Blog #5: WS2.1, #3

3. You observe a star and measure its flux to be $F_\bigstar$. If the luminosity of the star is $L_\bigstar$, 
a) Give an expression for how far away the star is. 

$F_\bigstar = \frac{L_\bigstar}{4\pi r^2}$
$r^2 = \frac{L_\bigstar}{4\pi F_\bigstar}$
$r=(\frac{L_\bigstar}{4\pi F_\bigstar})^{1/2}$

b) What is its parallax? 

$\theta = \frac{L}{D}$
$\theta = \frac{1AU}{(\frac{L_\bigstar}{4\pi F_\bigstar})^{1/2}}=1AU(\frac{4\pi F_\bigstar}{L_\bigstar})^{1/2}$

c) If the peak wavelength of its emission is at $\lambda_0$, what is the star's temperature? 

$\lambda_0 = \frac{b}{T}$
$T = \frac{b}{\lambda_0}$
$b = 2.9*10^{-3}mK$ (Wien's displacement constant)

d) What is the star's radius, $R_\bigstar$? 

$L_\bigstar = \sigma AT^4$
$A = \frac{L_\bigstar}{\sigma T^4} = 4\pi R_\bigstar ^2$
$R_\bigstar = (\frac{L_\bigstar}{4\pi \sigma T^4})^{1/2}$