### How many Starlink satellites will you see?

How many Starlink satellites will you see?

According to the current plan, there will be ~12000 satellites on 3 orbital shells on height 340km, 550km and 1150 km.

For estimation, it is good enough to assume the satellites will more or less evenly spread on each orbital shells.

We need to calculate how many will be visible to one point on the ground for satellites on each shells.

In the diagram left, the inner circle is the Earth. For all the satellites on the orbital shell h away from the ground, a person on the ground can see all the ones from the blue cap.

So the ratio of visible to all satellites are the ratio of area of the blue cap to the area of the sphere.

With  $h =\text{height of orbit}$ and $r = R_{earth} + h$

We have the ratio of visible satellites to all satellites on the same orbital shell:

$=\frac{2\pi r h}{4\pi r^2}=\frac{h}{2 r} = \frac{1}{2}\frac{h}{R_{Earth} + h}$

With the number from the current plan:

orbital shellHeight#% visible# visible
155016003.97%64
2115028007.65%214
334075002.53%190
Total119003.93%468

There will be ~468 satellites one can see at any time point.

The sky above us will never be the same.