Their current best satellite in the constellation is the SuperDove and it takes images ~637 sq km at a time so, as a naive calculation, to cover the whole earth

Their current best satellite in the constellation is the SuperDove and it takes images ~637 sq km at a time so, as a naive calculation, to cover the whole earth at any single instant you'd need over 800 thousand of Planet's SuperDove ignoring the difficulty of making a constellation that efficient and ignoring that you can also save a lot of birds by confining the area of interest to a narrower band of latitude without missing much activity. Your raw efficiency per satellite does take a small hit as you shrink the latitude coverage because you get a concentration of satellites along the edges but that's just orbital mechanics for you. (you can see this on the starlink constellation trackers, they're moderately denser right along the edge of the latitude band of their orbit: https://satellitemap.space/?norad=59877 https://satellitemap.space/?norad=59877) Now if we reduce the time resolution somewhat and accept we may not know at the exact moment where any particular plane is but that it will get captured on a satellite every X minutes you can really start cutting into those numbers.