# Anomalies

There are three types of anomalies[1] that can be used to describe the position of the satellite in the orbit plane with respect to the argument of perigee:

• The mean anomaly (M);
• The eccentric anomaly (E); and
• The true anomaly (f).

This package contains the following functions that can be used to convert one to another:

function M_to_E(e::Number, M::Number, tol::Number = 1e-10)
function M_to_f(e::Number, M::Number, tol::Number = 1e-10)
function E_to_f(e::Number, E::Number)
function E_to_M(e::Number, E::Number)
function f_to_E(e::Number,f::Number)
function f_to_E(orb::Orbit)
function f_to_M(e::Number, f::Number)
function f_to_M(orb::Orbit)

where:

• M is the mean anomaly [rad];
• E is the eccentric anomaly [rad];
• f is the true anomaly [rad];
• e is the eccentricity;
• orb is an instance of the structure Orbit;
• tol is used to select the tolerance for the cases in which the conversion is performed by a numerical method, such as the Newton-Raphson algorithm.

All the returned values are in [rad].

julia> M_to_E(0.04, pi/4)
0.8144932819286269

julia> M_to_f(0.04, pi/4)
0.8440031124631683

julia> f_to_M(0.04, pi/4)
0.7300148523821107

julia> M_to_f(0, 0.343)
0.3430000000000001

julia> M_to_f(0.04, 0.343)
0.37122803399203647
• 1In astronomy, anomaly is an angle.