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Learning objectives

By the end of this section, you will be able to:

  • Describe the methods used to determine star diameter s
  • Identify the parts of an eclipsing binary star light curve that correspond to the diameters of the individual components

It is easy to measure the diameter of the Sun. Its angular diameter—that is, its apparent size on the sky—is about 1/2°. If we know the angle the Sun takes up in the sky and how far away it is, we can calculate its true (linear) diameter, which is 1.39 million kilometers, or about 109 times the diameter of Earth.

Unfortunately, the Sun is the only star whose angular diameter is easily measured. All the other stars are so far away that they look like pinpoints of light through even the largest ground-based telescopes. (They often seem to be bigger, but that is merely distortion introduced by turbulence in Earth’s atmosphere.) Luckily, there are several techniques that astronomers can use to estimate the sizes of stars.

Stars blocked by the moon

One technique, which gives very precise diameters but can be used for only a few stars, is to observe the dimming of light that occurs when the Moon passes in front of a star. What astronomers measure (with great precision) is the time required for the star’s brightness to drop to zero as the edge of the Moon moves across the star’s disk. Since we know how rapidly the Moon moves in its orbit around Earth, it is possible to calculate the angular diameter of the star. If the distance to the star is also known, we can calculate its diameter in kilometers. This method works only for fairly bright stars that happen to lie along the zodiac, where the Moon (or, much more rarely, a planet) can pass in front of them as seen from Earth.

Eclipsing binary stars

Accurate sizes for a large number of stars come from measurements of eclipsing binary    star systems, and so we must make a brief detour from our main story to examine this type of star system. Some binary stars are lined up in such a way that, when viewed from Earth, each star passes in front of the other during every revolution ( [link] ). When one star blocks the light of the other, preventing it from reaching Earth, the luminosity of the system decreases, and astronomers say that an eclipse has occurred.

Light curve of an eclipsing binary.

Light Curve of an Eclipsing Binary. In this plot the vertical axis is labeled “Brightness” in arbitrary units, and the horizontal axis is labeled “Time” in arbitrary units. The plotted line is labeled “Light curve”. The plot begins as a horizontal line at upper left and is labeled “1”. The line then drops very sharply downward as it moves to the right, then quickly becomes horizontal again. This horizontal section is labeled “2”. The curve then rises sharply again back to the same brightness level as segment 1. This horizontal section is labeled “3”. After a time, the horizontal line drops, but not as deeply as segment 2, and becomes horizontal again. This horizontal segment is labeled “4”. The curve then rises again to the level of segment 1. Inset is a diagram of the binary star system. The larger star is drawn as a red sphere. A blue elliptical arrow surrounds the larger star with an arrowhead pointing to the right, indicating the motion of the companion star. The companion star is drawn on the elliptical arrow in four places corresponding to the sections 1-4 on the light curve. At position 1 the smaller star is separated from the larger star and the light curve is at its brightest. At position 2 the smaller star is behind the larger star and the light curve dips to its lowest brightness. At position 3 the smaller star emerges from behind the larger star and the full brightness is restored. Finally, at position 4, the smaller star is in front of the larger star, and the light curve dips to its next lowest level.
The light curve of an eclipsing binary star system shows how the combined light from both stars changes due to eclipses over the time span of an orbit. This light curve shows the behavior of a hypothetical eclipsing binary star with total eclipses (one star passes directly in front of and behind the other). The numbers indicate parts of the light curve corresponding to various positions of the smaller star in its orbit. In this diagram, we have assumed that the smaller star is also the hotter one so that it emits more flux (energy per second per square meter) than the larger one. When the smaller, hotter star goes behind the larger one, its light is completely blocked, and so there is a strong dip in the light curve. When the smaller star goes in front of the bigger one, a small amount of light from the bigger star is blocked, so there is a smaller dip in the light curve.

Questions & Answers

How long the duration was when the laws of physics became active after the big bang?And why the time is called plank's time?
Mostak Reply
how many galaxies in universe?
Shaikh Reply
10 to the power 11
Wwe
testing
Ahmad
thnx
Shaikh
if u can count all the sands on the beaches and on the deserts then u will know how much it will be.......some said more than 1,000,000,000 galaxies are there in our universe...
Gospel
it's ok bro
Wwe
I hope you will become a member of nasa
Wwe
just new in this area, from art background not science
Ahmad
what's ur name wwe
Shaikh
The Observable Universe Contains Between 200 Billion To 2 Trillion Galaxies.....
Adam
are u sure?
Caleb
It actually hasn't been proven, people have just made estimations.
Ariana
the thing is u can't count,maybe the our number system will collapse there...who knows?
Abdullah
What's the exact time when the laws of physics became active after the big bang ?
Mostak
Actually we still don't know the exact number of galaxies in the universe, since the universe is bigger than we can imagine and it is still expanding even bigger today than yesterday
Ismaee
hi i need a telescope would you help mee
Nauman Reply
i can only advice you to go to some museum
Gospel
wher is it?
Nauman
but before that.......... i wanna know where are you from and from which state...and if you are nearer to that of the museum or will be able to go then.,.. i donot have any more words.
Gospel
What Do Plan To Observe?
Adam
sorry . i am from asia
Nauman
Check on amazon.Celeston telescopes are good for beginners.
priyanshu
can yoy introduce your self
Nauman
can you
Nauman
Asia...? from which country you belong into ...,,is it India or where?
Gospel
Do You Want A Telescope With ALot Of Maintenance Or Zero Maintenance?
Adam
pakistan
Nauman
with alot offf
Nauman
Any second hand online stores in your area? great for unused Christmas gifts etc..
Collins
So You Want A Newtonian Reflector?
Adam
So what i would put for that answer ?
Abdulla Reply
The largest observatory complex in the world is on Mauna Kea, the tallest mountain on Earth. Whatare some factors astronomers consider when selecting an observatory site? Don’t forget practical ones.Should astronomers, for example, consider building an observatory on Denali (Mount McKinley) or MountEverest?
Abdulla Reply
i need help on the the second part
Abdulla
Should astronomers for example considered building an observatory on Denali (Mount Mckinley) or MountEverest ?
Abdulla
I would take into consideration. climate weather pattern.
basim
also, could an establishment be built and be able to sustain years of being beaten by the weather?
basim
so far Mount Everest to my understanding is a difficult mountain
basim
it is because of light pollution in the cities that the observatories are situated in extremely remote areas.
Ashish
Everest ist the tallest mountain
Paul
how far us milky way galaxy?
ShowsSpy Reply
oh man
madison
We are part of the Milky Way Galaxy. We are within it, so it's not really away from us. Our galaxy is 100,000 light years in diameter. The nearest big galaxy is Andromeda, around 2 million lightyears away.
Jignesh
its 200,000 light years
Gospel
Where is Rice University located?
Amanda Reply
it is in your vagina
world
that couldn't be any more wrong 😂😂
jay
what even is this conversation😂😂!?
Herrera
Show Some Class.....
Adam
Houston, Texas.....
Adam
Houston
Preston
what is the first step to take as far as getting into the field of astronomy?
john Reply
how are universe made up of?
madhu Reply
saksi
madhu
lanika
madhu
I think that your question is- What is the universe made up of?
priyanshu
Ever heard of matter?
priyanshu
Well,the universe is made up of matter and possibly antimatter
priyanshu
Actually,it's made up of matter's smaller units,fundamental particles
priyanshu
But for normal purposes,say that it's made of matter
priyanshu
If you're asking how was the universe made,
priyanshu
there are several theories,but the widely accepted one is the 'Big Bang Theory'.
priyanshu
In simple words,a veeeeeeery long time ago (20 billion years).
priyanshu
The universe was just inside a very small point.
priyanshu
Then,it started to expand.
priyanshu
It is still expanding today
priyanshu
But remember,it's just a theory,there is no hard and fast proof
priyanshu
oh d*mn😭😭😭😭 i cant do my astronomy quest
swagirl
up Down quarks atoms electrons proton neutrons
Blake
😭😭😭😭..
swagirl
usually in astronomy quest there's many math formula. i'm difficult on them
swagirl Reply
practice!
Collins
?
swagirl
what was the question? if you need any help CrashCourse/astronomy and physics channel on YouTube are a good help.
Collins
yeah like... you know venn diagram?
swagirl
yeah it's for sets
Vinit
***youtu.be/uR70knMr2Hg
Collins
this might help you understand Venn diagram. and yes they're sets of numbers.
Collins
tx for u
swagirl
why the dark side of moon never face us? because moon dont rotate? why tho
Rishabh Reply
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.....
Adam
***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
Tidal Locking?
priyanshu
what phases of the moon occurs when spring tide?
Florence Reply
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?
PARTHIB Reply
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
block Reply
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.....
Adam
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
Big Bang is a theory on the origin of the universe.It says that the whole universe started as an infinitely dense and hot point,which expanded with time to form the universe in which we live today.
priyanshu
but if you study about string theory then you will come to know that before big bang there were string ( vibrating particles) which cause to form the conditions for big bang.
YOG
Hmm,actually,I dont know much about string theory,just a little.I just wanted to tell this guy what is the Big Bang Theory.
priyanshu
and according to string theory black holes are giant fuzzball of strings,there is no infinity dense singularity and no smooth horizon there is just only a ball of string
YOG
I think that is the problem. why don't we ask what was before the big bang. to explode there must be a reason or a change so if there is change there must be time also. science can't solve this . never . unless it accepts the existence of God . it is a matter of scientists will accept God. and every
KUMNEGER
For those arguing Religious Dogma over Science, regarding the Origins of the Universe, as well as the Origin of Man... Please pick up and read a Chemistry Book first, particularly in regard to Atomic Structure, Composition & the creation of other Elements from the Periodic Table... To start with.😉
Bill
Next you can look up the terms... Potential Difference, particularly associated with Electrical Charge or Energy & the Transfer of electrons from the outer Valence Shell of an Atom...and the production of ENERGY or Electrical Charge and Heat...😉😁😎
Bill
You should now begin to see the dots connecting themselves, from a scientific perspective, pretty quickly...😉😁😎
Bill
is astronomy a hard subject to learn because i want to be an astronomer
FNAF Reply
No it not it just takes time and effort to learn
Glory
if your already interested/observing, your already an astronomer ! The more you look and read the more you'll learn.
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
your very welcome
Collins
No actually astronomy is a very interesting subject and it's not so hard if you'll make research and read some books you'll find it so simple
Ismaee
to become a actually astronomer you need to learn physics and after that you can take job of astronomy
Sir
Which books should I read as a beginner?
Aditya
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Source:  OpenStax, Astronomy. OpenStax CNX. Apr 12, 2017 Download for free at http://cnx.org/content/col11992/1.13
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