# 18.2 Measuring stellar masses

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## Learning objectives

By the end of this section, you will be able to:

• Distinguish the different types of binary star systems
• Understand how we can apply Newton’s version of Kepler’s third law to derive the sum of star mass es in a binary star system
• Apply the relationship between stellar mass and stellar luminosity to determine the physical characteristics of a star

The mass of a star—how much material it contains—is one of its most important characteristics. If we know a star’s mass, as we shall see, we can estimate how long it will shine and what its ultimate fate will be. Yet the mass of a star is very difficult to measure directly. Somehow, we need to put a star on the cosmic equivalent of a scale.

Luckily, not all stars live like the Sun, in isolation from other stars. About half the stars are binary stars    —two stars that orbit each other, bound together by gravity. Masses of binary stars can be calculated from measurements of their orbits, just as the mass of the Sun can be derived by measuring the orbits of the planets around it (see Orbits and Gravity ).

## Binary stars

Before we discuss in more detail how mass can be measured, we will take a closer look at stars that come in pairs. The first binary star was discovered in 1650, less than half a century after Galileo began to observe the sky with a telescope. John Baptiste Riccioli (1598–1671), an Italian astronomer, noted that the star Mizar, in the middle of the Big Dipper’s handle, appeared through his telescope as two stars. Since that discovery, thousands of binary stars have been cataloged. (Astronomers call any pair of stars that appear to be close to each other in the sky double stars , but not all of these form a true binary, that is, not all of them are physically associated. Some are just chance alignments of stars that are actually at different distances from us.) Although stars most commonly come in pairs, there are also triple and quadruple systems.

One well-known binary star is Castor, located in the constellation of Gemini. By 1804, astronomer William Herschel , who also discovered the planet Uranus, had noted that the fainter component of Castor had slightly changed its position relative to the brighter component. (We use the term “component” to mean a member of a star system.) Here was evidence that one star was moving around another. It was actually the first evidence that gravitational influences exist outside the solar system. The orbital motion of a binary star is shown in [link] . A binary star system in which both of the stars can be seen with a telescope is called a visual binary    .

Where is a moon HOW MANY KILLOMETER FAR FROM EARTH
On Average 383,000 Kilometers, Between Perigee And Apogee.....
how many stars are there in the world
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
why people go to other planet
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 was before big bang
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
how fast light travel around the earth
lol
Videos
If you could travel at the speed of light, you could go around the planet 7.5 times in one second
Greg
how was moon formed
what is steral evolution (star evolution
hi
Nisha
when a star's mass changes over time
Joe
hi
Joe
hi
Lisette
Hii
Asim
hi
Nisha
what big bang
Nisha
yes joe over time chang star mass
Nisha
star prouduce nucluer fusion first stag ( hydroge fusion helium- carbon-neon-oxygen-silicon- last fusion iron hevy star mass not handle iron blast super nova
Nisha
what is the worm hole theory
it states that you can travel back through time by this. It's like folding a paper into half and making two points, and there states that you can bend spacetime but according to Einstein's equation that it can break easily and only really small particles can pass through it.
Dark
dark dream what is dark matter
Nisha
what is the great filter theory
Nisha
the great filter theory it's just like the literally filtering it says that when once a civilization achieved its highest state or let's say the highest technology for instance their civilization will end.
Dark
Nisha
Nisha
what is the simulatin hypothies
Nisha
smart obsevatin
Nisha
In radio astronomy, a fast radio burst (FRB) is a transient radiopulse of length ranging from a fraction of a millisecond to a few milliseconds, caused by some high-energy astrophysical process not yet identified. We can say that this can be they way to at least know if there's other civilizations~
Dark
~out there
Dark
Simulation hypothesis it proposes that the earth, the universe and the reality you are in is just an artificial simulation or like you are living in a computer simulation.
Dark
sir possible time travel
Nisha
?
Nisha
Yes. Everything is possible.
Dark
replay
Nisha
thanks
Nisha
sir how to make neutron star
Nisha
replay
Nisha
?
Nisha
sir what is the white hole?
Nisha
hi good morning
Nisha
why does the matter of an objects density change the fabric of space time rather than the objects volume..? (hopefully I have expressed that question properly) thanks
because an objects density consists of it's energy & momentum. an objects volume, for example a photon can have no density (hopefully I expressed that answer properly)
Joe
I suppose each Individual has his or hers different laws and assumptions, so it can be difficult to ask and answer physics questions, but discussions are always positive
Joe
how
Melaku
which matter use rocket
Nisha
Does their is any procedure of star making
Hope That Helps.....
how to produce star and how to dead star?
Nisha
waad mahad santnihiin dhamaan waxaan doonayaa inaan wax ka barto astronomyga waa maxay xidigis?
understanding astronomy
yap
Janmarc
what is astronomy?
Janmarc
define..
Janmarc
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
Hey there I want to be an astrophysicist... and I'm grade 9... what should I do to be an astrophysicist
Aymen
Know more about space,watch movies related to space ,and to become an astrophysicist u should be very good in physics,train urself to think everything logically. Start to focus on JEE Exam ,train urself or join any institute which is good in coaching for JEE ,then if u score high ,u can join IIST
Sri
Which is the best university for Astronomy
Asim
Probably Massachusetts Institute Of Technology.....
Math Math Math, Get Familiar With All Types Of Math.....
Which subject is most important for Astronomy
Asim
Geometry, Algebra, Calculus, Trigonometry, Do Alot Of It And Often.....
I Can't Say It Enough, Math Is The Language Of The Cosmos.....
Adam you are in which university?
Asim
I Went To University But Never Finished My Degree..... Had To Work And Couldn't Afford School.....
MaryMount University..... Philosophy Of Science Major.....
It ia a cathloic University. Am i write
Asim
And its main campas is in Arlington country
Asim
No, It's In New York City.....
It's Not A Catholic University.....
Ohh sorry
Asim
Are you interested in Astronomy
Asim
IIT ain't so good for Pure Astronomy. If you want to know how the universe works,go for pure science. If you want to make spacecraft,go for Aerospace Engineering
priyanshu
Your are in which university brother
Asim
I Love Astronomy, I'm An Active Amateur Astronomer.....
I also love Astronomy very much
Asim
And to help me to solve some puzzling questions
Asim
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.....
Good Morning Asim Ali.....
I Can't Do That, You Can Ask Me What Ever You Want.....
If you don't mind can i ask why?
Asim
Do You Understand The Millions Of People Have Access To This Site, I Wouldn't Put My Information Out There, Knowing What People With Bad Intent Can Do With Personal Information.....
Ohh sorry
Asim
My question is that, there are many collision of stars in a day So that cause black hole. But is there any procedure of star making? Hopefully i ask my question properly.
Asim
No Need To Apologize, I Will Answer Anything You Need Answered And If I Can't Answer It I Will Guide You To The Answer.....
Thier Is Only One Way Stars Are Made, Gravity Makes Matter Come Together, And When The Amount Of Matter Gets Massive Enough Nuclear Fusion Starts Up And A Star Is Born.....
What is white drawft?
Asim
A White Dwarf Is A Low Mass Star That Has Exhausted All It's Central Nuclear Fuel And Lost It's Outer Layers As A Planetary Nebula.....
what is the great filter theory
Nisha
hi adam what is great filter theory
Nisha
Well First It's Not A Theory, It's A Hypothesis, The Great Filter Hypothesis States That What Ever Causes Dead Matter To Under Go Abiogenesis(Start Of Life) Must Be Very Hard And Very Rare In Our Universe, Because So Far We Only See 1 Civilisation That Made Through All The Requirements For.....
Intelligent Life, So Far Only Our Planet Has Intelligent Life, That We Know Of, And Again This Is Only A Hypothesis, No Evidence Exist To Back This Up.....
Nisha
Good Day.....
Good to see you sir
Asim
hi
Nisha
good day
Nisha
hi
Nisha
Same Here.....
What's The Good Word For The Day?