Hiding on the Sphere

Sometimes I orbit a gate or another object while cloaked to provide intelligence that the corporation and/or alliance may find useful.

Typically I'm on the telephone or otherwise at the computer but not able to provide the sort of concentration required for roaming, etc.

That started me wondering how likely it would be I'd be de-cloaked and caught while orbiting, so I broke out the math.

First we have to make some assumptions.  

I'm orbiting a stationary central point ( a jump gate) at a constant distance of 250km.

This allows me to keep an eye on the gate while also being able to warp to the gate or away as the situation requires.

So we need to work out the surface area of a sphere, now as we don't know the exact figure that Pi (π) is we will use 3.141592 which is close enough for this purpose.

So the surface area of a 250km sphere is approx. 785,398km, the de-cloak range of my ship is 2.5km.

All of which adds up to a very small chance of being caught!

Roughly 1 in 157079 ¹ ².

¹ To do this properly I would work out the odds of a single enemy ship entering my ships sphere of influence  also while orbiting at 250km and/or at plus or minus 2.5km (possibly 3km to be safe), differing speeds would also have to be taken into account. Maybe someday I will, however don't hold your breath.

² Very roughly.