# What does a low thrust apoapsis raising look like?

Say you are in a simple circular orbit, $$r = 1$$ and want to raise your apoapsis to some higher altitude, say an orbit $$r_P = 1, r_A = 2$$

A high thrust spacecraft would to this in one impulse, at $$\Delta v = \frac{2}{\sqrt{3}} - 1 \approx 0.15$$.

But how would a low thrust spacecraft quickly achieve this?

One could of course "emulate" an impulse by only using the engine a short while for each revolution at periapsis. But this does not sound very time-efficient, as the engine isn't in use most of the time. To illustrate this, a circular-circular transfer from $$r=1$$ to $$r=2$$ can be achieved by a spiralling low-thrust craft much faster than by "emulating" a Hohmann transfer.

Is there some similar strategy to "spiralling" when the target orbit is not circular?

• Surely the best "Low Thrust" apoapsis raising is to only use thrust at periapsis. Yes, it's time-consuming, but that is the trade-off. Oct 3, 2020 at 14:17
• @RoryAlsop "time-efficiency" is the metric here. Oct 3, 2020 at 14:19
• Okay - I think the two are pretty diametrically opposed. But I'm interested to see how much less fuel-efficient a spiral-type transfer would be. ie what is the actual trade-off. Oct 3, 2020 at 14:20
• None of these are duplicates but they address differences between impulsive and low-thrust maneuvers: Ratio of low-thrust slow spiral to Hohmann transfer ΔV? ahttps://space.stackexchange.com/q/28361nd Spiraling out from circular orbit to escape via low thrust, what is γ (gamma)? and Hohmann transfer orbit Burn Duration and Why would a slow spiral from a C3 of zero take about 2.4 times as much ΔV as an impulsive maneuver?
– uhoh
Oct 4, 2020 at 6:31
• Your example shows raising apoapsis without raising periapsis. Is that the intent, not to affect periapsis? If so, spiraling is precluded, and if it is truly low-thrust and the apoapsis raise is large (e.g., not a <1% increase), then multiple quasi-impulses at multiple periapsis passes would be required. The longer the thrust durations through periapsis, the more periapsis altitude will be affected, and might even require small retro apoapsis maneuvers to keep periapsis from creeping upward. Mar 4, 2021 at 18:57