UPDATE: On Reddit Tumerboy replied with a significantly lower expectation on the number of ships – but still large enough to scare the crap out of you – 70 trillion ships. See the full response at the bottom of this post.
The following is math performed by an idiot. On a napkin. While drinking. View accordingly.
Lets assume that the surface of the Iconian Dyson Sphere is ‘slightly’ less than 1 AU from its power-source star, matching to some degree the other two Dyson Spheres we have encountered.
1 a.u. = 149597871 kilometers.
Lets assume that you only need enough spindly star ships to blot out enough sky to prevent reflected light around the edges. For the purposes of this argument, lets say half of the surface area is all that is needed.
Area= 4 π r²
Area=2.87×10^17 Square Kilometers
or in this case half 14,400,000,000,000,000,000 sq.Km
That’s something between quadrillion and quintillion. Even Google has issues with this.
Lets be generous and say it only takes 10 starships to blot out 1 square kilometer of space. I know, I know, this is a guess. Or the 200 Garden gnomes per person as suggested by PWE’s tumerboy, x 1000 persons per km. My mind is having a hard time calculating garden gnomes/km. Just sayin. Mind BLOWN.
That would make the number of Iconian starships necessary to ‘blot out the sun’:
144 QUINTILLION (18 zeros) starships.
We are seriously in trouble – or – Cryptic is trolling us about the grind to come.
‘Just sayin we need 1 red matter torpedo.
You’re using 4πr² to calculate the area of a sphere. But you’re using the radius from the earth to the sun. Which means you’re making a sphere with radius 1AU. That’s a dyson sphere.
What I’m saying is, you don’t need a sphere that big in order to “blot out the sun” from Earth.
i.e. Let’s say you just make a sphere of ships at 1/2AU.
4 * 3.14 * (74798935.5)² i.e. 7,030,728,568,5862,787.63919 sq.km So, only 70 quadrillion ships.
The distance from Earth to the moon is only 384,400km. Let’s say you made a sphere only double that distance.
4 * 3.14 * (768800)² i.e. 7,423,631,206,400 sq.km So, a skant 70 trillion ships. (That’s roughly 2 million times fewer ships than your initial estimate.)
Though all of this is based on the assumption that a single layer of ships is all it takes to “blot out the sun.” In reality, Iconian ships are not tetris pieces, and would leave gaps around/between them. So you’d likely need at least 3 or 4 layers to do the job.