# 17.1 The brightness of stars  (Page 3/6)

 Page 3 / 6

The brightest stars, those that were traditionally referred to as first-magnitude stars, actually turned out (when measured accurately) not to be identical in brightness. For example, the brightest star in the sky, Sirius , sends us about 10 times as much light as the average first-magnitude star. On the modern magnitude scale, Sirius, the star with the brightest apparent magnitude, has been assigned a magnitude of −1.5. Other objects in the sky can appear even brighter. Venus at its brightest is of magnitude −4.4, while the Sun has a magnitude of −26.8. [link] shows the range of observed magnitudes from the brightest to the faintest, along with the actual magnitudes of several well-known objects. The important fact to remember when using magnitude is that the system goes backward: the larger the magnitude, the fainter the object you are observing.

## The magnitude equation

Even scientists can’t calculate fifth roots in their heads, so astronomers have summarized the above discussion in an equation to help calculate the difference in brightness for stars with different magnitudes. If m 1 and m 2 are the magnitudes of two stars, then we can calculate the ratio of their brightness $\left(\frac{{b}_{2}}{{b}_{1}}\right)$ using this equation:

${m}_{1}-{m}_{2}=2.5\phantom{\rule{0.2em}{0ex}}\text{log}\left(\frac{{b}_{2}}{{b}_{1}}\right)\phantom{\rule{3em}{0ex}}\text{or}\phantom{\rule{3em}{0ex}}\frac{{b}_{2}}{{b}_{1}}={2.5}^{{m}_{1}-{m}_{2}}$

Here is another way to write this equation:

$\frac{{b}_{2}}{{b}_{1}}={\left({100}^{0.2}\right)}^{{m}_{1}-{m}_{2}}$

Let’s do a real example, just to show how this works. Imagine that an astronomer has discovered something special about a dim star (magnitude 8.5), and she wants to tell her students how much dimmer the star is than Sirius . Star 1 in the equation will be our dim star and star 2 will be Sirius.

## Solution

Remember, Sirius has a magnitude of −1.5. In that case:

$\begin{array}{cc}\frac{{b}_{2}}{{b}_{1}}\hfill & ={\left({100}^{0.2}\right)}^{8.5-\left(-1.5\right)}={\left({100}^{0.2}\right)}^{10}\hfill \\ & ={\left(100\right)}^{2}=100\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}100=10,000\hfill \end{array}$

It is a common misconception that Polaris (magnitude 2.0) is the brightest star in the sky, but, as we saw, that distinction actually belongs to Sirius (magnitude −1.5). How does Sirius’ apparent brightness compare to that of Polaris?

$\frac{{b}_{\text{Sirius}}}{{b}_{\text{Polaris}}}={\left({100}^{0.2}\right)}^{2.0-\left(-1.5\right)}={\left({100}^{0.2}\right)}^{3.5}={100}^{0.7}=25$

(Hint: If you only have a basic calculator, you may wonder how to take 100 to the 0.7th power. But this is something you can ask Google to do. Google now accepts mathematical questions and will answer them. So try it for yourself. Ask Google, “What is 100 to the 0.7th power?”)

Our calculation shows that Sirius’ apparent brightness is 25 times greater than Polaris’ apparent brightness.

## Other units of brightness

Although the magnitude scale is still used for visual astronomy, it is not used at all in newer branches of the field. In radio astronomy, for example, no equivalent of the magnitude system has been defined. Rather, radio astronomers measure the amount of energy being collected each second by each square meter of a radio telescope and express the brightness of each source in terms of, for example, watts per square meter.

Similarly, most researchers in the fields of infrared, X-ray, and gamma-ray astronomy use energy per area per second rather than magnitudes to express the results of their measurements. Nevertheless, astronomers in all fields are careful to distinguish between the luminosity of the source (even when that luminosity is all in X-rays) and the amount of energy that happens to reach us on Earth. After all, the luminosity is a really important characteristic that tells us a lot about the object in question, whereas the energy that reaches Earth is an accident of cosmic geography.

To make the comparison among stars easy, in this text, we avoid the use of magnitudes as much as possible and will express the luminosity of other stars in terms of the Sun’s luminosity. For example, the luminosity of Sirius is 25 times that of the Sun. We use the symbol L Sun to denote the Sun’s luminosity; hence, that of Sirius can be written as 25 L Sun .

## Key concepts and summary

The total energy emitted per second by a star is called its luminosity. How bright a star looks from the perspective of Earth is its apparent brightness. The apparent brightness of a star depends on both its luminosity and its distance from Earth. Thus, the determination of apparent brightness and measurement of the distance to a star provide enough information to calculate its luminosity. The apparent brightnesses of stars are often expressed in terms of magnitudes, which is an old system based on how human vision interprets relative light intensity.

why the dark side of moon never face us? because moon dont rotate? why tho
im in 8th standard and my school teach us nothing about astronomy but i want to be an astronomer so i study from youtube and apps like this but sometimes i get language problems
Rishabh
dark**
Glory
side**
Glory
The Moon does actually rotate. It takes 27 days for the Moon to make a full rotation. Because it takes it so long and the Earth is rotating around the sun, it seems like the Moon is pretty much standing still. That's called "synchronous rotation".
steveh259
I ment to say "The Earth is orbiting around the sun"
steveh259
Tidal Locked.....
***svs.gsfc.nasa.gov/4442
Collins
thats cool
Gospel
ya gives you a look at how the moon orbits around us too and a perspective of how fast we are going. also gives the moon phases for the year! enjoy 😁
Collins
yes you are absolutely correct, it just like something like the milk of heaven
Subhasish
the far side of the moon is not the dark side of the moon.
Shawn
what phases of the moon occurs when spring tide?
the moon has a 28 day cycle. you can download a moon calander or follow the pattern and make your own calendar. 1st full moon of the year 21/22nd Jan, its also a blood moon and a wolf moon. if this info helps at all. 😊
Collins
***svs.gsfc.nasa.gov/4442
Collins
How to determine the velocity of light?
using this formula c=1/√absolute permeability×absolute permittivity of free space i.e. c=1/√8.854×10^-12×4π×10^-7~3×10^8ms^-1
Vidyashankar
what is mean by Big Bang
What it means by Big Bang is how the world was made and came in to exist
Glory
The Big Bang Is The Best Explanation For What We See Around Us, And For The Origin Of The Universe, All Our Evidence Points To The Big Bang Theory..... And Was Proposed By A Belgian Priest.....
if the big bang theory is really true than i would like to know what exploded and where did it came from and where did the energy came from and where come from for the matter to expand into amd where did the organization come from and where did the information come from.........
Gospel
Some say that on the otherside of the singularity was a black hole. They say that at the other end of all black holes is another universe. Hence the multiverse. It's all theoretical at this point but less than a 100 years ago people believed that there was only 1 galaxy in the universe. So why
Rafael
should there be only 1 universe?
Rafael
universe.
Rafael
is astronomy a hard subject to learn because i want to be an astronomer
No it not it just takes time and effort to learn
Glory
Collins
I want to become a scientist but my knowledge is very low. How I can improve my knowledge?
Wwe
any form of science courses, there's free crash course channel on you tube. I've learned alot from this channel. covers most topics, science: biology chemistry physics, astronomy, ranges to anatomy, history and many many more. it's a never ending subject!
Collins
suggest a channel as a example
Wwe
CrashCourse is the name of the channel and there is a picture of an apple. look through their play lists. They will have other related channels they follow also.
Collins
thank you so much
Wwe
Collins
Why are they so far away that their light takes hundreds of millions of years to reach us on earth?
what is comets , astroids ,
comets are broken pieces of dust frozen debris Asteroids are big soiled pieces of Ice that burst into flames when it in to earth's atmosphere
Glory
hi, I am yamini, I am in class 8 but very much interested in astronomy and go to NASA, what are the subjects in which I can master and lead to NASA.
Hello Yamini, Im Ken and I'm avery intrested in joining the NASA too. Is nice to meet you.
Ken
very*
Ken
nice to meet u ken
yamini
What I know about the subjects is that you have to be a master on science and math, also if you know about aviation is better too
Ken
I read that the Russian language is very important, is not a requirement but it's like an extra point!
Ken
yeah like physics, chemistry and maths, they are my most favorite.
yamini
than you can go free of cost
Arush
Yes, That's right!
Ken
how
yamini
Oh! Free of cost?
Ken
hello yamini nice to meet you
Burak
wow from NASA ur so lucky
FNAF
hello yamini nice to meet you
block
what is time
Time is relative
mrunal
pls elaborate
sakshi
the clear defination.I know that.
Abdul
In planet mars there the life exits or not and is there water there
see till now nothing can be found as u know that the curiosity rover has struck in mars
Maya
It has been proven that there are water molecules on Mars but not enough that most lifeforms could thrive upon.
Ariana
There are huge amounts of water in the ice caps and under the surface. The surface and chemistry indicate that Mars had cosiderable amounts of water on its surface in the past.
Julius
i think in some ways vedas are also correct but not everytime
Maya
I agree
sakshi
hmm even I agree
Samuel
Is there any patened theory about time relativitg in growth and development?
some astronomer's says that there is no alien exist but why search for extra terrestrial intelligence center is established
No One Knows That For Absolute Fact, The Universe Is Too Huge To Have Any Type Of Idea About What Exist In The Far Reaches Of Our Universe.....
Check Out The Drake Equation.....
their should be aliens as like ours there would be another planet
Maya
which could have existed life on it
Maya
Maya
can kepler 1st law be applied on all the planets of the universe
Maya
hello, anyone home?
Denise
guys listen we cannot ever find aliens because our technology is not that great.we don't know whether they exist or no because our universe is very large . Just for an example;even if we spot out aliens we cannot reach there because lot of time must have been passed and before us reaching there
Samuel
what if their species or existence might get vanished our have been extinct!! getting my point
Samuel
sjskskfhjkkktewqqw and try?
what is this ?
Samuel
hi I am Samuel from India mumbai
Samuel
nice to meet you
Samuel
thats my question, what is this?
penzias and wilson's a discovery of the cosmic microwave background is a nice example of scientific serendipity-something that is found by chance but turns out to have a positive outcome