CL_op_incdotSsoCirc

Description

• Long-term (that is doubly averaged) time derivative of inclination due to thirdbody perturbation for a circular and Sun-synchronous orbit.

  The formula is the result of an analytical calculation assuming a simplified model for the orbit of the perturbing body (circular orbit, constant inclination).

  

  Notes:

  - Inclination can be [] or not specified in which case it is recomputed.

  - The function could theoretically be used for another body than the Sun, provided the orbit plane (RAAN) rotates as the same angular rate as the perturbing body.

  - The default value used for the apparent inclination of the orbit of the perturbing body is the value at J2000 in ECI (23.44 deg). In reality the value is not constant: there is a long-term drift of about -0.014 deg/century and variations of maximum amplitude about 0.005 deg.

Parameters

mltan:

Mean local time of the ascending node [h] (1xN or 1x1)

sma:

Mean semi-major axis [m] (1xN or 1x1)

inc:

(optional) Mean inclination [rad]. Default is []. (1xN or 1x1)

mu_b:

(optional) Gravitational constant of perturbing body [m^3/s^2]. Default is %CL_body.Sun.mu (1x1)

r_b:

(optional) Distance from central body to perturbing body [m]. Default is %CL_au. (1x1 or 1xN)

inc_b:

(optional) Inclination of orbit of perturbing body [rad]. Default value is 23.44 deg. (1x1 or 1xN)

er:

(optional) Equatorial radius [m]. Default is %CL_eqRad.

mu:

(optional) Gravitational constant of central body [m^3/s^2]. Default is %CL_mu

j2:

(optional) Second zonal harmonic term. Default is %CL_j1jn(2)

rotr_pla_sun :

(optional) Mean apparent rotation rate of the Sun around the planet. Default is %CL_rotrBodySun

incdot:

Time derivative of inclination [rad/s] (1xN)

Examples

mltan = 0 : 0.1 : 24; // hours sma = 6378.e3 + 700.e3; // m // Inclination average time derivative (rad/s) incdot = CL_op_incdotSsoCirc(mltan, sma); // Plot result (deg/year) scf(); plot(mltan, incdot * (180/%pi) * 86400 * 365.25);