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Figuring for yourself

If two stars are in a binary system with a combined mass of 5.5 solar masses and an orbital period of 12 years, what is the average distance between the two stars?

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It is possible that stars as much as 200 times the Sun’s mass or more exist. What is the luminosity of such a star based upon the mass-luminosity relation?

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The lowest mass for a true star is 1/12 the mass of the Sun. What is the luminosity of such a star based upon the mass-luminosity relationship?

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Spectral types are an indicator of temperature. For the first 10 stars in Appendix J , the list of the brightest stars in our skies, estimate their temperatures from their spectral types. Use information in the figures and/or tables in this chapter and describe how you made the estimates.

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We can estimate the masses of most of the stars in Appendix J from the mass-luminosity relationship in [link] . However, remember this relationship works only for main sequence stars. Determine which of the first 10 stars in Appendix J are main sequence stars. Use one of the figures in this chapter. Make a table of stars’ masses.

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In Diameters of Stars , the relative diameters of the two stars in the Sirius system were determined. Let’s use this value to explore other aspects of this system. This will be done through several steps, each in its own exercise. Assume the temperature of the Sun is 5800 K, and the temperature of Sirius A, the larger star of the binary, is
10,000 K. The luminosity of Sirius A can be found in Appendix J , and is given as about 23 times that of the Sun. Using the values provided, calculate the radius of Sirius A relative to that of the Sun.

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Now calculate the radius of Sirius’ white dwarf companion, Sirius B, to the Sun.

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How does this radius of Sirius B compare with that of Earth?

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From the previous calculations and the results from Diameters of Stars , it is possible to calculate the density of Sirius B relative to the Sun. It is worth noting that the radius of the companion is very similar to that of Earth, whereas the mass is very similar to the Sun’s. How does the companion’s density compare to that of the Sun? Recall that density = mass/volume, and the volume of a sphere = (4/3)π R 3 . How does this density compare with that of water and other materials discussed in this text? Can you see why astronomers were so surprised and puzzled when they first determined the orbit of the companion to Sirius?

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How much would you weigh if you were suddenly transported to the white dwarf Sirius B? You may use your own weight (or if don’t want to own up to what it is, assume you weigh 70 kg or 150 lb). In this case, assume that the companion to Sirius has a mass equal to that of the Sun and a radius equal to that of Earth. Remember Newton’s law of gravity:
F = G M 1 M 2 / R 2
and that your weight is proportional to the force that you feel. What kind of star should you travel to if you want to lose weight (and not gain it)?

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The star Betelgeuse has a temperature of 3400 K and a luminosity of 13,200 L Sun . Calculate the radius of Betelgeuse relative to the Sun.

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Using the information provided in [link] , what is the average stellar density in our part of the Galaxy? Use only the true stars (types O–M) and assume a spherical distribution with radius of 26 light-years.

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Confirm that the angular diameter of the Sun of 1/2° corresponds to a linear diameter of 1.39 million km. Use the average distance of the Sun and Earth to derive the answer. (Hint: This can be solved using a trigonometric function.)

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An eclipsing binary star system is observed with the following contact times for the main eclipse:

Table C
Contact Time Date
First contact 12:00 p.m. March 12
Second contact 4:00 p.m. March 13
Third contact 9:00 a.m. March 18
Fourth contact 1:00 p.m. March 19

The orbital velocity of the smaller star relative to the larger is 62,000 km/h. Determine the diameters for each star in the system.

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If a 100 solar mass star were to have a luminosity of 10 7 times the Sun’s luminosity, how would such a star’s density compare when it is on the main sequence as an O-type star, and when it is a cool supergiant (M-type)? Use values of temperature from [link] or [link] and the relationship between luminosity, radius, and temperature as given in [link] .

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If Betelgeuse had a mass that was 25 times that of the Sun, how would its average density compare to that of the Sun? Use the definition of density = mass volume , where the volume is that of a sphere.

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Questions & Answers

what is siphon
pankaj Reply
what is mama radiation
Pragiti Reply
the time for planet formation must vary with the luminosity of the star? Disks must last much longer around a M-dwarft? please explain how planet formation varies as a function of star luminosity.
Jeffrey Reply
what do you mean by light year
Prabha
A lightyear is an astronomical distance of 5.9 trillion miles.
James
a light year is the speed of light times the total amount of seconds in a year. distance in physics is speed x time, so a light year refers to the total distance the light travels in a year
Levis
thanks for helping me
Prabha
Explain the formation of a black hole?
Prabha
what is atoms
Suman Reply
atoms are the smallest partiles that make the whole universe.For a measurement. if an atom were the size of a ball......The ball would be size of the Earth.
Sangeet
the smallest unit of an universe but it is not true the smallest thing in universe is quarks
Pragiti
The smallest thing in the universe is the arrogance of scientists who think they are never wrong.
Loren
You mean the greatest?
Cyclone
i believe so
daniel
do we are alone in universe
ninja Reply
is the astroid belt shaped like a torus? or like Saturn's disc?
Abhishek Reply
torus
ninja
torus
Robert
can i know deep about black hole
Monisha Reply
yupp ask questions about whatever you wanna know in black hole?
Paras
where does it lead
Vanessa
how black holes are detected in deep space as we are unable to see them.
jawad
if black holes are hypothetical then how do they detect them?
Alvis
who said blackholes are hypothetical?
Ehan
They are detected by their gravitational pull...
Ehan
also we can detect them by X-rays as they emit hawking radiation as they 'shrink'
Levis
hawking radiations are not detected yet...
Ehan
nopes that's not how you detect black holes. Gravity curves space, and light bends around heavy objects. Black holes have very very very high mass. So light bends so much that it cannot pass. When the light of the stars behind suddenly vanishes. => black hole is present in between us and that star.
Abhishek
to find astronomical units do you divide or multiply?
Bethany Reply
I think it depends what you're converting from. i.e. from km you divide
Fab
I tried that for question a in section 0.3 but the answer doesn't seem right
Bethany
make sure you're using consistent units m/m
Fab
i too had the same doubt
Monisha
hi dear
jawad
can you tell me what is ecliptic ?
jawad
the great circle formed by the intersection of the plane of the earth's orbit with the celestial sphere; 
Monisha
OK thanks
jawad
who is the father of Astronomy?
subhajit Reply
Me ;)
daniel
I think Galileo
Prabha
Copernicus, Nicolaus.....
Adam
which telescope is best for beginners ?
jawad
Do You Want Low Maintenance Or High Maintenance Optics? Do You Want To Look At Solar System Objects Or Deep Space Objects? Or May Be You Want To Split Doubles, Do You Live In A Big City Or Suburbs?
Adam
I want low maintenance. I want to see deep Space objects. I live in big light polluted city.
jawad
sir I have Nikon 16*50 binocular but now I want to buy a telescope.
jawad
i have got money that i earn with i am a doctor that working at st.louis jewish Centre.i am very helpful for people that they need help with.
Asali
What's Your Budget?
Adam
Deep Space Objects Are Gonna Hard To Come By In A Light Polluted City..... So Far I Would Recommend 8 To 10 Inch Schmidt Cassegrain Telescope, For Deep Space Objects You Need Light Gathering Power, Now A Decent Scope Like What I Just Described Is Gonna Run You About $800 To $1000 Dollars.....
Adam
And That's Just The OTA, Optical Tube Assembly..... Then We Gotta Talk Mount And Tripod, And For Good Stable And Steady Views We Need About Another $1000 Dollars For Mount And Tripod.....
Adam
my budget is almost 1000 dollars.
jawad
my budget is almost $1156.00 dollars each years
Asali
big diameter and lenth are good, i got my first telescope for $300 and it works real well for planets.
daniel
if you want to do amature astrophotography, what you can do is mount a webcam or your phone to your telescope and have a tracking mount attached so you can look for different deep space objects and take pictures. I have a couple I did using this method
Mark
A Big Dobsonian Might Be In Order, But That Scope Is Very High Maintenance..... But For $1000 Dollars, You Can Get A Real Nice Dobsonian And They Perform Excellent On Deep Space Objects, The Darker Your Observing Location Is The Better.....
Adam
guys this is my first day of i arrived in the u.s i need your help guys what does telescope means
Asali
so, a telescope is a thing you look through to see things far awY
Mark
A Tool Used To Observe The Sky.....
Adam
thank you guys for you help me i appreciate with that i will always thank you guys
Asali
what does physiognomys mean?
Asali
what happen if earth stop to rotate?
Sijan Reply
well first of all we wouldn't have day and night and it would get cold in the dark side humans and animals would have to get use to the darkness. plant would not he able to grow on the dark side either. Ad for the light side or "day" its the same thing but just...hot.
Ghost
and contestant datlight such could be harmful beacuase of the constant if rays
Ghost
Our gravitational field would collapse.
Hannah
Magnetic field sry. That means no shielding from cosmic rays.
Hannah
actually we would have day and night...but each day would last a year. We would also still have a magnetosphere unless the Earth's core also stopped rotating. Gravity would increase as we would lose any centripetal effect. We would only have one tide per 29 days as the moon orbits us.
Joe
we would still have gravity Hannah because we would still have mass!
Joe
pretty sure there would be no more rain or wind because any warm air and water vapour would just rise and fall above wherever it came from.
Joe
As we are rotating right now, if the earth suddenly stopped, objects that are not bound to the ground will get flung due east at very high speeds. It would be very catastrophic. That's the first thing that'll happen if such an event were to happen.
Cave
what is comets?
Ido Reply
the bottom of the page of chapter 13 thinking ahead describe it
Chelsea
I also don't know but I think it is star
Sijan
A comet is composed of small rocks and dust particles cemented together by frozen gas and ice.
shiela
and when the ice and the cold stuff on a comet heats up, by the sun as it closes by, some matter escape and we see a tail.
Abhishek
I once watched a show discussing finding dark matter ON planet earth, deep down inside caverns where sound and light are absent. I seem to remember them also saying that the slightest of sound would "charge" the matter up. If the solar system is primarily dark matter, could we use sound to travel?
Jamie Reply
I thought the same thing. If space is a vacuum and sound does not travel in a vacuum, it would be difficult?
James
What exactly is dark matter?
Sharadhi
from what i gathered, dark matter is incredibly motionless atoms. Almost dormant, and they are easily disturbed? i am by NO MEANS an expert on any of this. just a curious mind... if sound doesnt travel in a vacuum, maybe the light then? disturb the matter with light and maybe 'swim' it?
Jamie
yes, the sound can be converted as an electrical impulse, which can be converted to light. and if we can detect this light at the receiving end then we can convert it back to sound but only if a material medium is present for the sound to travel to our ears.
Abhishek
what are whitehole a wormholes
gajanan Reply
holes
xBeex
***en.m.wikipedia.org/wiki/White_hole ***en.m.wikipedia.org/wiki/Wormhole
xBeex
wormholes are those holes through which we can travel to past
ninja
is the reason why you can't see the carp nebula in some towns and city's due to other lights?
Ghost Reply
yes and the atmosphere fades the dimmer lights as well. and you can only see if the carp nebula emits visible light. otherwise you'll need appropriate detectors to detect the frequency.
Abhishek
in cities there are levels of light pollution which stop light from stars, nebulas, etc. also some nebulas are brighter than other's, but rural area are good places to see the sky with little light pollution.
daniel
Which of the following transformations is (are) fusion and which is (are) fission: helium to carbon, carbon to iron, uranium to lead, boron to carbon, oxygen to neon? (See Appendix K for a list of the elements.)
Nanea Reply
fission refers to conversion of helium into two hydrogen atoms fusion is combination of hydrogen atoms to helium
Aditya
but acc to the question helium to carbon is fission after hydrogen
Aditya
how is blackhole formed?
Prabha
When the center of a massive star collapses in on itself.
Radonwolf
collapse?
basim
is it exploding?
basim
what does ekg echocardiogram means?
Asali
The star does explode.
Radonwolf
what does gravity means?
Asali
it means to help people stay on ground but in space it makes things float around that would mean with out gravity we would be on cellings or even in space
Olivia
can you guys help me because i needs to know a lot about science i have a question that i would like to ask you. my question is what does conduction,convection,insulator,and thermal radiotion means?
Asali
conduction is when a source for some type of energy let's energy flow into things around it. convection is what happens with boiling water. currents of hot water form and heat the surrounding water. this is convection. an insulator is something that doesn't let energy flow into or out of it very wel
Mark
like rubber or glass. thermal radiation is heat energy being transferred to the surroundings
Mark
can you have heat feom convection?
Asali
convection is a way to transfer thermal energy and other types so yes.
Mark
and the definition of heat is the process of transferring thermal energy into or out of a closed system
Mark
id two object reffer to the other object and than what will happen?
Asali
what do you mean
Mark
what does newton third law of motion said?
Asali
i mean like when two object reffer to the other object what will happen to both of them?
Asali
it is understand by zeroth law of thermodynamics
Arun
what is the zeroth law anyway
Olivia
of two systems are in equilibrium with a third, then they're in equilibrium with each other
Mark
I think it was called the Zeroth law bc scientists discovered the first and the second law before it but they still thought they needed to state the obvious beforehand
Levis

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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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