The Andromeda galaxy pictured here is a vast whirl of 1.0×1011 stars, located 2.9 million light-years from the?
The Andromeda galaxy pictured here is a vast whirl of 1.0×1011 stars, located 2.9 million light-years from the Earth. Assume that, on average, each star in this galaxy emits radiation with the same power as the Sun. (a) What is the intensity of light from this galaxy as it reaches the Earth? (Treat this as an ideal problem and ignore any absorption due to interstellar dust or to the Earth's atmosphere.) (b) A candle emits radiation in all directions with a power of 4.2 W. What is the intensity of the candlelight at a distance of 9.3 km? (c) From which source is the light more intense, the galaxy or the candle?
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A) andromeda
Sun power Sp = 3.85*10^26 watt
total power Ap emitted by Andromeda :
Ap = Sp*10^11 = 3.85*10^26*10^11 = 3.85*10^37 watt
distance d in m :
s/year = 3.6*10^3*24*365 = 3.15*10^7 sec
s/yearlight = 3.15*10^7*3*10^8 = 9.46*10^15 m
d = 9.46*10^15*2.9*10^6 = 2.74*10^22 m
spherical surface A :
A = 4PI*d^2 = 4*3.14*(2.74*10^22)^2 = 9.43*10^45 m^2
Specific power Psp = Ap/A = 3.85*10^37/(9.43*10^45) = 4.08*10^-9 w/m^2 = 4.08 nw/m^2
b) candle
spherical surface A :
A = 4PI*d^2 = 4*3.14*(9.3*10^3)^2 = 1.09*10^9 m^2
Specific power Psp = Cp/A = 4.20/(1.09*10^9) = 3.85*10^-9 w/m^2 = 3.85 nw/m^2
Andromeda wins competition for a while : 4.08 against 3.85
I don't see the picture, but M31:
Apparent magnitude (V) 3.44
Absolute magnitude (V) â20.0