TY - JOUR

T1 - On non-coplanar Hohmann transfer using angles as parameters

AU - Rincón, Ángel

AU - Rojo, Patricio

AU - Lacruz, Elvis

AU - Abellán, Gabriel

AU - Díaz, Sttiwuer

N1 - Funding Information:
Á. Rincón acknowledges support by CONICYT/ALMA Astronomy Grants # 31110010 and CONICYT-Chile through Grant D-21151658, P. Rojo was supported by Fondecyt proyect #1120299, Basal PFB06 y Anillo ACT1120. E. Lacruz acknowledges support through the CIDA. The authors would especially like to thank Daniel Casanova Ortega, who agreed to review this work.
Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.

PY - 2015/9/7

Y1 - 2015/9/7

N2 - We study a more complex case of Hohmann orbital transfer of a satellite by considering non-coplanar and elliptical orbits, instead of planar and circular orbits. We use as parameter the angle between the initial and transference planes that minimizes the energy, and therefore the fuel of a satellite, through the application of two non-tangential impulses for all possible cases. We found an analytical expression that minimizes the energy for each configuration. Some reasonable physical constraints are used: we apply impulses at perigee or apogee of the orbit, we consider the duration of the impulse to be short compared to the duration of the trip, we take the nodal line of three orbits to be coincident and the three semimajor axes to lie in the same plane. We study the only four possible cases but assuming non-coplanar elliptic orbits. In addition, we validate our method through a numerical solution obtained by using some of the actual orbital elements of Sputnik I and Vanguard I satellites. For these orbits, we found that the most fuel-efficient transfer is obtained by applying the initial impulse at apocenter and keeping the transfer orbit aligned with the initial orbit.

AB - We study a more complex case of Hohmann orbital transfer of a satellite by considering non-coplanar and elliptical orbits, instead of planar and circular orbits. We use as parameter the angle between the initial and transference planes that minimizes the energy, and therefore the fuel of a satellite, through the application of two non-tangential impulses for all possible cases. We found an analytical expression that minimizes the energy for each configuration. Some reasonable physical constraints are used: we apply impulses at perigee or apogee of the orbit, we consider the duration of the impulse to be short compared to the duration of the trip, we take the nodal line of three orbits to be coincident and the three semimajor axes to lie in the same plane. We study the only four possible cases but assuming non-coplanar elliptic orbits. In addition, we validate our method through a numerical solution obtained by using some of the actual orbital elements of Sputnik I and Vanguard I satellites. For these orbits, we found that the most fuel-efficient transfer is obtained by applying the initial impulse at apocenter and keeping the transfer orbit aligned with the initial orbit.

KW - Hohmann transfer

KW - Non-coplanar orbit transfer

KW - Optimization

KW - Plane change

KW - Two-impulse

UR - http://www.scopus.com/inward/record.url?scp=84938633625&partnerID=8YFLogxK

U2 - 10.1007/s10509-015-2463-8

DO - 10.1007/s10509-015-2463-8

M3 - Article

AN - SCOPUS:84938633625

VL - 359

JO - Astrophysics and Space Science

JF - Astrophysics and Space Science

SN - 0004-640X

IS - 1

M1 - 6

ER -