# poliastro.core.perturbations¶

## Module Contents¶

### Functions¶

 J2_perturbation(t0, state, k, J2, R) Calculates J2_perturbation acceleration (km/s2) J3_perturbation(t0, state, k, J3, R) Calculates J3_perturbation acceleration (km/s2) atmospheric_drag_exponential(t0, state, k, R, C_D, A_over_m, H0, rho0) Calculates atmospheric drag acceleration (km/s2) atmospheric_drag_model(t0, state, k, R, C_D, A_over_m, model) Calculates atmospheric drag acceleration (km/s2) shadow_function(r_sat, r_sun, R) Determines whether the satellite is in attractor’s shadow, uses algorithm 12.3 from Howard Curtis third_body(t0, state, k, k_third, perturbation_body) Calculates 3rd body acceleration (km/s2) radiation_pressure(t0, state, k, R, C_R, A_over_m, Wdivc_s, star) Calculates radiation pressure acceleration (km/s2)
poliastro.core.perturbations.J2_perturbation(t0, state, k, J2, R)

Calculates J2_perturbation acceleration (km/s2)

$\vec{p} = \frac{3}{2}\frac{J_{2}\mu R^{2}}{r^{4}}\left [\frac{x}{r}\left ( 5\frac{z^{2}}{r^{2}}-1 \right )\vec{i} + \frac{y}{r}\left ( 5\frac{z^{2}}{r^{2}}-1 \right )\vec{j} + \frac{z}{r}\left ( 5\frac{z^{2}}{r^{2}}-3 \right )\vec{k}\right]$

New in version 0.9.0.

Parameters
• t0 (float) – Current time (s)

• state (numpy.ndarray) – Six component state vector [x, y, z, vx, vy, vz] (km, km/s).

• k (float) – gravitational constant, (km^3/s^2)

• J2 (float) – oblateness factor

• R (float) – attractor radius

Note

The J2 accounts for the oblateness of the attractor. The formula is given in Howard Curtis, (12.30)

poliastro.core.perturbations.J3_perturbation(t0, state, k, J3, R)

Calculates J3_perturbation acceleration (km/s2)

Parameters
• t0 (float) – Current time (s)

• state (numpy.ndarray) – Six component state vector [x, y, z, vx, vy, vz] (km, km/s).

• k (float) – gravitational constant, (km^3/s^2)

• J3 (float) – oblateness factor

• R (float) – attractor radius

Note

The J3 accounts for the oblateness of the attractor. The formula is given in Howard Curtis, problem 12.8 This perturbation has not been fully validated, see https://github.com/poliastro/poliastro/pull/398

poliastro.core.perturbations.atmospheric_drag_exponential(t0, state, k, R, C_D, A_over_m, H0, rho0)

Calculates atmospheric drag acceleration (km/s2)

$\vec{p} = -\frac{1}{2}\rho v_{rel}\left ( \frac{C_{d}A}{m} \right )\vec{v_{rel}}$

New in version 0.9.0.

Parameters
• t0 (float) – Current time (s)

• state (numpy.ndarray) – Six component state vector [x, y, z, vx, vy, vz] (km, km/s).

• k (float) – gravitational constant, (km^3/s^2)

• R (float) – radius of the attractor (km)

• C_D (float) – dimensionless drag coefficient ()

• A_over_m (float) – frontal area/mass of the spacecraft (km^2/kg)

• H0 (float) – atmospheric scale height, (km)

• rho0 (float) – the exponent density pre-factor, (kg / km^3)

Note

This function provides the acceleration due to atmospheric drag using an overly-simplistic exponential atmosphere model. We follow Howard Curtis, section 12.4 the atmospheric density model is rho(H) = rho0 x exp(-H / H0)

poliastro.core.perturbations.atmospheric_drag_model(t0, state, k, R, C_D, A_over_m, model)

Calculates atmospheric drag acceleration (km/s2)

$\vec{p} = -\frac{1}{2}\rho v_{rel}\left ( \frac{C_{d}A}{m} \right )\vec{v_{rel}}$

New in version 1.14.

Parameters
• t0 (float) – Current time (s)

• state (numpy.ndarray) – Six component state vector [x, y, z, vx, vy, vz] (km, km/s).

• k (float) – gravitational constant, (km^3/s^2)

• R (float) – radius of the attractor (km)

• C_D (float) – dimensionless drag coefficient ()

• A_over_m (float) – frontal area/mass of the spacecraft (km^2/kg)

• model (a callable model from poliastro.earth.atmosphere) –

Note

This function provides the acceleration due to atmospheric drag, as computed by a model from poliastro.earth.atmosphere

poliastro.core.perturbations.shadow_function(r_sat, r_sun, R)

Determines whether the satellite is in attractor’s shadow, uses algorithm 12.3 from Howard Curtis

Parameters
• r_sat (numpy.ndarray) – position of the satellite in the frame of attractor (km)

• r_sun (numpy.ndarray) – position of star in the frame of attractor (km)

• R (float) – radius of body (attractor) that creates shadow (km)

poliastro.core.perturbations.third_body(t0, state, k, k_third, perturbation_body)

Calculates 3rd body acceleration (km/s2)

$\vec{p} = \mu_{m}\left ( \frac{\vec{r_{m/s}}}{r_{m/s}^3} - \frac{\vec{r_{m}}}{r_{m}^3} \right )$
Parameters
• t0 (float) – Current time (s)

• state (numpy.ndarray) – Six component state vector [x, y, z, vx, vy, vz] (km, km/s).

• k (float) – gravitational constant, (km^3/s^2)

• perturbation_body (a callable object returning the position of the pertubation body that causes the perturbation) –

Note

This formula is taken from Howard Curtis, section 12.10. As an example, a third body could be the gravity from the Moon acting on a small satellite.

poliastro.core.perturbations.radiation_pressure(t0, state, k, R, C_R, A_over_m, Wdivc_s, star)

Calculates radiation pressure acceleration (km/s2)

$\vec{p} = -\nu \frac{S}{c} \left ( \frac{C_{r}A}{m} \right )\frac{\vec{r}}{r}$
Parameters
• t0 (float) – Current time (s)

• state (numpy.ndarray) – Six component state vector [x, y, z, vx, vy, vz] (km, km/s).

• k (float) – gravitational constant, (km^3/s^2)

• R (float) – radius of the attractor

• C_R (float) – dimensionless radiation pressure coefficient, 1 < C_R < 2 ()

• A_over_m (float) – effective spacecraft area/mass of the spacecraft (km^2/kg)

• Wdivc_s (float) – total star emitted power divided by the speed of light (W * s / km)

• star (a callable object returning the position of star in attractor frame) – star position

Note

This function provides the acceleration due to star light pressure. We follow Howard Curtis, section 12.9