# 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.

Currently, I'm studying in 10th grade. What should I do after my 10th so that I can get an astronomy career?
try jee exam and achieve a good score in jee advance to join in IIST(Space research institute)
Sri
okay.. thanks
Chaya
this famous person was the first to recognise earthshine on the moin
Leonardo Da Vinci.....
what is string theory?
A Cosmological Theory Based On The Exsistence Of Cosmic Vibrating Strings.....
Does MIT have good astrophysics courses ?
Probably The Best In The United States.....
But Don't Get Caught Up On Who's The Best, You Can Be The Next Noble Winning Astrophysicist.....
Gospel
How did ASTRONOMY helped you understand yourself ? 🤔
why do you want to study ASTRONOMY?
It is one of the natural sciences and therefore worth exploring. You are a part of the universe and it is a part of you. The sky is my classroom. (student of cosmology, Oxford Uni)
SuperNova
because everything in the space is just beautiful...interesting and worth studying and exploring...
Memo
I have been studying astrophysics an love it
Carla
I love to learn what makes up our lives an heavens an how it works there us so much more out there than books an our veiw of thw heavens can reveal
Carla
How did ASTRONOMY helped you understand yourself ?
Hussain
Because it proves the impossibles and the limitless.
Dark
It helped me realize that there are like countless possibilities in life and get all through it.
Dark
It honestly showed me to view the world in a balanced way. Because space beautiful and calm yet violent, and so is the world, and we should still help, but there will always be violent people much like violent astrophysical jets.
Da
Does anyone know where can I study astronomy in Spain? My budget is too low for traveling out there...
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?
how many galaxies in universe?
10 to the power 11
Wwe
testing
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
what's ur name wwe
Shaikh
The Observable Universe Contains Between 200 Billion To 2 Trillion Galaxies.....
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
we didn't actually find the exact number but may be it is around 100 billion
Smridhi
why this universe is expanding?
ATUL
Science Does Not Concern It Self With Why Questions, Science Is Geared For How And What Questions.....
Why Questions Form And Endless Loop.....
According to the universal law of cause and effect .any phenomenon that occur in this universe should have any reason , nothing happen without any reason.
ATUL
Can you tell me the expanding speed of this universe.
ATUL
yes that would be a great question to have answered what is the expanding speed of the universe?
Daijahrel
Remember that most of what you can see is light years away. We're looking back in time, we can never know the current nature of our observations, only glimpse the galaxies and stars as they once were. Strange but true, and a little sad.
SuperNova
Correct, That's Why Telescopes Are Like Time Machines, You See The Past.....
really telescope can see the past?....i meant everything is in its place, though it rotates or revolve or whatever it is.......but how can this telescope can see the past.....can we see how our Universe was created,how it formed out of it? thats my question to all of you guys can you plz tell me.
Gospel
Because We Dont See Any Object In Space As It Is, We See It As It Was..... Hope This Clears That Up For You.....
And One Day We Might Have A Telescope That Will Show Us The Big Bang.....
ok....... that will be nice one
Gospel
ok....... that will be nice one
Gospel
Travel at light speed in a spaceship at 186,000 miles every SECOND. At this speed it will take you 100,000 years just to cross our Milky Way galaxy, which is just a dot in the sky. Next stop, the Andromeda galaxy, after 2.5 million years, still in the Local Group, Virgo Supercluster, still a dot.
SuperNova
Pretty Much.....
there are nearly 200 million I suppose.
Amit
hi i need a telescope would you help mee
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?
sorry . i am from asia
Nauman
Check on amazon.Celeston telescopes are good for beginners.
priyanshu
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?
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?
hey guys I wanna ask you all that will it be safe or helpful to communicate with an intelligent civilization like are we safe ?
Samuel
Is the Orion Sky Quest XT6 a good Dobsonian?
TheDirtyGhost
Look for a Sky Watcher 130BKS, it has an upgraded dual speed 2" focuser. You can use 1.25" or 2" eyepieces with it and it is quite easy to pollinate using a simple visual collimating eyepiece. This scope is great and ready for prime focus astrophotography if you choose to go that route.
Robert
Sorry, spell check error. Pollinate should be collimate. lol
Robert
Dobsonians Require A Lot Of Maintenance, If You Don't Mind Cleaning And Collimating On A Regular Basis, Then Go Ahead A Dobsonian Puts Up Excellent Views Especially For Deep Space Objects..... Now If You Don't Want Constant Maintenance Then A Schmidt Cassegrain Might Be A Better Fit For You.....
So what i would put for that answer ?
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?
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?
oh man
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?
world
that couldn't be any more wrong 😂😂
jay
what even is this conversation😂😂!?
Herrera
Show Some Class.....
Houston, Texas.....
Houston
Preston
what is the first step to take as far as getting into the field of astronomy?
probably by being type 1or2 civilization...launching more telescopes into space...and stepping on mars. probably.
Memo
John, the first step is to want to focus a large part of your life studying, researching and investigating the universe... Including the planet we know the most about. Do well in math, physics, and chemistry, and attend a college that either owns astronomical equipment or facilities and has courses.
Vic