= Earth-rotation aperture synthesis
{c}
Earth-rotation aperture synthesis uses <Earth>'s changing orientation to vary a fixed ground baseline's projection onto the <plane of the sky>. In two dimensions, $u$ and $v$ are the components of $\mathbf b_\perp/\lambda$ along two perpendicular sky tangents. Tracking one field traces a curve in this $(u,v)$ plane; changing the physical baseline supplies other curves. A track samples <Fourier transform> coordinates, rather than the brightness along a track across the sky.
For a horizontal east–west baseline of length $B$, choose the sky-axis signs so that
$$
u=\frac{B}{\lambda}\cos H,\qquad v=\frac{B}{\lambda}\sin\delta\sin H,
$$
where $H$ is <hour angle> and $\delta$ is <declination>. The ellipse follows by projecting the rotating baseline onto sky tangents. At a <celestial pole> it is a circle; near the <celestial equator> its minor axis collapses. Thus the same ground layout constrains different sky directions unequally. Rotation improves coverage, but does not fill every <spatial frequency>, and synthesis across many hours assumes that the source changes negligibly during that interval.
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