Several quality-of-life and correctness upgrades across the multi-body simulation and Hohmann transfer visualisation.

Multi-body orbital mechanics (main.py)

• Added Saturn (5.683×10²⁶ kg, 9.537 AU, 9,690 m/s, goldenrod) as 6th planet
• Pause/Play button — freeze simulation state at any frame
• Elapsed time display — top-left overlay showing simulation time in years, derived from dt for accuracy (elapsed_days += dt / 86400)
• Planet name labels — each planet dot now annotated inline
• Reset now also clears elapsed_days
• Repositioned Sun Gravity button to avoid overlap with new Pause/Play button

Hohmann transfer visualisation (visualisation.py)

Replaced the inaccurate Δv ≈ |v_orbit − v_surface| approximation with the correct two-burn vis-viva formula:

v_perigee = np.sqrt(mu * (2 / r1 - 1 / a_transfer))
v_apogee  = np.sqrt(mu * (2 / r2 - 1 / a_transfer))
delta_v1  = np.abs(v_perigee - v_circ1)
delta_v2  = np.abs(v_circ2  - v_apogee)

Now plots Δv₁, Δv₂, and total Δv separately with a legend. LEO→GEO result: ~3.93 km/s (matches textbook).

README (multi-body-orbital-mechanics/README.md)

Fixed duplicated "Install dependencies" step — second step now correctly reads "Run the simulation."

Housekeeping

Added .gitignore to exclude __pycache__ bytecode.

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