/**
 * chebyshev.ts
 *
 * Chebyshev polynomial evaluation using the Clenshaw recurrence.
 * Used to evaluate SPK Type 2 ephemeris records.
 *
 * All positions are in km (barycentric J2000 equatorial rectangular).
 * Velocities are in km/s.
 */
/**
 * Evaluate a Chebyshev series at normalised argument τ ∈ [-1, +1].
 *
 * Uses the Clenshaw recurrence (numerically stable, O(n)):
 *   b_{n+1} = 0
 *   b_k     = 2τ·b_{k+1} − b_{k+2} + aₖ
 *   result  = τ·b₁ − b₂ + a₀
 */
export declare function evalCheby(coeffs: readonly number[], tau: number): number;
/**
 * Evaluate the derivative dF/dτ of a Chebyshev series.
 *
 * Uses the paired forward recurrences for the polynomials and their derivatives:
 *   T₀ = 1,  T₁ = τ,   Tₖ  = 2τ·Tₖ₋₁ − Tₖ₋₂
 *   T′₀ = 0, T′₁ = 1,  T′ₖ = 2·Tₖ₋₁ + 2τ·T′ₖ₋₁ − T′ₖ₋₂
 *
 * The previous implementation folded a `2k` weight into a Clenshaw-style loop
 * and closed with an unjustified factor of ½. It returned roughly 0.35× the
 * true derivative — Earth's barycentric speed came out as 10.7 km/s instead of
 * 30.2 km/s — which corrupted stellar aberration and every planet's daily
 * motion (and therefore retrograde detection).
 *
 * Records hold ~10–15 coefficients, so the explicit recurrence costs nothing
 * measurable and is far easier to verify than a folded form.
 *
 * To convert to physical velocity: vel = dF/dτ ÷ RADIUS, with RADIUS in seconds.
 */
export declare function evalChebyDeriv(coeffs: readonly number[], tau: number): number;
export interface Vec3 {
    /** km */
    x: number;
    /** km */
    y: number;
    /** km */
    z: number;
    /** km/s */
    vx: number;
    /** km/s */
    vy: number;
    /** km/s */
    vz: number;
}
/**
 * Evaluate an SPK Type 2 coefficient record at ephemeris time `et`.
 *
 * @param record   Flat array of doubles from the SPK data:
 *                 [MID, RADIUS, x₀…xₙ, y₀…yₙ, z₀…zₙ]
 * @param et       Ephemeris time (seconds from J2000.0 TDB)
 */
export declare function evalRecord(record: Float64Array | number[], et: number): Vec3;