Would it be possible to alter the orbit of one satellite, with the exhaust plume of a rocket sufficient to deorbit it?

Question

SpaceX plan to launch Starships towards Mars; many of them.

This will involve burning hundreds to thousands of tonnes of propellant in low(ish) orbit, since each may require several refueling steps.

When the Mars bound ships are being boosted first to a higher Earth orbit, would it be possible to use the exhaust to slow down a specific, targeted piece of space debris, removing just enough velocity that it will deorbit significantly sooner than it would otherwise.

I acknowledge that this would require precision and orbits lining up extremely precisely, and that there are several alternative ways to deorbit dead satellites, but as a thought experiment in orbital mechanics, exhaust dynamics and aerodynamics, would this at least be possible?

Answer 1

tl;dr: It will "blow away" too quickly to gain 100 m/s necessary to promptly deorbit, but you could at least make a dent in it's lifetime this way.

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Starship says it will have 6 Raptor engines with a total thrust of 12,000 kN.

Let's say a 1000 kg satellite is absurdly close and can intercept 1% of that for 1 second as it immediately accelerates, which is the same as 0.1% of that for 10 second.

$$a = F/m$$

$$v = a t$$

give us an acceleration of 120 m/s^2 for 1 second, or a delta-v of 120 m/s.

But of course that means that by 1 second it's 50 meters away, so not intercepting 1% of the exhaust even within that one secon.

Answers to How hard do you have to throw something off the ISS to make it deorbit? tell us that 95 m/s delta v will promptly deorbit something in a circular 400 km orbit; it will hit the Earth's atmosphere a half-orbit (46 minutes) later.

So this is a weird idea but it is not likely to be even plausible because it will just blow away from the rocket before it can gain 100 m/s to promptly deorbit.

I also don't think that it is attractive because it poses some risk to the Starship; while unlikely, bits of the disintegrating spacecraft could fly back at the Starship somehow outside of the exhaust plume (there could be fuel on board) or something else could go wrong, so I don't think they will take on even a tiny amount of extra risk for something that could be done more easily with a dedicated space-cleaning mission.

But this is a cool stunt and it might be doable to impart say 10 m/s delta-v thereby decreasing the deorbit time, and if you did it at 200 km instead of 400 km, a smaller kick will make a much bigger dent in deorbit time; a Starship could orbit for a few hours or a day or so at 200 km if it really, really wanted to.

Answer 2

We need to find out what mechanisms may work in space to stop the satellite and de-orbit it.

In LEO, Drag is a valid de-orbit method. You can take a look here and here.

The other effects can be :

1. The jet impacting on the satellite itself. In vacuum, the Weber number will approach infinite, as there is no surface tension. A large Weber number makes the plume unstable. In this regime, the flow will go out of hand. However, not all is lost. Impingement force of 800 Pa is observed at a distance of 40 mm, where a control thruster of 10 N was fired at a flat plate. The ambient pressue is 80 km. I am not adding any picture, as those are not my work. So if you are at that distance, then you are good to go. I do not have the computational resources to scale up the simulation for a spaceX thruster.

2. The radiation pressure of the hot gas is irrelevant. Again, the Weber number says that the jet will very quickly dissipate.

That brings us to the effect of total aerodynamic drag, and how this will affect the de- orbiting. We can take a look at solar events that change the drag at that height, and see how that is impacting the de-orbiting. This is a very difficult calculation to make. But fear not, for we have some steps in that direction.

In the study period, the proton density spiked by 40 particles per m³, and the satellite decayed by 0.52 km. This is NOT to say that the additional particles were the ONLY cause, but that gives you some ballpark idea. Similar ideas can be found here

So to conclude : The orbit will decay, but it may not be enough to de orbit the satellite within a short time span of few days. If there is sufficient decay, and no one recovers it, then over a few months it will go down.

References : ( I have not made them consistent sorry)

1. Bijiao He, Jianhua Zhang, Guobiao Cai, Research on vacuum plume and its effects, Chinese Journal of Aeronautics, Volume 26, Issue 1, 2013, Pages 27-36, ISSN 1000-9361, https://doi.org/10.1016/j.cja.2012.12.016.

2. Jennifer L. Rhatigan, Wenschel Lan, Drag-enhancing deorbit devices for spacecraft self-disposal: A review of progress and opportunities, Journal of Space Safety Engineering, Volume 7, Issue 3, 2020, Pages 340-344,

3. R.W. Fenn III and S. Middleman, Newtonian jet stability: The role of air resistance, AIChE J., 15: 379-383, 1969, https://doi.org/10.1002/aic.690150315

4. David Vallado & David Finkleman, A Critical Assessment of Satellite Drag and Atmospheric Density Modeling, Acta Astronautica, 95, 2014, 10.1016/j.actaastro.2013.10.005.

5. Victor U. J. Nwankwo, William Denig, Sandip K. Chakrabarti, Muyiwa P. Ajakaiye, Johnson Fatokun, Adeniyi W. Akanni, Jean-Pierre Raulin, Emilia Correia, and John E. Enoh, Atmospheric drag effects on modelled LEO satellites during the July 2000 Bastille Day event in contrast to an interval of geomagnetically quiet conditions, Ann. Geo. Dis., 2020, https://doi.org/10.5194/angeo-2020-33

6. S Khodairy, M Sharaf, M Awad, R Abdel Hamed and M Hussein,Impact of solar activity on Low Earth Orbiting satellites, International Symposium on Space Science : Journal of Physics: Conference Series, 1523 (2020) 012010, IOP Publishing, 2020, doi:10.1088/1742-6596/1523/1/0120101 .

Answer 3

TLDR: Yes, but they aren’t going to. Perhaps 52-71m/s dV is practical.

My model of a rocket exhaust (in a vacuum) in as cone, that extends out behind the rocket while it fires, which applies pressure on the flat circle of the cone, as the gas molecules slam into whatever they impact.

By my measurement, this vacuum raptor engine bell https://twitter.com/SpaceX/status/1302038129990279168/photo/1 is about 14cm tall and 11cm wide – note that we care about the ratio here, not the absolute measurement. That gives us a radius to height for this engine’s exhaust plume at about 14:5.5, or 2.5:1. According to the wikipedia entry, Starship will have ~12MN of thrust in a vacuum.

So – at some distance away the engine bell there will be a point where the plume would apply 1N per square meter, or one pascal. There’s effectively no chance that this could cause any risk to the starship in question – it’s safe. Using area =πr2, this gives us 12,000,000 = πr², or r = 1954m. How far away is that? Using the cone from earlier, that’s about 4886m away.

What does a pressure of 1Pa give us? Best case, we’re trying to push something like a centaur upper stage – large surface area, but low mass – travelling in an identical orbit, but a little distance behind the Starship. According to wikipedia, a Centaur III is about 3.05m diameter, 12.68m long and has a dry mass of 2247KG.

Assuming optimal positioning without rotation, that’s 3.05x12.68=38.7m2. So 38.7N exerted on a 2247KG object gives us, um, 0.017ms^-2 – that’s...not much. If sustained for a whole minute – which is a brave assumption, given the starship would be accelerating away – would give us 1m/s of deltaV. Per minute.

Now I’ve demonstrated methodology, here’s a table I calculated, which ends when the target object is subject to about one atmospheric pressue - which given it was constructed on Earth should be be fine - well, at least not catastophic. Atmospheric pressure assumed to be 100,000Pa, not 101325Pa.

Pressure (Pa)	Force (N)	Area (m2)	Radius (m)	Distance	Target area	Target Force	Target acceleration
1	12000000	12000000	1954.41004761168	4886.0251190292	38.7	38.7	0.0172229639519359
10	12000000	1200000	618.038723237103	1545.09680809276	38.7	387	0.172229639519359
100	12000000	120000	195.441004761168	488.60251190292	38.7	3870	1.72229639519359
1000	12000000	12000	61.8038723237103	154.509680809276	38.7	38700	17.2229639519359
10000	12000000	1200	19.5441004761168	48.860251190292	38.7	387000	172.229639519359
100000	12000000	120	6.18038723237103	15.4509680809276	38.7	3870000	1722.29639519359

Huh. So as long as SpaceX was willing to let the target get within 150-500m of the Starship, a meaningful amount of DeltaV could be imparted to our perfect target. Outside of 500m the thrust is negligible,

Next question – how long would a Starship be close enough to do this. After all, it’s burning to goto Mars. Thrust of 12MN, mass of around 1320T. 12,000,000/1320000 = 9.1ms^-2. Assuming constant mass for the first few seconds, and that once the starship is 500m away the thrust is negligible, starting at 150m - you have meaningful thrust for the first 350m of the Starship’s burn. Ignoring orbital mechanics, as this will be over in seconds – the formula s = ut + 0.5at2 gives a total time of… 8.8 seconds until it’s out of meaningful range.

I don’t trust my maths to integrate this entire mess to give a better estimate, but back of the envelope excel work gives me an estimate of range 52-71m/s, based on a series of calculations based on 1s intervals as they move apart.

52-71m/s isn’t enough to de-orbit from many orbits – but it’s enough to significantly decreased the orbital life of an object at 400km height, as per previous answers.

All you need is persuade SpaceX to let their rocket get within 150m of orbital spacejunk about as big as it is…