and the Sun is only average! Some stars can go up to 30,000 K.
Stars are also really really really huge. The radius of the Sun is 696,340 Km. That’s about 5,802,833.33 football fields. Wow I just used football fields as a unit of length…
Yes the name of the sport that plays in that pitch is called “football” not “soccer” ew.
Anyways, stars are also really really really bright. In fact they’re so bright that we have three separate quantities to measure their brightness:
- Luminosity
- Apparent Brightness/Magnitude
- Absolute Brightness/Magnitude
Luminosity
Luminosity is the amount of energy radiated from a celestial object per second. It has a units of Joules per second (J/s). The luminosity of a star can be calculated by:
Where L is the Luminosity of the star, σ is the Stefan Boltzmann Constant which is about 5.67 x 10⁸ W/m²/K⁴. A is the surface area of the star which can be calculated by A=4πR² where R is the radius of the star. T is the temperature of the star. σ is actually derived by this formula:
You don’t have to worry about what this formula means at all. KB is Boltzmann’s constant, h is Planck’s constant and c is the speed of light.
The Luminosity of the Sun is about 3.846 x 10²⁶ W. It can also be represented by this:
In fact anything with that symbol as a superscript has something to do with the Sun. For example a star with a radius of
Actually means that the star has a radius twice as large as the Sun’s.
Apparent Brightness
The Apparent Brightness of a celestial object is simply how bright an object is with respect to the Earth. It has units of W/m². It can be calculated like so:
Where L is the Luminosity of the Star and d is the distance of the Star from Earth. This is known as the inverse square law. In fact, we can find out how far a star is if we know the Star’s luminosity and apparent brightness. All we have to do is rearrange for d which gives us:
Absolute Magnitude
The absolute magnitude of a star is simply how bright a star is if it was 10 pc away from the Earth.
Where M is the absolute magnitude of the star, b is the apparent brightness and d is the distance of the star from the Earth in pc.
The reason we have absolute magnitude is because it helps us compare the intrinsic brightness of different celestial objects. This is because apparent brightness doesn’t really tell us much. Some stars may have a larger apparent brightness than others because they are closer to the Earth, some may have a smaller apparent brightness because they are further.
As such, absolute magnitude helps us compare the brightness of all celestial objects in a more fair way. We’ll look at why brightness is important to us later down the road
Conclusion
I’m going to end off here as I don’t want to overwhelm you with all these formulas and Maths. I hope you guys enjoyed!
Images can be found at:
- National Geographic Society. “Sun.” National Geographic Society, 13 Nov. 2012, www.nationalgeographic.org/encyclopedia/sun/.
2. www.SoccerCoachingPro.com
