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 -