TutorialA radio broadcast left Earth in 1923. How far in lightyears has it traveled?If there is, on average, 1 star system per 400 cubic lightyears, how many star systems has this broadcastreached?Assume that the fraction of these star systems thathave planets is 0.50 and that, in a given planetarysystem, the average number of planets that haveorbited in the habitable zone for 4 billion years is 0.40.How many possible planets with life could have heardthis signal?Part 1 of 3To figure out how many light years a signal hastraveled we need to know how long since the signal leftEarth. If the signal left in 1923, distance in light years =time since broadcast left Earth.d = tnow - broadcastd = 9797 light yearsPart 2 of 3Since the radio signal travels in all directions, itexpanded as a sphere with a radius equal to thedistance it has traveled so far. To determine thenumber of star systems this signal has reached, weneed to determine the volume of that sphere.V, =Vb =| light years)3Then multiply it by the number of star systems found inthe given volume.1 starN = V600 lv3N =

Given: The year in which the radio broadcast left the Earth is 1923. The average number of stars in a given volume is 1 star per 400 cubic light-years. The fraction of these stars having a planet is 0.50. The average number of the planet that has orbited in the habitable zone for 4 billion years is 0.40. Introduction: A light-year is the distance light travels in one year. Light moves at a velocity of about 300,000 kilometers (km) each second. So in one year, it can travel about 10 trillion km. More precisely, one light-year is equal to 9,500,000,000,000 kilometers.Calculation: Calculate the time light has left the Earth. t=tpresent-tleft Here, tpresent is the present year, tleft is the year in which the light left the Earth. Substitute 2020 for tpresent and 1923 for tleft in the above expression. t=2020-1923t=97 years Thus, the light has travelled a distance of 97 light-years. Calculate the total volume the radio broadcast has covered. V=43πr3 Here, r is the radius. Substitute 97 light-years for r in the above expression. V=433.1497 light years3V=3.8×106 light years3 Calculate the number of stars system this broadcast has reached. N=V1400 light years3N=3.8×106light years31400 light years3N=9552.64N=9553 Thus, the broadcast has reached 9553 star systems approximately. Calculate the number of planets with life that heard these signals. n=0.500.209553n=1910.5n=1911 Thus, the number of planets with life that heard these signals are 1911.

Answered: Tutorial A radio broadcast left Earth…