Defines the circular equatorial orbit model.
EquatorialOrbit¶
@dataclass(frozen=True)
class EquatorialOrbit:
r: float # Orbital radius [m]
mu: float = 3.986e14 # Earth gravitational parameter
nu_initial: float = 0.0 # Initial true anomaly [rad]Properties¶
n- Mean motion [rad/s]: \(n = \sqrt{\mu/r^3}\)period- Orbital period [s]: \(T = 2\pi/n\)
Methods¶
get_state(t)¶
Get satellite state at time \(t\).
def get_state(self, t: float) -> OrbitState:Returns: Position and velocity in ECI frame.
\[
\mathbf{r}(t) = r \begin{bmatrix} \cos\nu \\ \sin\nu \\ 0 \end{bmatrix}
\]
Where \(\nu = \nu_0 + n \cdot t\).
get_lvlh_basis(t)¶
Get LVLH basis vectors at time \(t\).
def get_lvlh_basis(self, t: float) -> tuple[np.ndarray, np.ndarray, np.ndarray]:Returns: (x_lvlh, y_lvlh, z_lvlh) in ECI coordinates.
For equatorial orbit:
\[
\mathbf{x}_L = \begin{bmatrix} -\sin\nu \\ \cos\nu \\ 0 \end{bmatrix}, \quad
\mathbf{y}_L = \begin{bmatrix} 0 \\ 0 \\ -1 \end{bmatrix}, \quad
\mathbf{z}_L = \begin{bmatrix} -\cos\nu \\ -\sin\nu \\ 0 \end{bmatrix}
\]