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A recent answer about communication satellites in VLEO (≤350 km) estimates a useful orbital life of about month without fuel.

I.e. Once the vehicle is out of fuel to maintain orbit, THEN it has the shortened lifespan.

As you can imagine, a constellation with 7000 satellites that last a total of one month each is impossible or at best improbable. Source

So how much fuel would/will it take to keep them in orbit for say a couple of years?

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    $\begingroup$ Interesting! Perhaps separate numbers would be appropriate for typical, and worst-case solar activity. See also this comment $\endgroup$ – uhoh Nov 16 '18 at 18:11
  • $\begingroup$ To some extent we simply can't answer this - it will depend on the mass and drag coefficient of the spacecraft, as well as solar weather. Perhaps someone can offer some reasonable approximations. $\endgroup$ – Saiboogu Nov 16 '18 at 18:23
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The answer is obviously that "it depends", and I would say a lot.

A good starting point is noting that the GOCE satellite was launched on 17 March 2009 and decayed on 21 October 2013, staying more than 4 years in a 250km altitude orbit. It used electrical propulsion and the fuel ran out on 21/10/2013 its launch mass was 1077 kg, which included up to 100 kg of propellant (Xenon gas).

Given the practical example, just keep in mind that basically, there is fuel to compensate for drag $D$ effect over $T$ time, which can be roughly estimated with:

$$ m_{tot} =\dot{m}T= \frac{DT}{v_{exhaust}}=\frac{c_D \rho A V^2 T}{2v_{exhaust}} $$

Now, note that this is pretty basic, you still fuel for orbital maneuvers, and safety margin, but a few more components come into play with this kind of (very poor approximation) formula:

-$T$ the mission time

-$c_D$ the drag coefficient

-$\rho$ the atmosphere density (which varies over years due to sun cycles)

-$V$ the orbital velocity (which may not be constant)

-$v_{exhaust}$ which is the exhaust velocity of your gas, but is more of a proxy for better engineering references such as the $I_{sp}$, but expresses that the fuel used and its efficiency is relevant.

-$A$ the relevant area of the spacecraft body

Things would also depend a lot on whether you use always-on electrical propulsion or periodic liquid fuel burns.

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Electric propulsion makes the most sense. Air-breathing propulsion is now possible - propellant-based missions have very restricted lifetimes and the weight makes them expensive.

The main cost is then electrical power, which is a double-edged sword. More power is needed, but more solar panels will cause more drag. There is a tradeoff somewhere between these two.

Edit: to summarise the linked article: ESA has developed the first electric thruster which takes in atmosphere as propellant, which would open up VLEO. ESA's GOCE flew at 250km for over 4 years using a xenon thruster but this lifetime was limited by the 40kg of xenon propellant it carried. If this onboard propellant were atmosphere instead, the satellite would have lasted longer.

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  • $\begingroup$ The link in your answer has some great info, maybe you should include more of the detail in your answer incase the link dies? $\endgroup$ – James Jenkins Nov 21 '18 at 14:04
  • $\begingroup$ Done! Added a brief summary. $\endgroup$ – Diamond Nov 21 '18 at 15:56

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