Rahul
Dead Member
explain how the colour index are obtained and why they r useful.
i understand a bit, but any explanation will be great.
cheers!
i understand a bit, but any explanation will be great.
cheers!
astrophysics DP (1 Viewer)
- Thread starter Rahul
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Rahul
Dead Member
one more,
explain the importance of binary stars in determining stellar masses.
some kind of simplified explanation.
explain the importance of binary stars in determining stellar masses.
some kind of simplified explanation.
...
^___^
u doing astro??
cool...
color index???? is that the spectrum ur on about?????
as for binary strar to determines the masses, i'll look that one up...
cool...
color index???? is that the spectrum ur on about?????
as for binary strar to determines the masses, i'll look that one up...
Rahul
Dead Member
yep i'm doin astro...i tried to read the texts but didnt really get it. prolly coz i had a mental block. maybe if i read it next tym, i might get it. i got 2 eng exams tomorrow, so that will have to wait.
haz_it_all
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the total mass of a binary star system can be calculated by using the radius of their rotation around the centre of the system and period OR time it takes to complete 1 revolution:
m1+m2 = (4pi^2 r^3)
--------------- where m1 + m2 = mass of total system
GT^2 4pi^2 is constant, r= radius
G=gravitational constant
T=period
tell me if that clears it up for ya rahul
m1+m2 = (4pi^2 r^3)
--------------- where m1 + m2 = mass of total system
GT^2 4pi^2 is constant, r= radius
G=gravitational constant
T=period
tell me if that clears it up for ya rahul
haz_it_all
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sorry that equation is supposed to be :
m1+m2 = (4pi^2 r^3) / GT^2
m1+m2 = (4pi^2 r^3) / GT^2
Rahul
Dead Member
got it haz. thanks.
any idea for the colour index one?
any idea for the colour index one?
Huy
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(Long post, please forgive me )
A star can have three different kinds of magnitudes depending on whether it is seen by:
1. The human eye
2. A photographic emulsion, or
3. A photocell.
These three detectors differ in their sensitivity to all the different colours of light radiated by a star.
1. The eye is most sensitive in the yellow-green portion of the spectrum.
2. Photographic emulsions are commonly more sensitive in the blue-violet portion of the spectrum. It follows that:
a) A blue star will hence appear brighter on a photograph than in the eye; and
b) A red star will appear duller in a photograph.
3. Photocells respond equally well to all wavelengths.
To improve precision, the magnitude of a star is actually measured in some preselected colour such as blue or yellow by the use of appropriate filters.
Colour Index
Stellar brightness is generally measured in three 'colours'
1. Ultraviolet (U).
2. Blue (B) - which approximates to the photographic response.
3. Yellow (V) - which approximates to the visual response.
If U, B and V are the magnitudes of a star in three colours, with B and V respectively, the photographic and visual magnitudes, then the difference (B V) is called the colour index of the star. That is:
C.I. = B V
Imagine that an astronomer is measuring the colour index of a blue star. Since it is blue, it will appear bright through a blue filter. Thus it would have a small magnitude (remember, magnitude decreases as brightness increases).
On the other hand, when viewed through a yellow filter, it will appear dull, since the yellow filter would absorb the blue light. Hence it would have a large magnitude. A calculation of B V would then have a large number subtracted from a smaller number; the result would be negative. It thus follows that CI = B V has negative values for blue stars and positive values for red stars.
Binary stars are important in determining the masses of stars (the mass of an isolated star cannot be directly measured). The two components of a binary star revolve in ellipses about a common centre of mass, with the centre of mass being closer to the more massive star.
Spectroscopic binary stars are preferred over visual binaries for mass determination because:
1. There are many more distant stars than nearer stars; and
2. Their speeds can be easily measured by their Doppler shift.
If the two stars have masses M1 and M2 (in units of solar masses) and are separated by distances R1 and R2 respectively from the centre of mass, then:
M1.R1 = M2.R2
It follows that:
R1 / R2 = M2 / M1
The massive star also moves slower than does the low-mass star and its spectral lines have a smaller Doppler shift.
From Keplers Third Law, we also have:
a^3 / T^2 = 4 pi^2 / G(M1+ M2)
where a is the distance separating the two stars in astronomical units (AU), T is the period of each component (in years) and the masses are in kg. If the masses are in terms of solar masses, this equation reduces to:
M1 + M2 = a^3 / T^2
Consider the stars moving in a circular orbit about the centre of mass with a period t. For star 1, moving with a speed of V1, it moves a distance given by:
S1 = V1t = 2 pi R1
Similarly,
S2 = V2t = 2 pi R2
Hence:
R1 / R2 = V1 / V2 = M2 / M1.
Since the velocities can be measured by the stars Doppler shift, the ratio of the masses can be calculated. Since the total mass can be found from Keplers Law, the individual masses can be calculated.
)Colour Index
A star can have three different kinds of magnitudes depending on whether it is seen by:
1. The human eye
2. A photographic emulsion, or
3. A photocell.
These three detectors differ in their sensitivity to all the different colours of light radiated by a star.
1. The eye is most sensitive in the yellow-green portion of the spectrum.
2. Photographic emulsions are commonly more sensitive in the blue-violet portion of the spectrum. It follows that:
a) A blue star will hence appear brighter on a photograph than in the eye; and
b) A red star will appear duller in a photograph.
3. Photocells respond equally well to all wavelengths.
To improve precision, the magnitude of a star is actually measured in some preselected colour such as blue or yellow by the use of appropriate filters.
Colour Index
Stellar brightness is generally measured in three 'colours'
1. Ultraviolet (U).
2. Blue (B) - which approximates to the photographic response.
3. Yellow (V) - which approximates to the visual response.
If U, B and V are the magnitudes of a star in three colours, with B and V respectively, the photographic and visual magnitudes, then the difference (B V) is called the colour index of the star. That is:
C.I. = B V
Imagine that an astronomer is measuring the colour index of a blue star. Since it is blue, it will appear bright through a blue filter. Thus it would have a small magnitude (remember, magnitude decreases as brightness increases).
On the other hand, when viewed through a yellow filter, it will appear dull, since the yellow filter would absorb the blue light. Hence it would have a large magnitude. A calculation of B V would then have a large number subtracted from a smaller number; the result would be negative. It thus follows that CI = B V has negative values for blue stars and positive values for red stars.
Using binaries to determine the masses of stars
Binary stars are important in determining the masses of stars (the mass of an isolated star cannot be directly measured). The two components of a binary star revolve in ellipses about a common centre of mass, with the centre of mass being closer to the more massive star.
Spectroscopic binary stars are preferred over visual binaries for mass determination because:
1. There are many more distant stars than nearer stars; and
2. Their speeds can be easily measured by their Doppler shift.
If the two stars have masses M1 and M2 (in units of solar masses) and are separated by distances R1 and R2 respectively from the centre of mass, then:
M1.R1 = M2.R2
It follows that:
R1 / R2 = M2 / M1
The massive star also moves slower than does the low-mass star and its spectral lines have a smaller Doppler shift.
From Keplers Third Law, we also have:
a^3 / T^2 = 4 pi^2 / G(M1+ M2)
where a is the distance separating the two stars in astronomical units (AU), T is the period of each component (in years) and the masses are in kg. If the masses are in terms of solar masses, this equation reduces to:
M1 + M2 = a^3 / T^2
Consider the stars moving in a circular orbit about the centre of mass with a period t. For star 1, moving with a speed of V1, it moves a distance given by:
S1 = V1t = 2 pi R1
Similarly,
S2 = V2t = 2 pi R2
Hence:
R1 / R2 = V1 / V2 = M2 / M1.
Since the velocities can be measured by the stars Doppler shift, the ratio of the masses can be calculated. Since the total mass can be found from Keplers Law, the individual masses can be calculated.