
Now please do try to keep up with this, Ski et al. It's tough mathematics and geometry but if you persevere, a glimmer of understanding may penetrate.
Observe stratellite A. It is broadcasting a signal that is picked up by dish Y, represented by the orange line between them. For an observer looking in the direction of the dish, the signal appears to be coming from a point on the celestial equator.
Now consider dishes X and Z. If they are also picking up signals from stratellite A, then to an observer at those sites the signal appears to be coming from a position either above or below the celestial equator for X or Z respectively. However, as we know from the observation of satellite dishes all over the entire world, they actually are angled to point at the celestial equator within a reasonably close tolerance. This means that dish X must therefore be picking up its signal from a second stratellite, B, in order to maintain this angle.
So why can't dish X be pointing at the equator but picking up a signal from stratellite A anyway? Simply because if you move the dish off position, the signal goes away. This proves that the dishes are directional and cannot pick up signals properly when angled in other directions.
So how do we arrive at the figure of 60km for the spacing of stratellites?
There will be a limit of precision for how the dishes must be angled, allowing for some tolerance of mis-alignment. However there will be a limit beyond which the dish will cease to pick up a signal. If the stratellites are at the top of the atmosphere, I estimated the distance on the ground between the upper and lower limits of precision to be about 60km. Of course the cunning mathematicians among you will realise that the higher the stratellites, the further apart you can have them for a given dish angle tolerance, and therefore higher altitude = less stratellites needed, and lower altitude = more stratellites needed.
Since I don't actually know what the tolerance of dish angulation is, the 60km figure is somewhat of a guesstimate, but its basis of estimation is sound.