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For many trajectories using engines with moderate ISP such as chemical or nuclear-thermal rockets, the exhaust velocity vector of various space operations is such that the rocket exhaust will end up in elliptical heliocentric orbit.

What is the ultimate fate of this (typically) volatile matter? Will anything (gravity? Orbital perturbations?) cause it to accrete into clouds, comet-like masses, or to move towards and stick to existing Solar System bodies?

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Presumably you are asking about engines that are used once a space vehicle has escaped the Earth's gravitational sphere of influence, or is close to that point. Rocket exhaust during launch becomes a part of the Earth's atmosphere. This continues to be the case beyond low Earth orbit.

The fate of a tiny particle in the solar system depends on the size of the particle. For molecule-sized particles, solar radiation pressure dominates over gravitational force toward the Sun. Extremely small particles (e.g., individual molecules of rocket exhaust) will spiral outward and eventually escape the solar system.

Suppose that by some chance, several billion molecules of rocket exhaust inelastically collide and bind with one another. The resulting picogram dust particle now has a different fate than the fate of individual molecules (or even a dust particle comprising only millions of molecules). At this size, Poynting-Robertson drag becomes dominant and makes the dust particle spiral inwards toward the Sun.

Our Sun ignited about 4.6 billion years ago. Once a protostar ignites, the combination of stellar radiation pressure, stellar wind, and Poynting-Robertson drag clears out the gas and dust in a protoplanetary disk that didn't combine to form protoplanets in ten million years or so.

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    $\begingroup$ @fraxinus Solar wind helps blow stuff away, but for very small particles, it's solar radiation pressure that currently dominates. This was not always the case. The very early solar system had reduced solar radiation pressure (about 70% of current) and drastically increased solar winds. For larger particles on the scale of micrometers to sub-millimeters, Poynting-Robertson drag dominates and eventually sweeps them into the Sun. These in-spiraling dust particles are the source of the zodiacal light. $\endgroup$ Mar 28 at 15:44
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    $\begingroup$ Some of the zodiacal dust comes from "a drift of interstellar material though the Solar System". See A survey of radial velocities in the zodiacal dust cloud by Brian May. Pity he was too busy being a legendary rock guitarist to publish that data sooner. ;) $\endgroup$
    – PM 2Ring
    Mar 28 at 23:11
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    $\begingroup$ @PM2Ring May was distracted by rocking us, by investigating what makes the rocking world go round, and accumulating 100s of millions of pounds sterling in the process. $\endgroup$ Mar 29 at 9:14
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    $\begingroup$ For those of you who do not know the rock group Queen, here are links to the two songs that I obliquely referenced in my previous comment: youtube.com/watch?v=-tJYN-eG1zk and youtube.com/watch?v=VMnjF1O4eH0 . Brian May wrote both of these. $\endgroup$ Mar 30 at 11:34
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    $\begingroup$ Bri also wrote (& sang) the "space shanty" '39, possibly the first pop song to reference time dilation. youtu.be/kE8kGMfXaFU $\endgroup$
    – PM 2Ring
    Mar 30 at 18:30
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No need to theorize. Astronomers have studied this problem for centuries, as there are natural objects that emit conspicuous plumes of rocket exhaust. We call them comets. The exhaust forms two "tails". Solar radiation ionizes molecules, which then attach themselves to magnetic field lines in the solar wind, and get carried along with the wind, forming an "ion tail". Dust particles stream away under the influence of solar radiation pressure, forming the "dust tail", generally in a different direction.

You say that's not a rocket? The escaping plumes thrust the comet, changing its trajectory. That's a rocket by definition.

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    $\begingroup$ @Uwe The solar wind is well above solar escape velocity, typically hundreds of km/s as it passes Earth's orbit, from which solar escape velocity is only ~40 km/s. $\endgroup$
    – John Doty
    Mar 28 at 19:35
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    $\begingroup$ @Uwe 300-500 km/s is much faster than 40 km/s. $\endgroup$
    – John Doty
    Mar 28 at 19:57
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    $\begingroup$ So my fault was to think only about the escape velocity at solar surface of 617..5 km/s and not of the escape velocity at earth orbit of 42.1 km/s. $\endgroup$
    – Uwe
    Mar 28 at 20:06
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    $\begingroup$ Rocket exhaust is chemically different from comet dust, and isn't on the same trajectories either. This is not answering the question at all. $\endgroup$
    – Innovine
    Mar 29 at 9:24
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    $\begingroup$ @Innovine The gases in rocket exhaust are mostly the same as gases in comet exhaust: CO2, H2O, N2, etc. For dust, the chemical composition isn't terribly important, light pressure operates regardless. The trajectories don't matter much, as plasma interactions and light pressure rapidly accelerate the material away from its original trajectory. $\endgroup$
    – John Doty
    Mar 29 at 13:28

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