A satellite passing the planet Neptune communicates with its controller on earth using a microwave transmitter with output power 22.0W and wavelength 79600 μm. Neptune is 4.35*1012 m from earth at the time when communication took place. Assuming that the power transmitted by the satellite is radiated uniformly in all directions, calculate the power received on the earth by a dish aerial with effective area 260m².
actual power received at dish aerial is 1.2*10-15 W.
1.) suggest why the actual power received is greater than calculated above.
2.) Calculate the actual rate at which photons of microwaves arrive at the dish aerial.
Answer:
Imagine a giant spherical area from the satellite till it reaches Earth. Then take the fraction of the aerial disc's surface area over the the spherical area, and multiply by 22W
Power received on the earth by the dish aerial= 260 / (4 * pi * Rneptune2) * 22
= 2.41 * 10-23 W
1) Cosmic rays from the surroundings add on to the total power 'received'.
2) E = hf = hc/λ for a photon
where c = 3.0 * 108 m/s
h = plank's constant = 6.626 * 10-34 m² kg / s
λ = 79600 μm
E = 2.497 * 10-24 J
In 1 second, 1.2*10-15 J is received.
Hence, the rate of photons arriving = 1.2*10-15 / 2.497 * 10-24 = 480M photons/s
