MARYAM1234567
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α-Centauri is one of the nearest stars to our Sun. The surface temperatures of these two
stars are about the same. α-Centauri has a 20% greater diameter than the Sun.
The ratio of the luminosity of α-Centauri to the luminosity of the Sun is about
A 1.2
B 1.4
C 1.7
D 2.1


the answer is supposed to be B
pls help me out
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Sheperd23
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damn don't spam
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MARYAM1234567
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(Original post by Kangaroo17)
damn don't spam
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Sheperd23
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(Original post by MARYAM1234567)
sorry was a bit harsh...

but i think its using the luminosity equation L=4(pi)R^2 x boltzman constant x T (surface temp)

since surface temp is the same you can ignore it for ratios
also 4(pi) and boltzmann constant are constants, so you ignore them for ratios

you have then :

L= R^2 to create the ratio with.
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Sheperd23
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And here is a hint. PLEASE USE IT AFTER YOU HAVE TRIED ALOT. It takes some thinking thats why, and you need to develop it on your own.


Spoiler:
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RATIO - since Centauri is 20% bigger in diameter, but you need it in radius form:

x d : 1.2x d (d - diameter)
1/2x d: 0.6x d
= x r: 1.2 x r (r - radius. as you can see i've halved diameter, which is equal to radius. thus its still times by 20%. catched me out lol)

The Sun: L = x2/100
Alpha Centauri: L = (1.2x)2 / 102
= 1.44x2/100

compare the numerators basically, as both are divided by 100, it has no effect:

x2: 1.44x2
Thus:

1:1.44
which is about : 1:1.4

you can also you numerical method, not algebraic, too:

d : 1.2d
r:1.2r = 10r : 12r

Sun: 102/102 = 100/100
Centauri: 122/102 = 144/100

100:144
1:1.44 which is about 1:1.4

hope it helped! Please practice more 'tricky' questions like these, it really got my brain thinking too! make sure you fully understand the process of WHY.
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MARYAM1234567
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(Original post by Kangaroo17)
sorry was a bit harsh...

but i think its using the luminosity equation L=4(pi)R^2 x boltzman constant x T (surface temp)

since surface temp is the same you can ignore it for ratios
also 4(pi) and boltzmann constant are constants, so you ignore them for ratios

you have then :

L= R^2 to create the ratio with.
don't be sorry, please...

(Original post by Kangaroo17)
And here is a hint. PLEASE USE IT AFTER YOU HAVE TRIED ALOT. It takes some thinking thats why, and you need to develop it on your own.


Spoiler:
Show
RATIO - since Centauri is 20% bigger in diameter, but you need it in radius form:

x d : 1.2x d (d - diameter)
1/2x d: 0.6x d
= x r: 1.2 x r (r - radius. as you can see i've halved diameter, which is equal to radius. thus its still times by 20%. catched me out lol)

The Sun: L = x2/100
Alpha Centauri: L = (1.2x)2 / 102
= 1.44x2/100

compare the numerators basically, as both are divided by 100, it has no effect:

x2: 1.44x2
Thus:

1:1.44
which is about : 1:1.4

you can also you numerical method, not algebraic, too:

d : 1.2d
r:1.2r = 10r : 12r

Sun: 102/102 = 100/100
Centauri: 122/102 = 144/100

100:144
1:1.44 which is about 1:1.4

hope it helped! Please practice more 'tricky' questions like these, it really got my brain thinking too! make sure you fully understand the process of WHY.
i asked this after trying soooooooo many times yesterday ...
but tried may time today as well..
thanks alot for taking out time and helping me get it ..:suith:
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Sheperd23
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(Original post by MARYAM1234567)
don't be sorry, please...



i asked this after trying soooooooo many times yesterday ...
but tried may time today as well..
thanks alot for taking out time and helping me get it ..:suith:
No problem!
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