$LastChangedDate: 27-Juil-2011 $

# CL_ip_insertionDv

Delta-V needed for an insertion around a planet

## Calling Sequence

       [dv, ecc, tanoe] = CL_ip_insertionDv(vinf, rph, sma [, tanoh, mu])

## Description

- Computes the delta-v needed for the transfer from an hyperbolic orbit to an elliptical orbit.

  The insertion maneuver is tangential, i.e. the delta-V is parallel to the velocity vector on the hyperbolic orbit.

  The initial orbit is defined by its velocity at infinity (vinf) and periapsis radius (rph).

  The final orbit is defined by its semi major axis(sma).

  The true anomaly of the maneuver on the initial orbit (tanoh) can optionally be specified. By default tanoh=0 (meaning 'at the periapsis').

  The planet is defined by its gravitational constant mu (default is %CL_mu)

## Parameters

vinf:

  Velocity on hyperbolic orbit at infinity [m/s]. (1xN)

rph:

  Periapsis radius of hyperbolic orbit [m]. (1xN)

sma:

  Semi-major axis of target (elliptical) orbit [m]. (1xN)

tanoh:

  (optional) True anomaly of the maneuvre (on the hyperbolic orbit) [rad]. Default value is 0. (1xN)

mu:

  (optional) gravitational constant [m3/s2]. Default value is %CL_mu.

dv:

  Norm of the delta-v. (1xN)

ecc:

  Eccentricity of the final (elliptical) orbit. (1xN)

tanoe:

  True anomaly on the elliptical orbit at the time of the maneuver [rad]. (1xN)

## Authors

- CNES - DCT/SB

## Examples

    // Insertion around Earth:
    vinf = [5 , 6] * 1.e3;
    rph = [%CL_eqRad+250.e3 , %CL_eqRad+500.e3];
    sma = [%CL_eqRad+350.e3 , %CL_eqRad+700.e3];
    [dv, ecc, tanoe] = CL_ip_insertionDv(vinf,rph, sma)

    // Insertion around Mars:
    global %CL_planetC;
    vinf = [5 , 6] * 1.e3;
    eqrad_mars = %CL_planetC.mars.eqRad;
    rph = [eqrad_mars+250.e3 , eqrad_mars+500.e3];
    sma = [eqrad_mars+350.e3 , eqrad_mars+700.e3];
    tanoh = [0, 0.1]; // radians
    mu_mars = %CL_planetC.mars.mu;
    [dv,ecc,tanoe] = CL_ip_insertionDv(vinf,rph,sma,tanoh,mu_mars)