Dense low-Earth-orbit (LEO) networks increasingly reuse spectrum across moving satellites and overlapping beams, making a spatial radio map essential for interference diagnosis and coordination. Constructing such a map from sparse ground power measurements is difficult because the active satellite subset and its cardinality are unknown, candidate footprints can be highly coherent, and beam pointing, width, effective power, Doppler, and background must be inferred jointly. Known ephemerides do more than enumerate visible candidates. Propagated positions determine candidate-specific ranges, viewing geometry, and spatial footprints, while radial velocities induce distinct time-frequency signatures. Their joint spatial--Doppler structure rejects candidates whose geometry or time--frequency signature conflicts with the observations before continuous beam inference. SateBeam therefore screens all candidates through Doppler-resolved nonnegative fitting. GPU-accelerated grid correlations initialize continuous off-grid refinement; a Gamma-likelihood Bayesian information criterion (BIC) selects model cardinality, and backward deletion and exchange repair greedy support errors. Across paired real-ephemeris scenarios, SateBeam recovers the exact support in every case and reduces independent-query RMSE from $0.655$ to $0.050$ dB relative to orthogonal matching pursuit, with consistent advantages under model mismatch and larger candidate sets. The code is available at https://github.com/UNIC-Lab/SateBeam.

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