Library

equation_of_time(t::Union{Number, DateTime})

Compute the difference between the Sun apparent local time and the Sun mean local time [rad], which is called Equation of Time, at the time t, which can be represented by a Julian Day or DateTime. The algorithm was adapted from [1, p. 178, 277-279].

References

• [1] Vallado, D. A (2013). Fundamentals of Astrodynamics and Applications. 4th ed. Microcosm Press, Hawthorne, CA.

ltan_to_raan(ltan::Union{Number, Time}, t::Union{Number, DateTime}) -> Float64

Compute the RAAN [0, 2π] [rad] so that the local time of ascending node (LTAN) is ltan at instant t [UT1].

ltan can be represented as a Number, indicating the hour, or by a Time object.

t can be represented as a Julian Day [UT1] or DateTime [UT1].

ltdn_to_raan(ltdn::Union{Number, Time}, t::Union{Number, DateTime}) -> Float64

Compute the RAAN [0, 2π] [rad] so that the local time of descending node (LTAN) is ltdn at instant t [UT1].

ltdn can be represented as a Number, indicating the hour, or by a Time object.

t can be represented as a Julian Day [UT1] or DateTime [UT1].

orbital_angular_velocity(a::Number, e::Number, i::Number; kwargs...) -> T
orbital_angular_velocity(orb::Orbit{Tepoch, T}; kwargs...) where {Tepoch<:Number, T<:Number} -> T

Compute the angular velocity [rad/s] of an object in an orbit with semi-major axis a [m], eccentricity e, and inclination i [rad]. The orbit can also be specified by orb (see Orbit).

Keywords

• perturbation::Symbol: Symbol to select the perturbation terms that will be used. (Default: :J2)
• m0::Number: Standard gravitational parameter for Earth [m³ / s²]. (Default = GM_EARTH)
• J2::Number: J₂ perturbation term. (Default = EGM2008J2)
• J4::Number: J₄ perturbation term. (Default = EGM2008J4)
• R0::Number: Earth's equatorial radius [m]. (Default = EARTHEQUATORIALRADIUS)

Perturbations

The keyword argument perturbation can be used to select the perturbation terms that will be considered in the computation. The possible values are:

• :J0: Consider a Keplerian orbit.
• :J2: Consider the perturbation terms up to J2.
• :J4: Consider the perturbation terms J2, J4, and J2².

If perturbation is omitted, it defaults to :J2.

orbital_angular_velocity_to_semimajor_axis(angvel::Number, e::Number, i::Number; kwargs...) -> T, Bool

Compute the semi-major axis [m] that will provide an angular velocity angvel [rad / s] in an orbit with eccentricity e and inclination i [rad].

Notice that the angular velocity angvel is related to the nodal period, i.e. the time between two consecutive passages by the ascending node.

Keywords

• max_iterations::Int: Maximum number of iterations allowed in the Newton-Raphson algorithm. (Default = 20)
• perturbation::Symbol: Symbol to select the perturbation terms that will be used. (Default: :J2)
• tolerance::Union{Nothing, Number}: Residue tolerances to verify if the numerical method has converged. If it is nothing, √eps(T) will be used, where T is the internal type for the computations. Notice that the residue function unit is [deg / min]. (Default = nothing)
• m0::Number: Standard gravitational parameter for Earth [m³ / s²]. (Default = GM_EARTH)
• J2::Number: J₂ perturbation term. (Default = EGM2008J2)
• J4::Number: J₄ perturbation term. (Default = EGM2008J4)
• R0::Number: Earth's equatorial radius [m]. (Default = EARTHEQUATORIALRADIUS)

Returns

• T: Semi-major axis [m].
• Bool: true if the numerical method converged, false otherwise.

Perturbations

The keyword argument perturbation can be used to select the perturbation terms that will be considered in the computation. The possible values are:

• :J0: Consider a Keplerian orbit.
• :J2: Consider the perturbation terms up to J2.
• :J4: Consider the perturbation terms J2, J4, and J2².

If perturbation is omitted, it defaults to :J2.

orbital_period(a::Number, e::Number, i::Number; kwargs...) -> T
orbital_period(orb::Orbit{Tepoch, T}; kwargs...) where {Tepoch<:Number, T<:Number} -> T

Compute the orbital period [s] of an object in an orbit with semi-major axis a [m], eccentricity e, and inclination i [rad]. The orbit can also be specified by orb (see Orbit).

Keywords

• perturbation::Symbol: Symbol to select the perturbation terms that will be used. (Default: :J2)
• m0::Number: Standard gravitational parameter for Earth [m³ / s²]. (Default = GM_EARTH)
• J2::Number: J₂ perturbation term. (Default = EGM2008J2)
• J4::Number: J₄ perturbation term. (Default = EGM2008J4)
• R0::Number: Earth's equatorial radius [m]. (Default = EARTHEQUATORIALRADIUS)

Perturbations

The keyword argument perturbation can be used to select the perturbation terms that will be considered in the computation. The possible values are:

• :J0: Consider a Keplerian orbit.
• :J2: Consider the perturbation terms up to J2.
• :J4: Consider the perturbation terms J2, J4, and J2².

If perturbation is omitted, it defaults to :J2.

raan_time_derivative(a::Number, e::Number, i::Number; kwargs...) -> T

Compute the time derivative of the right ascension of the ascending node (RAAN) [rad / s] in an orbit with semi-major axis a [m], eccentricity e, and inclination i [rad]. The orbit can also be specified by orb (see Orbit).

Keywords

• perturbation::Symbol: Symbol to select the perturbation terms that will be used. (Default: :J2)
• m0::Number: Standard gravitational parameter for Earth [m³ / s²]. (Default = GM_EARTH)
• J2::Number: J₂ perturbation term. (Default = EGM2008J2)
• J4::Number: J₄ perturbation term. (Default = EGM2008J4)
• R0::Number: Earth's equatorial radius [m]. (Default = EARTHEQUATORIALRADIUS)

Perturbations

The keyword argument perturbation can be used to select the perturbation terms that will be considered in the computation. The possible values are:

• :J0: Consider a Keplerian orbit.
• :J2: Consider the perturbation terms up to J2.
• :J4: Consider the perturbation terms J2, J4, and J2².

If perturbation is omitted, it defaults to :J2.

raan_to_ltan(raan::Number, t::Union{Number, DateTime}) -> Float64

Compute the local time of the ascending node (LTAN) given the raan at instant t [UT1].

t can be represented as a Julian Day [UT1] or DateTime [UT1].

raan_to_ltdn(raan::Number, t::Union{Number, DateTime}) -> Float64

Compute the local time of the ascending node (LTDN) given the raan at instant t [UT1].

t can be represented as a Julian Day [UT1] or DateTime [UT1].