Spacecraft Geodetic Translation Software

SWITCH TO API

Description

The Spacecraft Geodetic Translation Software converts spacecraft inertial state vectors into geodetic coordinates. This module transforms position and velocity from the Planet-Centered Inertial (PCI) frame to the Planet-Centered Planet-Fixed (PCPF) frame, and then computes geodetic latitude, longitude, and altitude. These outputs are essential for ground track visualization, communication link geometry, and any analysis requiring Earth-fixed or geographic reference frames.

---

Example Use Cases

• Ground Track Computation: Determine the sub-satellite point for coverage analysis and mission planning.
• Communication Geometry: Calculate spacecraft position relative to ground stations in Earth-fixed coordinates.
• Geolocation: Provide geodetic coordinates for payload pointing or Earth observation applications.

---

Module Implementation

The Spacecraft Geodetic Translation Software is a Software component that performs coordinate transformations from inertial to geodetic reference frames.

Coordinate Frames

The module operates with three coordinate frames:

Frame	Description
PCI ($\mathcal{N}$)	Planet-Centered Inertial frame (J2000)
PCPF ($\mathcal{P}$)	Planet-Centered Planet-Fixed frame (rotating with planet)
Geodetic	Latitude, longitude, and altitude above reference ellipsoid

PCI to PCPF Transformation

The spacecraft position relative to the planet center is first computed in the inertial frame:

$${\mathbf{r}}_{B/P}^{\mathcal{N}}={\mathbf{r}}_{B/N}^{\mathcal{N}}-{\mathbf{r}}_{P/N}^{\mathcal{N}}$$ $${\mathbf{v}}_{B/P}^{\mathcal{N}}={\mathbf{v}}_{B/N}^{\mathcal{N}}-{\mathbf{v}}_{P/N}^{\mathcal{N}}$$

The position and velocity are then transformed to the planet-fixed frame using the planet’s rotation state:

$${\mathbf{r}}_{B/P}^{\mathcal{P}}=[PN]{\mathbf{r}}_{B/P}^{\mathcal{N}}$$ $${\mathbf{v}}_{B/P}^{\mathcal{P}}=[PN]{\mathbf{v}}_{B/P}^{\mathcal{N}}+[\dot{PN}]{\mathbf{r}}_{B/P}^{\mathcal{N}}$$

where $[PN]$ is the direction cosine matrix from the inertial frame to the planet-fixed frame and $[\dot{PN}]$ accounts for the planet’s rotation rate.

PCPF to Geodetic Conversion

The geodetic coordinates are computed from the PCPF position vector. For a spherical planet model:

$$\lambda =\arctan \left(\frac{y}{x}\right)$$ $$\varphi =\arctan \left(\frac{z}{\sqrt{x^2+y^2}}\right)$$ $$h=\sqrt{x^2+y^2+z^2}-R$$

where:

• $\lambda$ is the geodetic longitude [rad]
• $\varphi$ is the geodetic latitude [rad]
• $h$ is the altitude above the reference sphere [m]
• $R$ is the planet’s equatorial radius [m]
• $(x,y,z)$ are the PCPF position components

---

Assumptions/Limitations

• The planet is modeled as a sphere; ellipsoidal Earth models (WGS-84) are not implemented.
• Both planet state and spacecraft state messages must be connected for the module to produce output.
• The transformation uses the instantaneous planet rotation state; no interpolation is performed.
• Geodetic latitude equals geocentric latitude for the spherical