It isn’t just an “area” concern, because the timing is also important. If one satellite arrives before the other, then they will also miss each other. It requires a calculation of a volume. Also, Andi, you need to make the calculation for radii of both satellites, not just one, but assuming that both are the same size then I think the calculation gives r = 44.7 m, which is still large.

The rules, however, use specific ovoid dimensions, because orbital perturbations are difficult to predict and calculate. Much of what they use for chance-of-collision calculation is rule of thumb rather than comparison of satellite size. Part of the reason is that satellites rarely are spherical or cubical but have protrusions such as antennas and solar panels.

Considering that there are quite a few thousand satellites in low Earth orbit, both active and dead, satellite operators are becoming more and more concerned with the consequences of collisions and the Kessler effect (or syndrome), as exaggerated in the movie “Gravity.” With so many objects in orbit, there are plenty of opportunities for collision, and even more if you include the tiny debris that cannot be tracked.

An example is the collision in 2009 between an active Iridium and a dead Kosmos satellite.
https://en.wikipedia.org/wiki/2009_satellite_collision#Cause

A four km radius gives a cross-sectional area of pi * 4000^2 square meters

In order to have a 1:1000 chance of collision, that would mean that [pi*(2r)^2] / [pi * 4000^2] = 1/1000.

Solving for r gives r = 4000 / [ 2 * sqrt(1000) ] = 63.2 m radius.

That’s an awfully big satellite!

“The two satellites were predicted to come within about four kilometers of each other”

Four km radius is a tremendously large cross-sectional area (50 million square meters). How does 50 million square meters translates into a 1:1,000 chance of collision? I have to presume that satellites come this close to each other all the time. So, from the get-go, something doesn’t smell right.

SpaceX’s four satellites at this level probably don’t make up a large percentage of the satellites in this region). So, why is ESA complaining about what appears to be an extremely low probability? And we have to consider the possibility that SpaceX was looking at precedence. Are they willing to move any of their thousands of future satellites every time someone else asks them too when SpaceX’s own algorithms say that there is not a sufficient risk of collision? SpaceX needs to clarify the situation.

My take as well. Best to get the other side of the story before forming a strong opinion.

… unless this was one of the dead satellites and Spacex couldn’t move it and the original article was basic B.S.