Question

Consider a civilization broadcasting a signal with a power of 1.2×104 watts. The Arecibo radio telescope, which is about 300 meters in diameter, could detect this signal if it is coming from as far away as 110 light-years. Suppose instead that the signal is being broadcast from the other side of the Milky Way Galaxy, about 70000 light-years away.

Answer 1

what's the question here? All I see is factual information

Answer 2

Sorry I forgot the last part

Answer 3

How large a radio telescope would we need to detect this signal? (Hint: Use the inverse square law for light.)

Answer 4

Okay. I believe I have finally figured out a solution to this, but I believe you seemed to have copied some of the factual information incorrectly. But going forward, we can look up the definition of the inverse square law of light and deduct from this:

The signal is weaker by the inverse square of the difference of distances. which means one over the square of the difference.
Twice as far away you get 1/4 of the signal strength.
Three times further away you get 1/9 of the signal strength.
Four times further away you get 1/16 of the signal strength
Ten times further away you get 1/100 of the signal strength

Therefore, if we want to find how much in distance we are away from the new point of the signal source (take notice I used 7,000 instead of 70,000 as it made more sense):

\[\frac{ 7000 }{ 110 } = 63.636\] so we know that the signal source is 63.636 times LESS than its original source. We could also note that it is: \[\frac{ 1 }{ 63.636 } \] of it's original power.
So to find the size of the new telescope that is needed to give the same amount of signal source we take the 63.636 and multiply it to the original area of the original telescope

\[Area = (\Pi(150m)^{2} )(63.636) = 4,498,163.777 m ^{2}\]

to find the diameter of the new telescope, divide your answer by pi and then square root it to find your new radius.

The power of the signal 1.02 x 10^4 was kept the same throughout the problem so we did not need to use it.

Answer 5

Thank you so much for your help.. When I divided the area by pi and then I square rooted it I got this answer 1196.88605753.. What should I do ? Sorry but I have never done this kinda Q's before

Answer 6

The question asked what the size of the new telescope should be. The size of the telescope usually is based on the area of it's reflective mirrors to amplify its vision. Therefore, we just need to find the new circle area of the new telescope, in which you found the new radius to be: 1196.88605753 m

so plug that into this the area of a circle equation:

\[Area = (\Pi)(r)^{2}\] to find the new area of the circle mirror that the new telescope should have.

Answer 7

Yaaay Thank you so much I finally get it.. The answer is 190909.090909

Answer 8

Wait, how did you get 190,909.090909 for your answer?