Jacchia-Roberts 1971

This is an analytic atmospheric model based on the Jacchia's 1970 model. It was published in:

Roberts, C. E (1971). An analytic model for upper atmosphere densities based upon Jacchia's 1970 models. Celestial mechanics, Vol. 4 (3-4), p. 368-377, DOI: 10.1007/BF01231398.

Although it is old, this model is still used for some applications, like computing the estimated reentry time for an object on low Earth orbits.

In this package, we can evaluate the model using the following functions:

AtmosphericModels.jr1971(instant::DateTime, ϕ_gd::Number, λ::Number, h::Number[, F10::Number, F10ₐ::Number, Kp::Number]) -> JR1971Output{Float64}
AtmosphericModels.jr1971(jd::Number, ϕ_gd::Number, λ::Number, h::Number[, F10::Number, F10ₐ::Number, Kp::Number]) -> JR1971Output{Float64}

where:

• jd::Number: Julian day to compute the model.
• instant::DateTime: Instant to compute the model represent using DateTime.
• ϕ_gd::Number: Geodetic latitude [rad].
• λ::Number: Longitude [rad].
• h::Number: Altitude [m].
• F10::Number: 10.7-cm solar flux [sfu].
• F10ₐ::Number: 10.7-cm averaged solar flux, 81-day centered on input time [sfu].
• Kp::Number: Kp geomagnetic index with a delay of 3 hours.

If we omit all space indices, the system tries to obtain them automatically for the selected day jd or instant. However, the indices must be already initialized using the function SpaceIndices.init().

This function return an object of type JR1971Output{Float64} that contains the following fields:

• total_density::T: Total atmospheric density [1 / m³].
• temperature::T: Temperature at the selected position [K].
• exospheric_temperature::T: Exospheric temperature [K].
• N2_number_density::T: Number density of N₂ [1 / m³].
• O2_number_density::T: Number density of O₂ [1 / m³].
• O_number_density::T: Number density of O [1 / m³].
• Ar_number_density::T: Number density of Ar [1 / m³].
• He_number_density::T: Number density of He [1 / m³].
• H_number_density::T: Number density of H [1 / m³].

Examples

julia> AtmosphericModels.jr1971(
           DateTime("2018-06-19T18:35:00"),
           deg2rad(-22),
           deg2rad(-45),
           700e3,
           79,
           73.5,
           1.34
       )Jacchia-Roberts 1971 Atmospheric Model Result:
      Total density :     9.6849e-15  kg / m³
        Temperature :         832.02  K
   Exospheric Temp. :         832.02  K
  N₂ number density :     2.8435e+07  1 / m³
  O₂ number density :         174223  1 / m³
  O  number density :    1.41391e+11  1 / m³
  Ar number density :        8.97257  1 / m³
  He number density :    8.77389e+11  1 / m³
  H  number density :    5.70278e+10  1 / m³

julia> SpaceIndices.init()
julia> AtmosphericModels.jr1971(DateTime("2022-06-19T18:35:00"), deg2rad(-22), deg2rad(-45), 700e3)Jacchia-Roberts 1971 Atmospheric Model Result:
      Total density :    6.03113e-14  kg / m³
        Temperature :        1108.65  K
   Exospheric Temp. :        1108.69  K
  N₂ number density :    3.28087e+09  1 / m³
  O₂ number density :    4.11164e+07  1 / m³
  O  number density :    1.88625e+12  1 / m³
  Ar number density :        8826.28  1 / m³
  He number density :    1.50861e+12  1 / m³
  H  number density :    9.14578e+09  1 / m³

If we use the automatic space index fetching mechanism, it is possible to obtain the fetched values by turning on the debugging logs according to the Julia documentation:

julia> using Logging
julia> with_logger(ConsoleLogger(stderr, Logging.Debug)) do
           AtmosphericModels.jr1971(DateTime("2022-06-19T18:35:00"), deg2rad(-22), deg2rad(-45), 700e3)
       end┌ Debug: JR1971 - Fetched Space Indices
│   Daily F10.7           : 143.6 sfu
│   81-day averaged F10.7 : 126.9604938271605 sfu
│   3-hour delayed Kp     : 1.333
└ @ SatelliteToolboxAtmosphericModels.AtmosphericModels ~/work/SatelliteToolboxAtmosphericModels.jl/SatelliteToolboxAtmosphericModels.jl/src/jr1971/jr1971.jl:75
Jacchia-Roberts 1971 Atmospheric Model Result:
      Total density :    6.03113e-14  kg / m³
        Temperature :        1108.65  K
   Exospheric Temp. :        1108.69  K
  N₂ number density :    3.28087e+09  1 / m³
  O₂ number density :    4.11164e+07  1 / m³
  O  number density :    1.88625e+12  1 / m³
  Ar number density :        8826.28  1 / m³
  He number density :    1.50861e+12  1 / m³
  H  number density :    9.14578e+09  1 / m³