# 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(t0, state, k, C_D, A_over_m, rho) Calculates atmospheric drag acceleration (km/s2) third_body(t0, state, k, k_third, perturbation_body) Calculate third 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 () – Six component state vector [x, y, z, vx, vy, vz] (km, km/s).

• k (float) – Standard Gravitational parameter. (km^3/s^2)

• J2 (float) – Oblateness factor

• R (float) – Attractor radius

Notes

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

• k (float) – Standard Gravitational parameter. (km^3/s^2)

• J3 (float) – Oblateness factor

• R (float) – Attractor radius

Notes

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

• k (float) – Standard Gravitational parameter (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) – Exponent density pre-factor, (kg / km^3)

Notes

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(t0, state, k, C_D, A_over_m, rho)

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

• k (float) – Standard Gravitational parameter (km^3/s^2)

• C_D (float) – Dimensionless drag coefficient ()

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

• rho (float) – Air density at corresponding state (kg/km^3)

Notes

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

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

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

• k (float) – Standard Gravitational parameter of the attractor (km^3/s^2).

• k_third (float) – Standard Gravitational parameter of the third body (km^3/s^2).

• perturbation_body (callable) – A callable object returning the position of the body that causes the perturbation in the attractor frame.

Notes

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)

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

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

• k (float) – Standard Gravitational parameter (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 (kg km/s^2).

• star (callable) – A callable object returning the position of radiating star in the attractor frame.

Notes

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