# Is there a (low-thrust) thrusting strategy to change a single orbital element alone?

In literature, I have found the optimal thrusting directions (in terms of pitch and yaw) for maximizing changes in each orbital element.

These optimal changes, while maximizing one element, have an effect on the other elements. That is, in-plane thrusting arcs will change the axis but also the eccentricity and the argument of perigee; and out-of-plane maneuvers will change the inclination but also the RAAN.

For inclination and RAAN, given the fact that thrusting occurs in arcs and the fact that they depend only on one direction of thrust, it might be impossible to change only one element without changing the other.

However, since the semi-major axis, the eccentricity and the argument of perigee seem to change affected by more than one component, I suspect there might be a way to obtain a thrusting strategy that sacrifices optimality while making sure that only one element is changed throughout the whole transfer time.

I am only referring to the aforementioned 5 orbital elements, leaving the true anomaly aside for obvious reasons.

Are there any developments on that? Are hypothetical single-element maneuvers ever used in real life?

In practical terms, these hypothetical single-element manoeuvrers are not useful, as one cares very little for what intermediate path one takes through empty space, while the propellant consumption is an absolute bottleneck.

Argument of periapsis can be changed the way you describe, by applying zenith thrust at apoapsis or nadir thrust at periapsis:

$$acceleration = \frac{\mu}{r^2} - \frac{\mu}{ar}$$

Where $$r$$ is the current radius, either apoapsis or periapsis. Depending on the orbit, this may qualify as "low thrust".

This manoeuvrer effectively keeps altitude, and thus rotates the orbit.

Changing semi-major axis alone without changing eccentricity may not be possible, as scaling an orbit without changing eccentricity requires the spiral to have a descent angle of 0, and therefore 0 thrust.

Changing only inclination should also not be possible with a low-thrust spacecraft, as the node line stays fixed while the spacecraft inevitably passes through the nodes. But if impulse manoeuvres are allowed, inclination can also be changed separately from everything else.

At the time of writing, I'm not sure if eccentricity can be changed independently.
• Could you clarify "the propellant consumption is an absolute bottleneck"? I am not that good at English and I am a bit confused. – Paek Se Apr 18 at 16:44
• @PaekSe I was referring to how sending mass into space is expensive, and therefore using optimal (minimal propellant) transfers is preferred. – SE - stop firing the good guys Apr 18 at 16:46
• @PaekSe I would add that optimal when it comes to modern rockets generally refers to minimum cost. Once you're already in space, this generally means minimum propellant, though there are additional considerations in-atmosphere. It does not mean minimum-time, though wouldn't that be nice – TheEnvironmentalist Apr 18 at 17:13