sphere_of_influence Function

public pure function sphere_of_influence(mu_primary, mu_secondary, r_ps) result(r_soi)

Computes the sphere-of-influence radius of the secondary body.

See also

  • R.H. Battin, "An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition", AIAA, 1999.
  • This is the approximate formula (8.74 from Battin).

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: mu_primary

primary body gravitational parameter [km^3/s^2]
real(kind=wp), intent(in) :: mu_secondary

secondary body gravitational parameter [km^3/s^2]
real(kind=wp), intent(in) :: r_ps

distance between the two bodies [km]

Return Value real(kind=wp)

sphere of influence radius [km]


Source Code

    pure function sphere_of_influence(mu_primary, mu_secondary, r_ps) result(r_soi)

    implicit none

    real(wp),intent(in)   :: mu_primary   !! primary body gravitational parameter [km^3/s^2]
    real(wp),intent(in)   :: mu_secondary !! secondary body gravitational parameter [km^3/s^2]
    real(wp),intent(in)   :: r_ps         !! distance between the two bodies [km]
    real(wp)              :: r_soi        !! sphere of influence radius [km]

    real(wp),parameter :: two_fifths = two/five

    if (mu_primary>zero .and. mu_secondary>zero .and. r_ps>zero) then
        r_soi = r_ps * (mu_secondary/mu_primary)**two_fifths
    else
        r_soi = zero
    end if

    end function sphere_of_influence