How many exhaust photons struck Frank’s floating telescope?

We know Unexpected Finger's exhaust flux, as measured at Earth, was
8×10^{‑8}*W*/*m*^{2}.
This means each square meter of Earth was hit by photons with total energy of
8×10^{‑8}*J/S* .
We also know each photon delivered
1.9×10^{‑10}*J*, so each square meter received
(8×10^{‑8} *J/S*) / (1.9×10^{‑10}* J/photon)*
or 420 photons per second.

Only a fraction of those photons would be captured by Frank's floating telescope, since its effective aperture was only 100 square inches, which is one sixteenth of a square meter. So Frank's telescope was struck by one sixteenth of 420, or 26 photons per second. Plus another 26 of the (comparatively tiny) electron-derived photons, for a total of 52 photons per second.

This number would grow, as Finger approached.