Computation of low energy Earth-to-Moon transfers with moderate flight time

Yagasaki, Kazuyuki

doi:10.1016/j.physd.2004.07.005

Cited by 44 publications

(36 citation statements)

References 18 publications

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“…In contrast, in the present work we found periodic orbits and arcs which, besides being fast and of low energy, perform repeated passages around the primaries. Moreover, it must be noted that Bollt and Meiss (1995); Ross et al (2003), and Yagasaki (2004a) only address the Earth-Moon RTBP, and though the most recent work by Yagasaki (2004b) introduces the solar perturbation, it does it through the BCP, which is not a self-consistent model (Andreu 1998) and is less accurate than the QBCP. In contrast, in this work we addressed the problem in the frame of the QBCP, which is a far more realistic model.…”

Section: Periodic Orbits and Periodic Arcs In The Qbcpmentioning

confidence: 99%

Extension of fast periodic transfer orbits from the Earth–Moon RTBP to the Sun–Earth–Moon Quasi-Bicircular Problem

Leiva

Briozzo

2008

Celest Mech Dyn Astr

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Starting from 80 families of low-energy fast periodic transfer orbits in the Earth-Moon planar circular Restricted Three Body Problem (RTBP), we obtain by analytical continuation 11 periodic orbits and 25 periodic arcs with similar properties in the Sun-Earth-Moon Quasi-Bicircular Problem (QBCP). A novel and very simple procedure is introduced giving the solar phases at which to attempt continuation. Detailed numerical results for each periodic orbit and arc found are given, including their stability parameters and minimal distances to the Earth and Moon. The periods of these orbits are between 2.5 and 5 synodic months, their energies are among the lowest possible to achieve an EarthMoon transfer, and they show a diversity of circumlunar trajectories, making them good candidates for missions requiring repeated passages around the Earth and the Moon with close approaches to the last.

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Section: Periodic Orbits and Periodic Arcs In The Qbcpmentioning

confidence: 99%

Extension of fast periodic transfer orbits from the Earth–Moon RTBP to the Sun–Earth–Moon Quasi-Bicircular Problem

Leiva

Briozzo

2008

Celest Mech Dyn Astr

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“…It was shown in Yagasaki (2004) that when the first injection Dv s and the starting and arriving parking orbits are fixed, the total velocity change Dv becomes minimum at r 0 ¼ r e . So we search a trajectory of (3) such as (i) it starts on the Earth parking orbit of the radius r s and arrives on the Moon parking orbit of the radius r e ; (ii) its velocities at the starting and arriving points are tangent to the circular orbits in the non-rotating coordinate systems fixed at the Earth and Moon, respectively; and (iii) Dv is as small as possible.…”

Section: Earth-to-moon Transfersmentioning

confidence: 99%

“…This model has been proven to exhibit very complicated dynamics and to have a variety of trajectories including periodic, quasiperiodic and chaotic ones (see Koon et al, 2000a and references therein). Such a property was used to propose new Earth-to-Moon transfers in Belbruno (1987), Belbruno and Miller (1993), Bollt and Meiss (1995), Schroer and Ott (1997), Belbruno and Carrico (2000), Bello Mora et al (2000), Koon et al (2000bKoon et al ( , 2001, Ott (1997) and Yagasaki (2004). The possibility of low energy transfers associated with chaotic dynamics of the PCR3BP was first discussed in Belbruno (1994).…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, Yagasaki (2004) used the simple PCR3BP of the Earth-Moon system and found transfers with 4.1-7.5% lower cost and 0.92-8.2 times flight time (110 h-41 days), as well as one with the same cost but 22% shorter flight time, compared to the Hohmann type transfer. He reduced computation of optimal transfers to a non-linear boundary value problem (BVP) and solved it and continue its solutions numerically to obtain the optimal transfers.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we take into account the influence of the Sun and extend the approach of Yagasaki (2004) to obtain a more efficient Earth-to-Moon transfer trajectory. We show that the use of the solar gravitation further lowers the transfer cost drastically as in Belbruno and Miller (1993) and Koon et al (2000bKoon et al ( , 2001.…”

Section: Introductionmentioning

confidence: 99%

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Sun-perturbed earth-to-moon transfers with low energy and moderate flight time

Yagasaki

2004

Celestial Mech Dyn Astr

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We construct a spacecraft transfer with low cost and moderate flight time from the Earth to the Moon. The motion of the spacecraft is modeled by the planar circular restricted three-body problem including a perturbation due to the solar gravitation. Our approach is to reduce computation of optimal transfers to a non-linear boundary value problem. Using a computer software called AUTO, we solve it and continue its solutions numerically to obtain the optimal transfers. Our result also shows that the use of the solar gravitation can further lower the transfer cost drastically.

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On the construction of low-energy cislunar and translunar transfers based on the libration points

Yan

2013

Astrophys Space Sci

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There exist cislunar and trans-lunar libration points near the Moon, which are referred as the LL 1 and LL 2 points respectively and can generate the different types of low-energy trajectories transferring from Earth to Moon. The time-dependent analytic model including the gravitational forces from the Sun, Earth and Moon is employed to investigate the energy-minimal and practical transfer trajectories. However, different from the circular restricted three-body problem, the equivalent gravitational equilibria are defined according to the geometry of instantaneous Hill's boundary due to the gravitational perturbation from the Sun. The relationship between the altitudes of periapsis and eccentricities is achieved from the Poincaré mapping for all the lunar captured trajectories, which presents the statistical feature of the fuel cost and captured orbital elements rather than generating a specified Moon-captured segment. The minimum energy required by the captured trajectory on a lunar circular orbit is deduced in the spatial bi-circular model. It is presented that the asymptotical behaviors of invariant manifolds approaching to/from the libration points or halo orbits are destroyed by the solar perturbation. In fact, the energy-minimal cislunar transfer trajectory is acquired by transiting LL 1 point, while the energy-minimal trans-lunar transfer trajectory is obtained by transiting LL 2 point. Finally, the transfer opportunities for the practical trajectories escaped from the Earth and captured by the Moon are yielded by transiting halo orbits near LL 1 and LL 2 points, which can be used to generate the whole trajectories. Conley had achieved the low-energy cislunar trajectories from the viewpoint of LL 1 point (Conley 1969). Bolt and Meiss obtained a low-energy cislunar transfer trajectory by the shooting method developed in chaotic dynamics with the total fuel consumption of V =750m/s and the flight duration of t =748 days (Bolt and Meiss 1995). Schroer and Ott improved the shooting method to achieve the transfer trajectory with similar fuel consumption but cutting off half of the transfer time (t =377.5 days) (Schroer and Ott 1997). Macau gained a transfer trajectory with a little more fuel consumption but much less transfer time than Schroer and Ott, i.e., V =767m/s and t =284 days (Macau 1998). Ross and Koon optimized the transfer time and fuel consumption to yield the better result, i.e., V =860m/s and t =65 days (Ross and Koon 2003). Topputo and Vasile employed the Lambert equation 3 in CR3BP to solve the two-point boundary problems and obtained the similar result with Ross and Koon (Topputo and Vasile 2005). Xu et al. investigated the occurrence condition for low-energy transfer and discovered that the transiting trajectories near LL 1 point are preferred to generate the low-thrust cislunar trajectory (Xu et al. 2012). On the other hands, Belbruno et al. raised a new type of trans-lunar trajectories by the numerical method, which has a great application in rescuing Japanese lunar spacecraft "Hiten" ...

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Computation of low energy Earth-to-Moon transfers with moderate flight time

Cited by 44 publications

References 18 publications

Extension of fast periodic transfer orbits from the Earth–Moon RTBP to the Sun–Earth–Moon Quasi-Bicircular Problem

Extension of fast periodic transfer orbits from the Earth–Moon RTBP to the Sun–Earth–Moon Quasi-Bicircular Problem

Sun-perturbed earth-to-moon transfers with low energy and moderate flight time

On the construction of low-energy cislunar and translunar transfers based on the libration points

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