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The recently launched Starlink satellites are designed to use their HAL Ion thrusters to seek their own independent orbits, evade collisions, and de-orbit at the end of their lives. That's a lot of maneuvering.
Does anyone know, or can make an educated guess what the Delta-V is for one of these?
update: It's been two years and Starlinks are now being deployed at much lower altitudes! I am revising this "ballpark spherical-cow envelope-back estimate" based on @BrendanLuke15's answer to What orbits are Starlink satellites now deployed into? How low to do they go on their first perigee?.
Here is a rough estimate.
tl;dr:
raising 250 to 550 km 170 m/s
keeping it there 20 m/s
bringing it down 112 m/s
Total 380 m/s
using about 4.8 kilograms of krypton, which is about 12 liters at 100 atmospheres.
I looked at the current TLEs and plotted eccentricity versus altitude and they seem to all be in nearly circular orbits at about 250 to 270 kilometers. This is based on @BrendanLuke15's answer to What orbits are Starlink satellites now deployed into? How low to do they go on their first perigee? and seems now to be the norm in 2020-2021.
I used (from here)
$$T \approx \frac{24 \times 3600}{\text{revs per day}} $$ $$a \approx \left( \frac{T^2 GM_E}{4 \pi^2} \right)^{1/3}$$
to estimate the semimajor axis, then subtracted 6378137 meters to obtain an altitude (from here).
Orbital velocity is given from the vis-viva equation
$$v=\sqrt{GM_E \left( \frac{2}{r} - \frac{1}{a} \right)}$$
which reduces to
$$v=\sqrt{\frac{GM_E}{a}}$$
for a circular orbit. At 250 km altitude the velocity will be about 7755 m/s. At it's final altitude of 550 km the orbital velocity will be about 7585 m/s. That's 170 m/s slower, and as it turns out it happens to require about 170 m/s delta-v thrust forward, to raise (and slow down) the orbit from 250 km to 550 km. (currently looking for @MarkAdler's answer that first points this out)
Let's estimate how much delta-v is necessary to keep a Starlink satellite at 550 km for say one year starting with an estimate of drag force
$$F_D = \frac{1}{2} \rho v^2 C_D A.$$
Let's use a coefficient of drag $$C_D$$ of 1 and use a cross-sectional area of 3.5 x 0.2 meters. Interpolating http://www.braeunig.us/space/atmos.htm at 550 km gives atmospheric densities of 2.3E-14, 3.4E-13 and 1.0E-11 kg/m^3 for Low, Mean, and Extremely High solar activity. Using the mean value, we get about 7E-06 Newtons.
With a mass of about 227 kg, that's an acceleration of 3E-07 m/s^2. Over five years, that's only about 5 m/s! However, let's say 10% of the time is high solar activity (30x higher density) and call this part of the budget 20 m/s.
At E would like to bring them well below the ISS's orbit and most other satellites in LEO, let's be aggressive and say we need to go from 550 km to 350 km to ensure rapid decay. The velocity there is 7697 m/s, so that's a delta-v of 112 m/s.
raising 250 to 550 km 170 m/s
keeping it there 20 m/s
bringing it down 112 m/s
Total 380 m/s
Choosing an arbitrary Isp of 2000 seconds (exhaust velocity of 20,000 m/s) it means that at least 2% of the satellite's mass would have to be krypton to do this, or at least 4.6 kg.
At 3.8 g/liter at standard atmosphere, a bottle at 100 atmospheres for example would have to be say 12 liters, and also fairly heavy to safely hold the pressure.
The krypton system is a nontrivial component of the whole spacecraft in terms of both volume and mass!
