Download Comparing Earth, Sun and Jupiter

1.
There is a famous binary star system in the Big
Dipper, made up of Mizar (mag 2.4) and Alcor
(mag 3.99). Which star is brighter? By how
much? What is their combined magnitude if
unresolved?
Mizar has the smaller magnitude, so is the brighter
star.
f

mMizar  m Alcor  2.5 log  Mizar 
 f Alcor 
f Mizar
 10 0.4mMiza rmAlcor 
f Alcor
 10 0.42.43.99
 4.32
If the stars are unresolved, the total flux is the
sum of their fluxes (not their magnitudes!)
fTotal  f Alcor  f Mizar
fTotal
f
 1  Mizar
f Alcor
f Mizar
 1  4.32
 f

mTotal  mAlcor  2.5 log  Total 
 f Alcor 
 3.99  2.5 log( 5.32)
 2.17
2. Imagine a hypothetical source which has a
constant flux of 10 Jy at all frequencies.
What is its magnitude in the U band? In the V
and K bands?
mU  2.5 log  f   2.5 log  f Vega,U 
 2.5 log 10   2.5 log( 1780)
 5.6
Since the flux is the same in all bands we then
have simply:
mV  mU  2.5 log  f Vega,V   2.5 log  f Vega,U 
 f Vega,V 

 mU  2.5 log 
f

 Vega,U 
 3600 
 5.6  2.5 log 

1780


 6.4
 636 
m K  5.6  2.5 log 

 1780 
 4.48
2.
What is the B-V colour of a source that has a
flux proportional to-4?
The central wavelengths in the B and V band are
B=0.45 m and V=0.55 m. Therefore the ratio
of fluxes is given by:
 f B   B 
    
 fV   V 
4
 0.45 


0
.
55


 2.23
4
 fVega, B 
 fB 

mB  mV  2.5 log    2.5 log 


f
Vega
,
V
 fV 


 4000 
 2.5 log 2.23  2.5 log 

3600


 0.757
3. As we’ll see next lecture, Cepheid variable
stars are a type of standard candle, that
always have (approximately) the same absolute
magnitude M=-5.5. If a Cepheid variable is
found with an apparent magnitude m=8.2, how
far away is it?
 Dstar 

m  M  5 log 
 32.616ly 
Dstar  32.616  10
 32.616  10
 17,923ly
mM
5
8 .2  5 . 5
5
3.
What is the total luminosity of a galaxy with
absolute magnitude M=-21?
L / LSun  80.2  10
 2  1010
i.e. as bright as 20 billion Suns.
0.421