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A deep dive into optimizing the SGP4 satellite position prediction algorithm using Zig's SIMD capabilities. The author achieved 11-13M propagations per second in native Zig (2x faster than scalar implementations) and ~7M/s through Python bindings by leveraging branchless hot paths, compile-time precomputation, vectorized operations, and cache-conscious tiling. The implementation handles three propagation modes: time-batched (single satellite, multiple times), satellite-batched (multiple satellites, single time), and constellation mode (many satellites, many times). Includes detailed explanations of SIMD thinking patterns, custom atan2 polynomial approximation, struct-of-arrays data layout, and performance comparisons against Rust sgp4 and heyoka.py implementations.