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 Keldysh Institute preprints, 2018, 268, 32 pages (Mi ipmp2625)

“Not full” two-boundary problem for finding multi-orbital transfers with zero low thrust in the shadow

R. Z. Akhmetshin

Abstract: A lot of calculations of multi-orbital transfers from elliptical orbit (with perigee distance $\approx 15.6$ and apogee distance $\approx 83.2$ thousand km, and inclination $13^{\circ}$) to geostationary orbit of spacecraft with low thrust, which becomes zero in the Earth shadow, is done. To find such trajectories so called “not full” two-boundary problem that do not include a condition of optimal crossing the shadow line is solved. That's why trajectories are not optimal, but in many cases expenditure of working substance is not much more than on a trajectory without switching off the low thrust. For longitude of ascending node equal to $180^{\circ}$ and different start dates the difference is later than $1%$. The peculiarity of two-boundary problem is that in some cases more than one solution may exist.

Keywords: multi-orbital trajectories, spacecraft, low thrust, geostationary orbit, Earth shadow, two-boundary problem.

DOI: https://doi.org/10.20948/prepr-2018-268

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Document Type: Preprint

Citation: R. Z. Akhmetshin, ““Not full” two-boundary problem for finding multi-orbital transfers with zero low thrust in the shadow”, Keldysh Institute preprints, 2018, 268, 32 pp.

Citation in format AMSBIB
\Bibitem{Akh18} \by R.~Z.~Akhmetshin \paper “Not full” two-boundary problem for finding multi-orbital transfers with zero low thrust in the shadow \jour Keldysh Institute preprints \yr 2018 \papernumber 268 \totalpages 32 \mathnet{http://mi.mathnet.ru/ipmp2625} \crossref{https://doi.org/10.20948/prepr-2018-268}