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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

can you tell me what is a quantam elighment? Lets see how many people give write answers
gdjm Reply
can you tell me what is a fomalhaut?
gdjm
Fomalhaut Is The Brightest Star In The Constalellation Of Piscis Austrinus.....
Adam
joe.
Tracy
Do You Mean Quantum Entanglement?
Adam
can anyone tell me daily rotation of the sun in tokyo
Liridona Reply
tokyo has it's own personal sun
Tracy
can you send me any pictures of the tokyo sun
Liridona
sure! ig?
Tracy
here can u?
Liridona
no it wont let me sadly
Tracy
or
Liridona
snapchat
Liridona
i dont have snapchat 😰
Tracy
okay ig
Liridona
my ig is fatwigga37 if you'd like to see :)
Tracy
Can we use SI units in the equation of Kepler's third law?
Naiyu Reply
can u tell the equation pls
sasmita
how does religion enters to this topic when god created this world
Sakira
How Do You Know A God Created Our Planet?
Adam
you must read bible
Sakira
u must the bible
Sakira
How Do You That Book Is Authentic? And I Have Read The Bible, The Koran, The Torah And The Urantia.....
Adam
The law is T^2 is proportional to R^3 where t is planet's time period and r is average of semi major axis and semi minor axis. Also,don't turn this place into a religious warzone. We already have idiots fighting about religion.
priyanshu
If I Had A Book That Said Insects Created The Universe, Would That Make It Fact?
Adam
Have You Ever Heard Of The Council Of Nicaea?
Adam
Through Out History Mankind Has Worshipped Over 5000 Different Gods, How Do You Know Christ Is The True God?
Adam
God Is A Hypothesis..... The Definition Of Faith Is Belief Without Proof.....
Adam
Thank You Prianshu Roy, This Is A Forum For Science Not Archaic Stories Written By Sheep Herders, Well Said.....
Adam
Hebrew 13:1
onome
P2 = a3
Adam
So You Quote A Bible Verse, Now What?
Adam
Science Discourse Nothing Else.....
Adam
god is real he's not just a wise guess
Sakira
god bless you
Sakira
u know what,u are not here if god werent there!
Sakira
Science Discourse, Nothing Else.....
Adam
Thier Are Many Religious Sites You Can Go To, To Discuss God.....
Adam
hahahaha
Sakira
Have A Great Day.....
Adam
night time here
Sakira
Look Up The Definition Of Day, Instead Of Trying To Look Witty, Again Have A Great Day.....
Adam
😈😈😈
Sakira
such an socratic person?
Sakira
What Was Your Intention In Stating "Night Time Here" ?
Adam
please don't fight over silly stuffs!
Romancho
tangina mo
Sakira
No I Don't Believe A God Exist, But I Will Fight For Your Right To Worship Any God You Wish.....
Adam
no fighting
Sakira
But This Venue Is For Science Discourse.....
Adam
i know!
Sakira
No Fighting, Just Discussion.....
Adam
yes Naiyu, we have to use SI unit in the equation for the Kepler's every laws
Madhav
Thanks.
Naiyu
what's the scene of voyager 1,did we get any information through it
Aarushi Reply
we are getting a lot of info yet more to be received check official mission report from the officials site ....
Ganeshan
what are the best astronomy books?
neehar Reply
what is the parallel space?
neehar
how to measure the brightness of a star in w\m^2
Aarushi Reply
it's based on the percentage of helium I think
neehar
ok TQ😊
Aarushi
it's based planet colour and brightness which called lumiosity
gdjm
Are there planets that has the same characteristics as earth.
Nito Reply
yes ofcourse there are earth like planets but they aren't completely like earth.still scientists have a hope of life existence in there.
Aarushi
yeah of course example is Mars but they only discover water at mars
neehar
there's a much possibility of presence of earth like planets in the universe if they were present at goldilock zones
Jashwanth
what are goldilock zones?
Aarushi
How to become an astronomy
Aakarsh Reply
astronomer*
Emilya
Yes
Aakarsh
Astronomer
Aakarsh
yes i Also want to know the answer
Mehar
How to become?
Aakarsh
Me too
Romancho
By hard study
Zulker
Try to keep all the basics of science subjects and also English
Zulker
Ya i know that I will do hard work but
Aakarsh
I have always found astronomy fascinating, but my first love is philosophy.
GARY
I wanna become astromer as neel armstrang
Aakarsh
that's an astronaut
Emilya
Neil Armstrong
antman
what is your name who are you where are you why are you there
GARY
Neil Armstrong was an astronaut. You first work is to know the meaning of astrophysicist, astronomer, astronaut, astrologer and to find the work of the individual. And the most important thing is to be good in English. Because u have done some mistakes while doing chat with me like :an astronomer
Zulker
sorry I'm talking to somebody else someplace else on the internet
GARY
The heading will be "How to become an astronomer"
Zulker
jus be yourself and follow your passion and I think there is no need to copy anyone
Aarushi
hey it's simple yaar, it's based on your curiosity
neehar
what is the length of Earth
comedy Reply
The Earth is not a perfect sphere, however it's roughly 25,000 miles, or 131.5 million feet, or 1.6 Billion inches. In the Metric system its HUGE!
Jocofranc
Thank for your knowledge.Sr
nyo
But can I also know and calculate the whole weight of earth includeing flora, funa,water on earth even air's weight.Depending on super compruter, I think it can be.For the very detail in the Metric System.Such as kilogram and pound.
nyo
Earth is about 6 Sextillion metric tons check out formula at ***science.howstuffworks.com/environmental/earth/geophysics/planet-earth-weigh.htm
Jocofranc
thank again Sr.I wanna ask another question if you don't mind.The earth had 4.5billion years age old.My question is from fire ball to today more and more stable geology was how happen.Please answer me starting of life on this planet and how many era are there and the earth history.
nyo
My friend you have asked a question(s) that scientists struggle with. There is no short cut...the information is lenghty. Here is an additional site for you. It is a good place to start. ***newscientist.com/article/dn17453-timeline-the-evolution-of-life/
Jocofranc
Sr,your web site is very useful to me.And another question is how gene or DNA transfer from parent to sibling.how we know the first DNA of our first human from arfarica.
nyo
Good morning Nyo; ur question is out of my league, although fascinating. Maybe you'll find this page helpful: ***genetics.thetech.org/ask/ask445
Jocofranc
If speed is so many thousand time of light and start to travel from one point,how speed will return to it starting point even in straight line back.Will time and energy be limit it?Can it be posible.Please let me explain Sr.
nyo
hey neo ur curiosity is great, where r u from?
neehar
in physics actully no but thory make possible
gdjm
there is aliens or parallel universe
Chithra Reply
There may be both who knows
Debabrata
It would be quite surprising to me to learn that there is no aliens in our very own galaxy. The size of our galaxy alone seems to favour life. There's so many reasons why we haven't made contact but as our technology grows we will undoubtedly find answers. I also think that it's possible that ...
Jocofranc
But I don't think that that alien species might be developed.... Because if they were developed or advanced than us then they must have located us first and might have even contacted us
Debabrata
many other universes exist. I don't think that they would be parallel universes in the purest sense of the word. Only speculations on my part. We simply dont know with certainty.
Jocofranc
Hi Debabrata; You may be right. It's hard to say with certainty. An ugly truth (guess really) is that Tellurian are simply not interesting. We are not all that!
Jocofranc
Yeah Jocofranc you are also right about parallel universe. Who knows what lies ahead.
Debabrata
the parallel universe theory is something secondary but first let's focus on the nearby objects like titan which shows great hope
Aarushi
I read it before about aliens, but I have to research on it
neehar
yeah of course
neehar
What about XTs... Exo-Tellurians. Ancient people who could have obtain a spurt of technology and left home. Progression of men r not always linear but sometime cyclic. Civilization comes and goes. Geo-upheaval can easily erase any evidence. Our bros r out there. (have fun 😁)
Jocofranc
sir jocofranc I think u didn't listen about aliens who send a message to our space research organization.
neehar
what is inside Jupiter how it will rain there
Chithra Reply
interesting question!
Mahesh
would love to learn about it 😃
Morrie
jupiter is a gas gaint so you can't walk on the surface like here on earth, but there is a solid core.
Yannick
The latest term being used is a 'fuzzy core'. An inbetween of solid and liquid. Check ***sciencemag.org/news/2019/08
Jocofranc
I think it based on the nature of the source in Jupiter
neehar
Scientists believe that onJupiter and Saturn, it rains diamonds. New atmospheric data for the gas giants indicates that carbon is abundant in its dazzling crystal form, the BBC reports. Lightning storms turn methane into soot which hardens into chunks of graphite and then diamond as it falls.
gdjm
Where is a moon HOW MANY KILLOMETER FAR FROM EARTH
Guddi Reply
On Average 383,000 Kilometers, Between Perigee And Apogee.....
Adam
386,000 km
neehar
3.6×10^5 km
gdjm
how many stars are there in the world
ZERO Reply
we can't count them because there are infinity no. of Star
YOG
but in night sky there are approximately 100 thousand million stars
YOG
Visually speaking, there's only one in the day and a few thousand in my Tellurian corner of the world at night. And some of those stars may even be galaxies, too far to properly discern as billions points of light. The longer you gaze into the skies the more they manifest themselves. Keep watching!
Jocofranc
it's impossible to count, what a silly question?
neehar
100 thousands million stars in milky way alone!
gdjm
Between 200 And 400 Billion Stars In Our Galaxy Alone.....
Adam
why people go to other planet
Rehan Reply
to explore mysteries and also for some new resources and life form
YOG
Presumably to find an alternative for our earth, since our population has been increasing at a crazy rate and we'd slowly be running out of space here, if we'd continue. Another point would be the scientific value. Apart from testing our knowledge we always hope to find a new form of life.
creative
and in future when life from earth will vanished then to maintain our existance we need a new planet.
YOG
History shows our insatiable appetite for energy. The mass tends to congregate around developed communities where energy is readily accessible. It's inevitable we will be become exo-tellurians. Necessity fuels our explorations.
Jocofranc
👏 Well said! @jocofranc knight
Jennifer
what are you think about ancient ETHIOPIAN astronomy
Eyoseyas
please
Eyoseyas
is there any book to learn about ancient Ethiopian astronomy?
Mahesh
and please tell me where I can get that book
Mahesh
you can search
Eyoseyas
the best book that can tell is ANDROMEDA
Eyoseyas
you know that many european use ancient ETHIOPIA BOOKS
Eyoseyas
fine
Mahesh
can you tell me astronomical blogs
Eyoseyas
please
Eyoseyas
because of our planet filled with pollution all over the world
neehar
what was before big bang
Manish Reply
The creator and their empire
Mahesh
Like ur answer but submitting a light-hearted suggestion of my own : Our universe a galactic-verse of many other billions that are clustered tightly together in a super-constellate. The Big Bang was the result of a magnetic wave originating from inside the constellate desrupting our serene corner.
Jocofranc
nice to here jocofranc, please explain what is before big bang
Mahesh
This increasingly hypothetical scenario suggest that the Big Bang was created when a superwave from this so-call Super-Constellate destabilized our dormant singularity. The wave was the catalyst. When this wave stops buckling our galactic-verse, it will recede back to a singularity. Ok it was God.
Jocofranc
after big bang Earth is formed
neehar
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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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