sphere_of_influence_earth_moon Function

public pure function sphere_of_influence_earth_moon(mu_primary, mu_secondary, r, r_sp) result(r_soi)

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

Notes

  • r and r_sp should be in the same inertial frame.
  • The mass of the spacecraft is neglected.

See also

  • R.H. Battin, "An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition", AIAA, 1999.
  • This is the more complex formula, on p. 397 of Battin, which is better for the Earth/Moon system.

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), dimension(3) :: r

vector from the secondary body to the spacecraft [km]
real(kind=wp), intent(in), dimension(3) :: r_sp

vector from the secondary to the primary body [km]

Return Value real(kind=wp)

sphere of influence radius of the secondary body [km]


Calls

proc~~sphere_of_influence_earth_moon~~CallsGraph proc~sphere_of_influence_earth_moon orbital_mechanics_module::sphere_of_influence_earth_moon proc~angle_between_vectors vector_module::angle_between_vectors proc~sphere_of_influence_earth_moon->proc~angle_between_vectors proc~cross vector_module::cross proc~angle_between_vectors->proc~cross

Source Code

    pure function sphere_of_influence_earth_moon(mu_primary, mu_secondary, r, r_sp) 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),dimension(3),intent(in) :: r            !! vector from the secondary body to the spacecraft [km]
    real(wp),dimension(3),intent(in) :: r_sp         !! vector from the secondary to the primary body [km]
    real(wp)                         :: r_soi        !! sphere of influence radius of the secondary body [km]

    real(wp) :: r_mag, r_sp_mag, alpha, ca, ca2, denom

    r_mag    = norm2(r)
    r_sp_mag = norm2(r_sp)

    if (mu_primary>zero .and. mu_secondary>zero .and. r_mag>zero .and. r_sp_mag>zero) then

        alpha = angle_between_vectors(r,r_sp)
        ca    = cos(alpha)
        ca2   = ca * ca

        denom = (mu_secondary**2/mu_primary**2)**(one/five)*(one+three*ca2)**(one/ten) + &
                (two/five)*ca*((one+six*ca2)/(one+three*ca2))

        r_soi = r_sp_mag / denom

    else
        r_soi = zero
    end if

    end function sphere_of_influence_earth_moon