Download Binaries

PHYS
205
Multiple Star Systems
PHYS
205
Binary systems
Question: Why are the binaries important??
Answer: They allow us to measure the mass of other stars.
Using the Moon’s orbit we can calculate Earth’s mass:
Centripetal force:
F = Mmv2/Rm
Gravitational force:
F = GMeMm/Rm2
Gravitational Force = Centripetal Force  Me = v2Rm/G
Similarly we can calculate the Sun’s mass using Earth’s orbit. 
We need at least two object rotating around each other to calculate
the mass of them.
PHYS
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Visual Binaries
Some binaries are close enough
to be seen separately  Visual
Binaries
Castor system is an example.
Observed by Hershell in
1790.
The binary can have any
angle of sight towards
us (the observer).
PHYS
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Motion of the Center of Mass
It is very rare to be able to
observe both of the stars
of a pair.
We usually detect the
influence of the unseen
companion  Astrometric
binaries.
PHYS
205
Spectroscopic Binaries
If the plane of rotation of the binaries is parallel to our line of
sight, we might not see them, but their light will give us enough
info about their nature.
PHYS
205
Eclipsing Binaries
If the angle is close to 90 degrees,
the two stars can eclipse each
other  eclipsing binaries.
Using the eclipsing binaries we can find the diameter of stars.
PHYS
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Measuring the Diameter
From the shape of the light curve
and the duration of the eclipse we
can calculate the diameter of the
larger star.
Not only binaries, but also planet
systems are discovered this way.
We can also use the Stefan-Boltzmann law L = 4  R2 T4. From the
amount of light we are receiving, we measure the luminosity, and from
the spectral analysis, we measure the color of the star and determine its
temperature  we can calculate the diameter indirectly.
PHYS
205
Algol Binary
PHYS
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Mass-Luminosity Relation
From the study of the binaries we
learn the mass of the stars.
When we plot the mass of the stars
vs. the light we receive from them,
we see that there is a very strong
dependence of luminosity on mass.
Luminosity  Mass
3.5
We have discovered this
relationship using the binaries,
however, it is not unique to
binaries, but it can be applied to
all the main sequence stars.