# 18.4 The h–r diagram  (Page 11/25)

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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?

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?

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?

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.

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.

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.

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

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

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?

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:
$F=G{M}_{1}{M}_{2}\text{/}{R}^{2}$
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)?

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.

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.

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.)

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.

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] .

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 $\text{density}=\frac{\text{mass}}{\text{volume}}$ , where the volume is that of a sphere.

why the energy cost
what is sagittarius
what is gimine
Black hole of Milky way galaxy
deepanshu
thanks a lot for your sympath and information
thanks a lot for your sympath and information Deepanshu
this question is for atheists what created humans , how did they evolve
not entirely sure what this question has to do with Atheism but, firstly, there is no "who", life evolved in multiple paths, humans are simply one of those paths. The process of how life evolves is a very complicated but very well researched field of biology, so it would be worth doing research...
ben
...into that field, evolution isnt disputed. However, the direct path from the common ancestor (that we share with chimps) has not yet been completed. But know for sure that humans didn't just magically appear one day, it was over millions of years of evolution
ben
(I must ask though, what has this got to do with Atheism?)
ben
idk i thought believers will say god created us
ilyes
there are many types of believers one say that god created consciousness, one say we just magically appeared out of nowhere, and one say universe was created by God(all based on people I have met so far)
Tanmay
Hey
Asim
Tanmay!
Asim
Hello
Asim
hello Asim
Tanmay
hi my friends asim and tqnmay we hhave lern okay
Eyiba
did u forget me!!
Amit
Could God have created evolution? Nope, no way, too complicated.
Bennett
yes god can do that in theory
Tanmay
@Eyiba hello
Tanmay
@Amit seems like that XD
Tanmay
haha🤣🤣
Amit
This question is for theists, what created God?
Anthony
hi
UFOLIENS
God was begotten, not made. More of a concept than an entity.
Bennett
hello
Stuart
yes why not you don't need to ask anyone for permission
Tanmay
sure, why not?
ca
-Why there are moons in every planet but there's note in mercure ?
Well with mercury Venus also does not have moon.The reason that Mercury is not having moons is since it is too close to sun and thus if it would have any moon orbiting it ,then the moon will eventually attracted by sun due to it's high gravitational force whereas mercury has the lowest gravity
Anjali
The gravitational force of mercury is lowest in solar system and it won't be able to hold a moon in it's orbit
Anjali
Nice explanation
Asim
Thank you brother
Anjali
Did general theory of relativity leads us to singularity?
Asim
yes the general theory of relativity leads us to singularity
Anjali
But Einstein was not a believer of big bang. And singularity lead us to big bang?
Asim
yes Einstein was really astonished by his mathmatical answers that came fron his equations (this is what almost every one says)
Tanmay
and there are many theories stating how our universe came in which one is big bang
Tanmay
Einstein was against the fact that anything can come from nothing that our big bang says and he also thought that singularity (infinite mass in zero volume) can not be real(also what most people say)
Tanmay
also what most people say means that there is no evidence that he was against all these things
Tanmay
Okay
Asim
Tanmay
Asim
anything else
Tanmay
Do you believe that grand unified theory can be complete in future?
Asim
Do you believe that grand unified theory will be complete in future?
Asim
yes I do believe in it as I also believe big bang
Tanmay
Well i don't believe in big bang like Einstein didn't.
Asim
do you believe in wormholes are real?
Amit
@Asim then what do you think our universe came from or how it started
Tanmay
Well it's a myth.
Asim
@Amit I believe wormholes are real
Tanmay
It came from nothing Tanmay.
Asim
Even I believe in wormholes
Anjali
So Tanmay you must believe in baby universes.?
Asim
I believe that they are many things we can't explain or give prove but they are theories,imaginations and they are the basics for new discoveries
Anjali
So ,it is useless to argue over them
Anjali
But we should try to find new possibilities if we don't believe in old ones
Anjali
you are right @anjali
Amit
what is dark matter?
Amit
can a star turn into planet?
Amit
I have doubt on how Stephen hawking posses ideas of black hole by himself?
why do people believe in God and how are humans made
ilyes
No amit star can't turn into planet.
Asim
you are wrong asim
Amit
also Asim, please tell me why you think the big bang is a myth?
ben
@Asim what do you mean by it came from nothing what came from nothing
Tanmay
@Asik I don't know what baby universe is if you mean early universe then the question doesn't make sense
Tanmay
@Amit starts can become cold enough for us to live at high altitude but their surface will still be made of plasma
Tanmay
@Amit dark matter is a type of substance that doesn't interact with normal matter and also gives galaxies enough mass to hold its stars rather than to fly out by its rotation
Tanmay
Sorry Asim for wrong spelling of your name
Tanmay
Amit
@Tanmay but a star can turn into a planet, but this transformation only happens for a very particular type of star known as a brown dwarf.
Amit
ben
I will check and then I will tell you if it's true or not thanks for the question
Tanmay
I will check as it is really wierd but thanks for your question
Tanmay
(oh no I was joking hahaha, Amit just took the definition that you see first on google and pasted)
ben
Tanmay baby universes is when something fell in black hole it's went into another universe called baby universe according to Stephen hawking. Well i don't know weather to believe it or not.
Asim
Amit brown dwarf are not planet or stars they have their own classification these are basically failed star, not massive enough to power hydrogen fission reaction.
Asim
ahh, didn't he use that to explain where "information" goes? because recently a paper was published stating that information may actually be re-emitted by the black hole as 'encoded' hawking radiation
ben
(so it may not be going to another universe, but instead coming back into our own)
ben
Hawking radiation are basically the the radiation emitted by black hole boundaries called event horizon.
Asim
Amit
So re-emitting doesn't make scene.
Asim
every black hole contains a singularity?
Amit
Yep absolutely.
Asim
ohhh, no worries dude, and yeah hawking radiation is a consequence of both quantum mechanics and relativity, really cool. And look it up Asim, it's a really interesting read
ben
but a singularity is a point in space where there is a mass with a infinte density. the problem is that infinities never exist in real world.
Amit
Ben it's really difficult to relate quantum mechanics to relativity.
Asim
Dude if you have done nobel price is waiting for you. (haha)
Asim
consequence of both quantum mechanics and relativity.!!!
Amit
Amit read theory of relativity and black hole singularities in Google. Everything will be cleared.
Asim
🤣🤣🤣
Amit
Amit
hahahahaha, yeah that's true I'm being lazy as hell there haha, I mean more it's something relates the big and small (it's cool to see quantum phenomena having a direct effect on something predicted by relativity)
ben
(if a GUT is found I genuinely doubt I'd be able to comprehend the maths hahaha, maybe a long a way down the road but not yet)
ben
ben you are nominated for nobel as well as oscar for your thoughts..(hahaha)
Amit
what's you thinks about gravitational waves gentlemen?
Amit
hahahaha, and I love what I know so far but honestly dude, I've learnt essentially nothing about gravitational waves at university yet, I'm hoping that's going to be next year
ben
I would love to ask someone what the effects of constructive ans destructive interference of gravitational waves would be. Would total destructive interference lead to black holes?
ben
good luck for your next year... ben
Amit
if such things happen that's gonna be amazing.....
Amit
eyy thank you dude, likewise man, wish you all the best for your endeavours
ben
eyy cheers dude, likewise for you man, wishing all the best for you
ben
thanks buddy..
Amit
💝❤
Amit
(my bad, sometimes my phone wont show the first message as being sent, so I send another just in case)
ben
Gravitational Waves could help us travel faster in the space, if we are to set on an adventure like the one in The Interstellar, lol. Just saying
Awesh
what do u think created the universe
ilyes
m curious
ilyes
I believe in the theory where it states that our universe came from death of another universe and after our universe's death another universe will come from it
Tanmay
@Amit if that's what baby universe is then
Tanmay
my current understanding of universe and black holes, I would have to disbelief it
Tanmay
@Asim @Amit there is a feild in physics where we study about the physics of those objects who have intermediate size and follow some rules of quantum physics and relativity
Tanmay
@Ben what is full form of GUT?
Tanmay
@Ben I have never seen anyone spotting interference with gravitational waves but most of the people think that it will just be like interference in waves like light or sound. Do that means it's amplitude will change and will not create and black holes or stuff
Tanmay
@Awesh yes many people in youtube(some have good degrees and are astrophysicist) say that warping space is possible using gravitational waves
Tanmay
Do you all believe in multiverse
Anjali
I believe in multiverse
Tanmay
The relation between quantum physics and relativity is like sky and the land (hahaha)
Amit
what about the air between sky(let's assume height of clouds is sky) and land. It basically means that there is a field like that you should google it up
Tanmay
it's the most mysterious field and we almost know nothing about it. there are no laws(like Newton's law of motion) or something like that
Tanmay
The most undifined and fascinating theory is string theory what do u think about it?
Amit
how can I learned quantum mechanics
Harsh
what is the model about the earth being the center of the universe called?
geocentric model
SCIENCE
SCIENCE
heliocentric universe
Jason
you are wrong Jason skerbinc
SCIENCE
in heliocentric model sun is at the center of the universe
Tanmay
what is black hole and stellar black hole
does Millikan consider electron axial spin in his discovery of electrons mass using q/m ratio ? If No how it is possible that he found rest mass of electron (9×10^31 Kg) ?
how did light from up
Before there stars , there was matter and radiation . Before there were neutral atoms ,there was an ionized plasma ,and when that plasma froms neutral atoms , those allow the Universe to deliver the earliest light we see today .......
Apsara
how to know the distance of a star
What is time
Sourav
Technical Infinite Measurement of Evolution
Doc
not by the book but the simplicity of word play ....
Doc
to calculate the distance of a star we use parallax method (as far as my school has taught me).
Tanmay
in this method we see the star from one point and then after traveling some distance perpendicular to the distance of star we see it again. With this we can make a triangle and then it's median will give our distance
Tanmay
And time is just a way of defining when an event happened
Tanmay
oh and we will know the distance of all the 3 sides of triangle formed above if we multiply the time taken by light with speed of light and the third side will be known to us as it is dependent on our will
Tanmay
what is space fabric
Harsh
what are wormholes?
Neil
What is the difference between black hole and white hole ?
Apsara
black hole is the place where the massive body makes a large disturbance in space time fabric causing large gravity even light can't escape from it and all the bodies enter into on reaching a specific distance.
SCIENCE
A white hole is a hypothetical region of spacetime and singularity which cannot be entered from the outside, although energy-matter and light can escape from it. In this sense, it is the reverse of a black hole, which can be entered only from the outside and from which energy-matter and light can
SCIENCE
White holes appear in the theory of eternal black holes
SCIENCE
worm holes join 2 distant region of spacetime through which you can travel, covering large distance in short time
Tanmay
for example if you need to travel from A to B on a plane of paper then you can travel in a straight line joining those points but a worm hole will join those points using 3rd dimention which will make you travel that distance in short time
Tanmay
Hi,Do you known Kyaw Nyein Chan Hein!
No
Astrophysicist
Hello : I'm Kyaw Nyein Chan
zin
Hi I'm Kyaw Nyein Chan
Hello : good moring, I'm Kyaw Nyein Chan
hello good morning
Astrophysicist
good morning bro
Tanmay
how do you do?
Astrophysicist
I am fine what about you?
Tanmay
same as you
Astrophysicist
cool
Tanmay
Hiii can I joined your group
Harsh
How the Big Bang is made .
Kyaw Nyein Chan
zin