# Why do the optimal thrust vectors point so far away from the velocity vector for the Psyche mission?

The question Psyche 16 - What will be learned in 2026? got me reading Wikipedia's Psyche (spacecraft) which links to the 35th International Electric Propulsion Conference paper Development of the Psyche Mission for NASA’s Discovery Program (IEPC-2017-153) which says:

B. Mission Architecture: Cruise Trajectory

Accomplishing the project’s science objectives requires traveling to Psyche and orbiting the asteroid for a period of 21 months. In order to reduce operations costs and receive science data as early as possible, it is desirable to minimize the trip time from Earth to Psyche. Therefore, the fundamental objective of the mission design effort is to deliver the necessary spacecraft mass (including margins) to the asteroid Psyche as quickly as possible. The constraints on the trajectory imposed in the Discovery 2014 Announcement of Opportunity (AO) included a maximum allowed launch vehicle performance capability (which corresponded to an Atlas V 411 launched from Cape Canaveral, Florida) and a launch readiness date prior to December 31, 2021.1 (The AO guidelines allowed the use of higher performing launch vehicles, but at an additional cost to the project). To enable the selection of multiple winners with staggered launch dates, the AO also asked teams to identify an alternative launch period in 2023. The final Psyche proposal included launch options in both 2021 and 2023, and ultimately NASA selected the 2023 launch opportunity.

Early studies showed that the amount of chemical propellant required to reach and orbit Psyche within a reasonable time is prohibitively high. This led naturally to the use of electric propulsion and low thrust trajectories for the mission. Prior to the first down selection in September 2015 ("Step 1”), Psyche’s low thrust trajectory design work was conducted using MALTO.14 From that point onward (“Step 2”), all trajectory design work was conducted with the trajectory optimization program Mystic.15 Mystic is a high-fidelity optimization tool that was used for all mission design and maneuver design work for the Dawn Mission to Vesta and Ceres. Mystic has assisted other flight projects including the Cassini and Artemis missions. Mystic uses a second order optimal control algorithm called Static-Dynamic Optimal Control (SDC)16 based on Bellman’s principal of optimality. SDC achieves both the necessary and sufficient conditions.

The illustration shows thrust vectors almost 30 degrees away from the velocity vector at the end of the propulsive segment before Mars flyby gravitational assist.

Question: - Using low thrust electric propulsion, what benefit does the strong radial component of thrust provide for raising an orbit? - Does the large density of arrows near this point indicate a boost in thrust or reduction in velocity, or is it just a peculiarity of the drawing?

Figure caption:

Figure 2: Example 2022 launch trajectory plotted as a green line. Thrust acceleration is indicated by the yellow vectors, arcs without vectors are either forced to coast or coasting is optimal.

Cropped and annotated section, followed by screen shot of complete figure

• It looks like they have a fairly large coast before the Mars swing-by, I wonder if that's to verify orbital parameters and have time to make corrections in the event something is off. I think the coast at the bottom of the image is forced though. Do you think that's enough content for another question? – Magic Octopus Urn Sep 23 '19 at 20:48
• @MagicOctopusUrn I've included a quote of Figure 2's caption: "...arcs without vectors are either forced to coast or coasting is optimal." If you search the paper for the word coast you'll see "coast arcs for tracking and communications" and "forced coast" appears a few times, so I think you are on the right track and there is definitely a good question there. – uhoh Sep 23 '19 at 22:49

There are several effects, that all seem to apply in this case.

1. Radial thrust adds a radial velocity component. To maximise the effect of a flyby, one would want to have a high $$v_{\infty}$$. If one instead of having some radial thrust continued a prograde burn, the orbit would match that of Mars more closely, and therefore have a lower $$v_{\infty}$$. Some radial thrust is a way to add energy, which at the same time doesn't sacrifice the flyby speed. The eccentricity gained can be cancelled out by the Mars flyby angle.

The next two are likely from this motivation:

Therefore, the fundamental objective of the mission design effort is to deliver the necessary spacecraft mass (including margins) to the asteroid Psyche as quickly as possible.

The plotted trajectory tries to push the aphelion closer at all parts of the journey. Without the thrust provided (ignoring matching velocities for a moment), the Mars flyby would put the encounter at a point counter-clockwise from Psyche, which means missing the asteroid

It's just not desirable to wait for a better planetary alignment given the time restraint.

1. Radial thrust by itself helps rotating the aphelion, on both the legs before and after the flyby of Mars.

2. Pushing the aphelion closer reduces time to aphelion, which reduces transfer time.

• Wow, there's a lot to think about here! So are there two reasons 1) timing/phasing since the Mars flyby has to address the second object (asteroid Psyche) and 2) it provides more $v_{\infty}$ than tangential thrust, or is one of those a result of the other? – uhoh Sep 19 '19 at 8:29
• I guess you can argue that 2) results in changes to 1), but in the end they are both contributing to the same, less costly, Psyche transfer. – SE - stop firing the good guys Sep 19 '19 at 10:28
• So the burn is being done in this manner because it's a low impulse thruster? Does this type of transfer have a name so I can find more materials on how low-impulse transfers are calculated? Ion transfer? Low impulse transfer? Neither of those get good results. – Magic Octopus Urn Sep 23 '19 at 18:06
• @MagicOctopusUrn "Low thrust transfers/trajectories" is a common term. – SE - stop firing the good guys Sep 23 '19 at 19:15
• en.wikipedia.org/wiki/Low_thrust_relative_orbital_transfer - That's it! Believe it or not for "Low impulse transfer" google thinks the most related search term is "signal processing and transformers". – Magic Octopus Urn Sep 23 '19 at 20:45