module

Kozai::Doppler

Doppler shift on a satellite link.

A satellite in low earth orbit closes at up to about 7.5 km/s at acquisition and recedes just as fast at loss of signal, which on a 435 MHz downlink swings the received frequency by roughly ±10 kHz over a pass. That is far wider than an SSB or a narrow FM channel, so a receiver left on the nominal frequency hears the satellite only briefly in the middle of the pass.

angles = station.look_angles(satellite, Time.utc)
if angles
  tune_to = Kozai::Doppler.downlink(435_000_000.0, angles.range_rate_km_s)
end

Constants

SPEED_OF_LIGHT_KM_S = 299792.458

Speed of light in kilometres per second.

Class methods

downlink(frequency_hz : Float64, range_rate_km_s : Float64) : Float64

The frequency an observer hears when the transmitter radiates frequency_hz and the range is changing at range_rate_km_s.

Range rate is positive while the satellite is receding, so a receding satellite sounds lower — which is the sign convention Frames::LookAngles uses.

NOTE: the classical first-order expression. The relativistic correction at 7.5 km/s is around 3 parts in 10^10, which on a 435 MHz downlink is 0.13 Hz — some four orders of magnitude below the frequency error of the crystal oscillator in any amateur satellite, and far below the error contributed by a few hours of element set age. It is not modelled, and the omission is listed in the README.

Source

downlink(frequency_hz : Float64, angles : Frames::LookAngles) : Float64

Convenience form taking look angles directly.

Source

duplex(downlink_hz : Float64, uplink_hz : Float64, range_rate_km_s : Float64) : Tuple(Float64, Float64)

Doppler on both halves of a duplex link, as a linear transponder needs.

Returns the frequency to listen on and the frequency to transmit on.

Source

maximum_shift(frequency_hz : Float64, maximum_range_rate_km_s : Float64) : Float64

The largest shift a link will see over a pass, in hertz.

Useful for choosing a receiver bandwidth, and for warning that a channel is too narrow to hold the satellite without tuning.

Source

shift(frequency_hz : Float64, range_rate_km_s : Float64) : Float64

How far frequency_hz is shifted, in hertz.

Negative while the satellite is receding.

Source

uplink(frequency_hz : Float64, range_rate_km_s : Float64) : Float64

The frequency to transmit on so that the satellite receives frequency_hz.

The correction is the opposite sign to .downlink: closing on the satellite raises what it hears, so the station must transmit lower.

Source

uplink(frequency_hz : Float64, angles : Frames::LookAngles) : Float64

Convenience form taking look angles directly.

Source