= Solution
The <wavelength> at $12\,\mathrm{GHz}$ is $\lambda=c/f\simeq0.0250\,\mathrm m$. For an ideal circular <aperture> of <diameter> $D=0.850\,\mathrm m$, the <Rayleigh criterion> places one source at the first minimum of the other's <Airy disk>:
$$
\boxed{\theta_R=1.22\frac\lambda D=0.03588\,\mathrm{rad}=2.056^\circ.}
$$
The customary full-ring packing estimate for the number of resolvable positions in a <geostationary orbit> is
$$
\boxed{N_{\max}\simeq\left\lfloor\frac{2\pi}{\theta_R}\right\rfloor=175.}
$$
This is an ideal angular-packing estimate. It identifies apparent angular spacing with spacing around the orbital ring and disregards Earth's occultation and station location. An individual ground station cannot see the whole ring; exact conversion from orbital longitude to sky direction requires its location and the orbital <radius>. Also, a practical tapered <antenna> illumination changes the ideal circular-<aperture> response.
Back to article page
