Considering the answer of user Mark Adler here, to calculate how much ΔV is needed to raise orbit we can simply approximate it as the change in orbital velocity.
Starlink satellites seem to be deployed at around 270km.
So, from 270 km to reach 550 km we have:
$u_{270} = \sqrt{\frac{GMe}{a}} = 7.743 km/s$
$u_{550} = 7.58 km/s $
$ΔV = 163 m/s ~ 170 m/s $
Τo maintain orbit at 550 km we have to calculate atmospheric drag expected at this altitude and as per here and here we have:
$F_D = 0.5 ρ u^2 C_D A = 0.387 mN.$
Cd: ~1 (coeff)
A: assuming the solar panel is deployed and facing perpendicular to the wind direction when operating (to at least figure out the max area/max drag), $A_{panel} = 3.4 m * 10m $ + $A_{body} = 3.5m * 0.2m = 0.7$. To approximate density at this altitude I used this table.
Now that we have the force we need to counter to stay at the same altitude we can do:
$F = ma $ with initial mass 260 kg and after burning some fuel to reach there approx. 257 kg. using the Tsiolkovsky rocket equation with Isp = 1600 as per Musk's tweet.
That means that $a = 1.5 * 10^{-6}$ m/s**2 Let's say $a * 1 year = 47.45 m/s/year.$ is the acceleration we need.
The incident as described in my other post says that the atmospheric drag on those days increased by approx. 50% and the altitude of the satellites was 210 km.
Same source as above for density at 210 km during mean solar activity gives $2.2 * 10^{-10} kg/m3$. With that:
$Fd(mean solar) = 4.82 mN$ at 210 km
$Fd = 7.24 mN$ at 210 km (incident w/ 50% increase)
However, this outcome does not seem correct, because from what I read here, Figure 3 or Figure 4 where they compare specific impulse with thrust power at 1600 Isp we get at least 45 mN/kW.
Typical krypton ion engines with Isp = 1600 produce 100 mN which is way more than what they experienced during the incident. Approximating the power can give is something between 5-7 kW.
So, how come they couldn't overcome these conditions? Is it something wrong in the calculations?