13.[3pt] The star UV Ceti lies at a distance of 8.7 light-years and has an appar

Question

13.[3pt] The star UV Ceti lies at a distance of 8.7 light-years and has an apparent brightness in our night sky of 1.8x10-13 w/m2. Use the inverse square law for light to calculate the luminosity of UV Ceti Answer: Submit All Answers Suppose you have a light bulb that emits 200 watts of visible light. (Note: This is not the case for a standard 200-watt light bulb, in which most of the 200 watts 14.(3pt] goes to heat and only about 20-30 watts is emitted as visible light.) How far away would you have to put the light bulb for it to have the same apparent brightness as UV Ceti in our sky? Answer Submit All Answers

Explanation / Answer

13) given I = 1.8*10^-13 W/m^2

distance from the star to the given point, r = 8.7 light years

= 8.7*365*24*60*60*3*10^8

= 8.23*10^16 m

now use, Intensity = power/Area

==> power or luminosity = Intensity*Area

= I*4*pi*r^2

= 1.8*10^-13*4*pi*(8.23*10^16)^2

= 1.53*10^22 W

14)

Intensity of light bulb = Inetnsity of light from star

200/(4*pi*r^2) = 1.8*10^-13

==> r^2 = 200/(4*pi*1.8*10^-13)

r = sqrt(200/(4*pi*1.8*10^-13))

= 9.40*10^6 m

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