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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

why are the hyperlinks not working?
Gregory Reply
If the atmosphere blocks the view of Venus' surface, what am I seeing that looks like craters?
Michael Reply
clouds?
Michele
If the surface of Venus is shrouded by white clouds, making it impossible to see the surface, what looks like craters when view the planet?
Michael Reply
I don't Know! perhaps the mountains?
Michele
my question is if the surface of Venus is shining y not our earth
Tahir
when we look at venus we can't see any crater like things... check it once again
RIEM
and venus shines because of the clouds that are made up sulpher dioxide and sulphuric acid droplets. and the clouds are so dense. the case of earth is different
RIEM
also because of Venus's 70% albedo phenamenon
Shivam
and plus it reflects 70 percent of its light back into space earth don't shine because it's not a cloudy planet and its farther than the sun
americantuber
can I become an astronaut without taking mathematics as a subject in 11th class
UNIVERSAL Reply
If the surface of Venus is shrouded by white clouds, making it impossible to see the surface, what looks like craters? Are these atmospheric storms?
Michael
can a death of a massive star be the new big bang
Neeta Reply
No it might be a supernova. The big bang was much more massive.
Nick
It created the universe as we know it
Nick
the big bang is just a new beginning
Neeta
the death of a gigantic star makes it possible for a new begging
Neeta
Only in the local area of space
Nick
so many smaller universes are created and destroyed
Neeta
i think it created a supernova!
Michele
you still think? I am sure I created one supernova of my own
Neeta
I'm sure you did
Nick
neeta the death of a massive star could lead to an explosion that leads to a super nova and when the supernova explodes it becomes a nebula like messier 1
americantuber
a supernova remnant
americantuber
what is means by earthbound
Satyam Reply
you are earthbound, arnt we all earthbound? except the ISS etc.
Collins
I don't agree we may be earthbound because of our gross body/physical body...but there is also a subtle body which does not limit us to earthly existence
Neeta
good questions, as humans our habitat is earth, we are bound to this and have to alter ourselves to stay alive off land and outside the atmosphere, do you not agree? I'd guess you could also say the moon is earthbound. anything earthbound is restricted to earth. hope this helps, love your question
Collins
how do you describe astral projection
Neeta
Astral projection is spiritual. I'm assuming Satyam was talking about the physical world.
TheDirtyGhost
ah yes spiritually we are bound only to what we chose, like nothing, I like to think that way
Collins
anyone here also participating in seti@home?
dreamer
what is seti?
Mahesh
what has extraterrestrial entity got to do with this why @seti project..we are discussing human existence on earth and beyond earth
Neeta
please join me at the cosmic Diner where all your intergalactic dreams come true.
Alba
I was just thinking what if somebody ignorantly mistaken a cosmic microwave Background with a conventional microwave we be in a lot of trouble.
Alba
don't kno
dreamer
You mean the Restaurant at the end of the Universe...right we can come back and visit again but not sure of the mode of payment
Neeta
yeah I'm already heading there
dreamer
how to read stars
Amresh Reply
you don't
Max
astrology i guess
Uttam
astrologer is the study of star systems and constellations...but astronomy is the study of formation of universes multiverses birth and evolu of stars
Neeta
cool
Uttam
what is astronomy
babul Reply
study of formation evolution and the death of star star systems and galaxies
Neeta
astronomy is the study of universe
UNIVERSAL
astronomy and physics are basically the same except physics is the study of the motion and behavior of the universe
americantuber
What is 12 constellation of zodiac and why it is important to study astrology
MUHIBULLAH
And also what is main purpose of these 12 constellation of zodiac in astronomy
MUHIBULLAH
astronomy and astrology with two different things
Deja
it Is the study of universe and of life speaking generally! i think!
Michele
universe is born 13,7 miliardi of years with big Bang if i remember well! but there are also other theories for the universe, speaking generally! i remember so!
Michele
universe is actually about 13.7 billion years old
Nick
is astrology like astronomy
debjani Reply
Astrology is a lower dimension.. astronomy is much more vast and multidimensional
Neeta
yes.. astrology is about constellations only, and astronomy is about all stars, galaxies, gravity, dark matter, dark energy.. etc everything including astrology
Mahesh
can you become an astronaut without taking mathematics as a subject in 11th class
UNIVERSAL
I was reading the chapter on Cosmic Microwave Background. And, I can not seem to find it now. If anyone could help me find that portion of the Astronomy Textbook I would really appreciate it. AZ
Alba Reply
Where or which chapter discusses Cosmic Microwave Background?
Alba
29.4
Andrew
29 the big bang ch 29.4
Andrew
yes
pratham
interesting
Orlando
what's cold dark matter?
pratham Reply
How are Roche Worlds formed?
AlteredEdge Reply
In need to read some books about Astronomy so how can in get it actually leg live in Ethiopia can uh help me with that?
Mom Reply
I am sri Sharan .m .what is my best favourable numbers
Madhesh Reply
how can we know it
sruthi
😂😂
Rango
bahut hard
Rango
Why no object can travel with speed greater than light?
geometry Reply
Because the mass of light particles is zero
Asim
Can mass be negative?
geometry
No
Asim
anybody stated that the light is the only thing is speed
sruthi
geometry are you a korean or kpop fan
sruthi
in this universe anything can be faster than light because we simply can't get to an conclusion
sruthi
I am a an Army but lets not bring spam here.
geometry
But why mass can't be negative. What I mean is how can we claim an object made of strange matter has positive mass. In other words, theoretically can negative mass exist?
geometry
in our observable universe nothing is faster than the speed of light
Rango
Thanks
geometry
But theoretically, is it possible? Sorry I'm being very curious..
geometry
I don't know about dark matter but may be you should think about dark matter because dark matter are really strange
Rango
Exactly so theoretically, an dark matter lazer can be greater in speed. Also maybe quartz..
geometry
may be but i am not sure about quartz and btw techyons travel faster than light but techyons are hypothesized
Rango
there are many objects which are perceived to be faster than light
Ganeshan
The object have their own declination rate in speed,the air friction can develop higher temperature resulting the object to be disappear in molecules,not considering the Physical conditions in space.The object should be unaffected with the air friction and also speed should proportionate with fuel.
Near
the early universe expanded faster than the speed of light. Consider, at the speed of light in vacuum, time stops.
Robert
Does this mean something moving beyond the limit experiences negative time?
Robert
Under such conditions, would matter exist as wave-fronts?
Robert
When examining a cosmology it is possible to find quite unbelievable conditions. I like to imagine life at the tip of an asymptote, but to surpass it seems perilously remote.
Robert

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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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