Solution (source code)

= Solution

<Spatial coherence> compares the <electric fields> at different positions at a common time; <temporal coherence> compares the field with itself at a delay. Experimentally, they control whether separated apertures or unequal optical paths can form stable <interference> fringes. They are correlation properties, not a requirement that every emitted wave have a deterministic <phase>.

The source diameter is $\alpha=40/206265=1.94\times10^{-4}\,\mathrm{rad}$. At a representative visible <wavelength> $\lambda=550\,\mathrm{nm}$,
$$
\boxed{\ell_\perp\sim\frac{\lambda}{\alpha}=2.8\,\mathrm{mm}.}
$$
For a uniformly bright circular disc, the first visibility zero is at $1.22\lambda/\alpha=3.5\,\mathrm{mm}$; the coefficient depends on the chosen coherence criterion and brightness distribution. Atmospheric <phase> fluctuations can further spoil measured coherence.

For an explicitly assumed broad visible band from $400$ to $700\,\mathrm{nm}$, the <frequency> span is $\Delta\nu=c(1/\lambda_{\min}-1/\lambda_{\max})=3.21\times10^{14}\,\mathrm{Hz}$. Consequently
$$
\boxed{\ell_\parallel\sim\frac c{\Delta\nu}\simeq0.93\,\mathrm{\mu m},\qquad
\tau_c\sim\frac1{\Delta\nu}\simeq3.1\,\mathrm{fs}.}
$$
Thus broadband planetary <light> has millimetre-scale transverse and micrometre-scale longitudinal coherence. The receiver band is not supplied: a narrow filter would increase the <temporal coherence> length, so this is a stated broadband estimate, not a unique source-only constant.