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A particular star is 5.2*10^18 meters away from Earth and has a luminosity of 8.9*10^29 watts. Ignoring the effects of the atmosphere, what is the brightness of the star, in watts per square meter, as observed from earth?

physics
Guest Aug 27, 2015

Best Answer 

 #2
avatar+94101 
+5

I'm guessing here but

the lioght will spread out in a sphere

the surface area of a sphere is   4*pi*r^2

r=5.2*10^18

So the surface are of THIS sphere is 

$$\\SA=4*\pi*(5.2*10^{18})^2\\
SA=4*\pi*5.2^2*10^{36}\\$$

 

$${\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{5.2}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{\pi}} = {\mathtt{339.794\: \!661\: \!412\: \!272\: \!036\: \!7}}$$

 

 

$$\\SA= 3.39797946614122720367 * 10^{38}\;\; M^2\\\\
Brightness \approx 8.9*10^{29}/(3.39797946614122720367 * 10^{38}) \;\;$watts per square metre$\\\\
Brightness \approx 8.9*10^{-9}/(3.39797946614122720367 ) \;\;$watts per square metre$\\\\
Brightness \approx 2.62*10^{-9} \;\;$watts per square metre$\\\\$$

 

I got the same as anon so maybe we are both correct    

Melody  Aug 27, 2015
 #1
avatar
+5

A particular star is 5.2*10^18 meters away from Earth and has a luminosity of 8.9*10^29 watts. Ignoring the effects of the atmosphere, what is the brightness of the star, in watts per square meter, as observed from earth?

 

Brightness-Luminosity-Distance relationship 

Brightness=8.9*10^29 / 4 x Pi x (5.2*10^18)^2

=2.619 x 10^-9 W/M^2

Guest Aug 27, 2015
 #2
avatar+94101 
+5
Best Answer

I'm guessing here but

the lioght will spread out in a sphere

the surface area of a sphere is   4*pi*r^2

r=5.2*10^18

So the surface are of THIS sphere is 

$$\\SA=4*\pi*(5.2*10^{18})^2\\
SA=4*\pi*5.2^2*10^{36}\\$$

 

$${\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{5.2}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{\pi}} = {\mathtt{339.794\: \!661\: \!412\: \!272\: \!036\: \!7}}$$

 

 

$$\\SA= 3.39797946614122720367 * 10^{38}\;\; M^2\\\\
Brightness \approx 8.9*10^{29}/(3.39797946614122720367 * 10^{38}) \;\;$watts per square metre$\\\\
Brightness \approx 8.9*10^{-9}/(3.39797946614122720367 ) \;\;$watts per square metre$\\\\
Brightness \approx 2.62*10^{-9} \;\;$watts per square metre$\\\\$$

 

I got the same as anon so maybe we are both correct    

Melody  Aug 27, 2015

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