Question

Problem 22.52-Copy Part A ReviewI Constants Periodic Table Using the inverse square law for light from Mathematical Insight 15.1 in the textbook, determine the apparent brightness of the Sun in our sky. Express your answer to two significant figures and include the appropriate units. According to Olbers' paradox, the entire sky would be as bright as the surface of a typical star if the universe were infinite in space, unchanging in time, and the same everywhere. However, conditions would not need to be quite that extreme for the nighttime' sky to be as bright as the daytime sky. apparent brightnessValue Units Submit Part B Using the inverse square law for light, determine the apparent brightness our Sun would have if it were at a distance of 11 billion light-years. Express your answer to two significant figures and include the appropriate units apparent brightness-alue Units Submit Part C From your answers to parts a and b, estimate how many stars like the Sun would need to exist at a distance of 11 billion light-years for their total apparent brightness to equal that of our Sun.

Answer 1

Apparent brightness = luminosity/4 pi d^2 luminosity of Sun's = 3.8 times 10^26 watts part (A) distance b/w Sun and Earth d = 149.6 million km = 1.496 times 10^11 m Apparent brightness = 3.8 times 10^26/4 pi times (1.496 times 10^11)^2 = 1351.2 Watts/m^2 part (B) d = 11 billion light years d = 11 times 10^9 light year times 9.46 times 10^15 m/1 light year d = 10.406 times 10^25 m Apparent brightness = 3.8 times 10^26 Watts/ 4 pi times ()10.406 times 10^25)^2 = 2.7926 times 10^-27 Watts/m^2 part (c) number of stars that will produce same apparent brightness like Sun n = brightness at Sun's distance/brightness at 11 billion light year n = 1351.2 Watt/m^2/2.7926 times 10^-27 w/m^2 n = 4.84 times 10^21 Stars