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fomenos
2 years ago
8

Consider a civilization broadcasting a signal with a power of 2.0×104 watts. The Arecibo radio telescope, which is about 300 met

ers in diameter, could detect this signal if it is coming from as far away as 141 light-years. Suppose instead that the signal is being broadcast from the other side of the Milky Way Galaxy, about 70000 light-years away.
Mathematics
1 answer:
Vitek1552 [10]2 years ago
7 0

For light: Inverse Square Law 

<span>
The signal is weaken by the inverse square of the difference of distances this means that one over the square of the difference. </span>

<span>
</span>

Therefore, 70000LY / 141 LY =496.45 and that squared =246462.602 times less signal, or 1/246462.602.


 2 For a circular telescope like the Arecibo radio telescope that equals Pi times the radius squared. Sensitivity of the telescope depends on its area.<span>
The new telescope needs 246462.60 times that area to have enough sensitivity </span>

<span>
<span>(150 x 150 x Pi) = 70 685 sq m area for the Arecibo telescope and that times 246462.60
= 1.74212 x 10^10</span></span>

<span><span>
</span></span>

What is the diameter of a circle with that area?

 <span>
<span>1. Divide the area by Pi = 5.548156 x 10^9
2. Take the square root of the result to find the radius = 74485.94293</span></span>

3. Multiply by 2 to find the diameter = <span>148971.886</span>

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