Radiation Intensity

The R Markdown code is available on GitHub

The R script is also available on GitHub

Radiation Intensity

Inverse-square law for light and other electromagnetic radiation

See Inverse-square law on Wikipedia

Formula: \[I = \frac{P}{A} = \frac{P}{4\pi r^{^{2}}}\]

Where I is the intensity or power per unit area

Given an antena with radius r gives area A as: \[A = \pi r^{^{2}}\]

Naming with transmitter, antena and solving for power of the transmitter gives: \[P_{transmitter} = 4\pi d^{^{2}}\times \frac{P_{received}}{A_{antena}}\]

where d is the distance

Formulating as function

transmitter_power <- function(distance, Preceived, Rantena) {
  Aantena <- pi * Rantena * Rantena
  4 * pi * distance * distance * Preceived / Aantena
}

Proxima Centauri

Distance to Proxima Centauri is 4.2465 ly and one ly is 9.46E12 km

See Proxima Centauri on Wikipedia

Dpc <- 4.2465 * 9.46E12 * 1000 # to meters

Example

1. How powerful does a radio transmitter on Proxima Centauri need to be to detect a signal of 1W with a radio telescope with radius of 100 meter

transmitter_power(Dpc, 1, 100) / 1E15 # in Petawatt

## [1] 6.455123e+14

2. How powerful does a radio transmitter on Proxima Centauri need to be to detect a signal of 0.1W with a radio telescope with radius of 100 meter

transmitter_power(Dpc, 0.1, 100) / 1E15 # in Petawatt

## [1] 6.455123e+13

3. How powerful does a radio transmitter on Proxima Centauri need to be to detect a signal of 0.01mW with the FAST a radio telescope with illuminated radius of 150 meter

Preceived <- 0.01 / 1E3
transmitter_power(Dpc, Preceived, 150) / 1E15 # in Petawatt

## [1] 2868943549