# What area of Proxima Centauri would need to be occluded for the effect to be observable on Earth?

One of ideas of how Breakthrough Starshot could communicate data from Proxima Centauri is to have a massive swarm of the solar sail powered craft to pivot (with their sails) synchronously, taking either 'sideways' or 'head on' orientation to the star - in effect either obstructing it or revealing for an observer 'behind' - on Earth. If the swarm is big enough, it would cause an observable dimming of the star - and timing the pivots right it could encode data in the star's visible luminosity.

The primary question of viability of this idea lies in 'how big a swarm?'. What percentage, or what absolute area or a star like Proxima would need to be occluded for the effect to be observable? We can notice transition of exoplanets quite reliably so that would be the upper bound, but what's the smallest object area that would make a detectable difference?

• If you divide the absolute error of our best flux density (apparent brightness in W/m^2) measurement system by the apparent brightness of Proxima Centauri, you ought to get the minimum percentage that guarantees a transit if the apparent brightness of Proxima Cen drops by it. I have no idea what this absolute error is. – Tosic Nov 29 '18 at 19:57
• Please can you give a reference for this idea. Typical precisions of a space borne photometer are 100ppm. So you would need to obscure more than $10^{-4}$ of the surface. About $10^{12}$ m$^2$. ? – Rob Jeffries Nov 29 '18 at 20:51
• @RobJeffries Well then, that means the idea is not viable, period. – SF. Nov 29 '18 at 22:39

The radius of the star is 0.15 that of the Sun. So the physical area to be obscured is $$\sim 10^{-5} \pi R^2 = 3.4\times 10^{11}$$ m$$^2$$.
The web page referred to in the question suggests that Starshot consists of a thousand space craft with light sail areas of 16 m$$^2$$. It thus seems to fall short of providing detectable modulation by 7 orders of magnitude (unless I have misunderstood the proposal, which isn't mentioned on that web page).