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The Lucy trajectory described in several excellent answers to this question involves a number of fairly large (in delta-V terms) deep space maneuvers, totalling (same source) about 1.5 km/s over almost ten years.

What form of propulsion will be used for these? I can't see any information about the spacecraft on any of the project web pages, just the destination and instrumentation. What fuels are efficient enough for such large delta-V but stable enough for such long term storage?

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    $\begingroup$ There's some sketchy info on page 70 of this GAO report: gao.gov/assets/700/691589.pdf It contains these hinty comments: main engine was the same model used on a series of environmental satellites that have had engine performance problems. The engine has failed in flight more than once and was a single point failure for the Lucy project. As a result, the project completed an engine trade study in July 2017 and decided to select a different engine. $\endgroup$ – Organic Marble Jan 31 '19 at 19:43
  • $\begingroup$ The mission is still in the design phase, so engine selection may not be final yet. The design will be finalized by the end of 2019. $\endgroup$ – Hobbes Jan 31 '19 at 21:17
  • $\begingroup$ @Hobbes fair point, although given the unusually large delta-V needed, I would imagine they must at least have checked that some feasible options exist. I would accept an answer that gave credible details of engines that could meet these requirememts. $\endgroup$ – Steve Linton Jan 31 '19 at 21:24
  • $\begingroup$ Perhaps the question Flying fuel tanks! Which deep-space spacecraft had the largest fuel mass fraction? needs a companion question "...largest delta-v?" $\endgroup$ – uhoh Jan 31 '19 at 23:23
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This article on the Psyche mission says Lucy's propulsion is to be chemical (in contrast to Psyche's electrical propulsion).

Since the fuel needs to be stored long-term, it's almost certainly a non-cryogenic hypergolic combination like MMH/NTO.

There are a number of proven thrusters using that combination which are used for primary propulsion in deep space missions; another question here is dedicated to figuring out exactly what engine Lucy intends to use, but let us say for sake of argument that it's the Aerojet R-4D. With a moderately large nozzle that thruster achieves 311 seconds of specific impulse. We can apply the rocket equation to work out the necessary mass ratio. I saw another source give 1.68km/s required for Lucy's maneuvers, so I'll use that figure.

$$\Delta v = v_\text{e} \ln \frac {m_0} {m_f}$$

$v_\text{e}$ is 311s x 9.801 m/s^2 = 3048 m/s

Thus the log of the mass ratio is 0.5512, and so the initial-mass to final-mass ratio is 1.735.

This requires ~43% of the mass of the spacecraft be propellant at the beginning of these maneuvers. The QA that @uhoh referred to in comments shows that this is towards the high end of tankage ratios for deep space missions, but not unusually high.

R-4D might be overkill for a small spacecraft like Lucy, but most smaller thrusters will have poorer specific impulse, so they might cost more mass in propellant than they save in engine hardware.

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