Sidereon.Doppler (Sidereon v0.8.0)

Doppler shift calculation for satellite-ground links.

Given a satellite's GCRS state vector (position and velocity), a ground station, and a carrier frequency, computes the radial velocity (range rate) and the resulting Doppler shift.

Summary

Types

datetime()

gcrs_state()

ground_station()

result()

vec3()

Functions

shift(map, datetime, ground_station, frequency_hz)

Compute Doppler shift for a satellite-ground link.

Types

datetime()

@type datetime() ::
  DateTime.t()
  | {{integer(), integer(), integer()}, {integer(), integer(), integer()}}

gcrs_state()

@type gcrs_state() :: %{position: vec3(), velocity: vec3()}

ground_station()

@type ground_station() :: %{
  latitude: number(),
  longitude: number(),
  altitude_m: number()
}

result()

@type result() :: %{
  range_rate_km_s: float(),
  doppler_hz: float(),
  doppler_ratio: float()
}

vec3()

@type vec3() :: {number(), number(), number()}

Functions

shift(map, datetime, ground_station, frequency_hz)

@spec shift(gcrs_state(), datetime(), ground_station(), number()) :: result()

Compute Doppler shift for a satellite-ground link.

Parameters

gcrs_state - map with :position {x, y, z} (km) and :velocity {vx, vy, vz} (km/s) in GCRS
datetime - observation time (DateTime or {{y,m,d},{h,m,s}} tuple)
ground_station - %{latitude: deg, longitude: deg, altitude_m: meters}
frequency_hz - carrier frequency in Hz

Returns

A map with:

:range_rate_km_s - radial velocity in km/s (positive = approaching)
:doppler_hz - Doppler shift in Hz (positive = frequency increase)
:doppler_ratio - dimensionless Doppler ratio (-range_rate / c)

Example

gcrs = Sidereon.teme_to_gcrs(teme, datetime)
station = %{latitude: 40.0, longitude: -74.0, altitude_m: 0.0}
result = Sidereon.Doppler.shift(gcrs, datetime, station, 437.0e6)
result.doppler_hz  # => ~10_000.0 (for typical LEO pass)