numbat/examples/voyager.nbt

# How many photons are received per bit transmitted from Voyager 1?
#
# This calculation is adapted from a Physics Stack Exchange answer [1].
#
# [1] https://physics.stackexchange.com/a/816710

# Voyager radio transmission:
let datarate = 160 bps
let f = 8.3 GHz
let P_transmit = 23 W

let ω = 2π f
let λ = c / f

@aliases(photon)
unit photons

let energy_per_photon = ℏ ω / photon

let photon_rate = P_transmit / energy_per_photon -> photons/s

print("Voyager sends data at a rate of {datarate} with {P_transmit}.")
print("At a frequency of {f}, this amounts to {photon_rate:.0e}.")

# Voyager dish antenna:
let d_voyager = 3.7 m

# Voyagers distance to Earth:
let R = 23.5 billion kilometers  # as of 2024

# Diameter of receiver dish:
let d_receiver = 70 m

let irradiance = P_transmit / (4π R²)
let P_received: Power = irradiance × (π d_voyager / λ)² × (π d_receiver² / 4)

print("A {d_receiver} dish on Earth will receive {P_received -> aW:.1f} of power.")

let photon_rate_receiver = P_received / energy_per_photon -> photons/s
let photons_per_bit = photon_rate_receiver / datarate -> photons/bit

print()
print("This corresponds to {photon_rate_receiver}.")
print("Which means {photons_per_bit:.0}.")