Question

The Voyager 1 spacecraft is now beyond the outer reaches of our solar system, but earthbound scientists still receive data from the spacecraft's 20-W radio transmitter. Voyager is expected to continue transmitting until about 2025, when it will be some 25 billion km from Earth.

1) What's the diameter of a dish antenna that will receive 10−20W of power from Voyager at this time?

 

Answer 1

The power received is,

\(P_{\text {recerid }}=I A=\frac{P_{\text {transmitted }}}{A}\left(\pi r_{\text {dish }}^{2}\right)\) \(10^{-20} \mathrm{~W}=\frac{20 \mathrm{~W}}{4 \pi\left(25 \times 10^{12}\right)^{2}}\left(\pi\left(r_{\text {dish }}^{2}\right)\right)\) \(r_{\text {dish }}=1.118 \times 10^{3} \mathrm{~m}\) diameter of the dish is, \(d=2.24 \times 10^{3} \mathrm{~m}=2.24 \mathrm{~km}\) \(d=2.24 \times 10^{3} \mathrm{~m}=2.24 \mathrm{~km}\)