SPICE Analysis

Objective:

This study investigates the one-year trajectory of a space station orbiting Mars by applying the two-body equations of motion and comparing the results with the trajectories of Mars' moons, Phobos and Deimos, which were plotted using NASA's SPICE software in MATLAB. By calculating orbital elements at initial points for the space station, Phobos, and Deimos using both analytical methods and SPICE, the study evaluates the accuracy and reliability of these approaches.

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Technical Details:

1. Trajectory Computation and Simulation:

The study focuses on analyzing the trajectory of a space station orbiting Mars and comparing it with Mars' moons, Phobos and Deimos, over a one-year period (January 1, 2024, to December 31, 2024).
MATLAB was employed to numerically solve the two-body problem using the ODE45 solver, incorporating Mars' gravitational parameter (μ = 4.28284e+04 km³/s²) and initial conditions for the space station.

2. Orbital Elements Calculation:

Orbital elements for the space station and Mars' moons were determined using both analytical equations and SPICE software, allowing for a comparative analysis.
Key Orbital Elements Computed:
- Angular Momentum (h)
- Semi-major Axis (a)
- Inclination (i)
- RAAN (Ω)
- Eccentricity (e)
- Argument of Perigee (ω)
- True Anomaly (θ)

3. Software Implementation and Kernel Integration:

SPICE software was utilized to calculate orbital elements and simulate trajectories, with kernels such as "de430.bsp", "mar097.bsp", and "naif0012.tls.pc" loaded to represent Mars' moons accurately.
The frame of reference for simulations was MARSIAU, and Mars' barycenter was used as the observer.

4. Results and Comparison:

Both the analytical and SPICE-derived orbital elements showed high consistency, with the highest percent difference being 1.72% for Phobos' semi-major axis.
The overall accuracy between methods confirmed the reliability of the SPICE software in predicting orbital elements, with most differences being negligible.

5. Plotting and Visualization:

MATLAB was used to generate 3D plots of the space station's trajectory around Mars, alongside Phobos and Deimos. Despite a visualization issue with the space station's orbit (displayed as a disk rather than a path), the orbital elements calculated were consistent and accurate.

Results:

The study successfully demonstrated the effectiveness of both analytical methods and SPICE software in determining orbital elements. The minimal discrepancies between methods affirm the validity of the calculations, though the MATLAB visualization warrants further investigation.