Survey of Ballistic Lunar Transfers to Near Rectilinear Halo Orbit

June 29, 2022

How are Ballistic Lunar Transfers Used to Transfer from Earth in Near Rectilinear Halo Orbit?

This paper presents a survey of ballistic lunar transfer (BLT) trajectories from Earth launch to insertion into a near rectilinear halo orbit (NRHO). Results are described from a detailed set of related mission design studies: the evolution over time of families with and without an outbound lunar flyby; analysis of eclipses; analysis of the 𝛥V requirements of changing arrival time to rendezvous; and description of the trade space for time of flight vs deterministic 𝛥V. An ephemeris model is used throughout. These analyses are presented in order to inform future missions to NRHOs.


Introduction & Motivation

BLTs are a type of low-energy transfer in which a spacecraft launches 1-2 million kilometers away from the Earth (where the Sun’s gravity perturbation becomes dominant), then returns to Earth with a larger radius of perigee than before and a different geocentric orbit plane. When designed with the proper geometry, it is possible to choose the perigee to coincide with the Moon’s orbit, bringing the spacecraft into the vicinity of the Moon. For many three-body target orbits, it is possible to design the transfer such that it arrives at the target orbit with very little insertion 𝛥V required. In the ideal case, the transfer is ballistic (zero deterministic 𝛥V) after launch.1 This type of transfer is being considered to deliver the Logistics Module, lander elements, and other cargo to the lunar Gateway. Background information on NRHOs is given below. This paper identifies and studies several favorable families of BLTs, where a family is defined as a set of solutions that are topologically distinct from other sets of solutions. Tens of thousands of possible trajectories have been generated, optimized, and evaluated in order to understand the trade space.

In order to quantify the benefits of a BLT compared to a direct lunar transfer in terms of delivered mass, an analysis is performed. The expected performance of the SLS Block 1 launch vehicle2 (characterized as maximum launch mass as a function of characteristic energy C3) is used in conjunction with an assumed spacecraft propulsion system Isp of 300 seconds. The resulting mass delivered to NRHO is shown in Figure 1. Proportional benefits exist for other launch vehicles as well.

The benefits of BLTs to an NRHO include:

  • Reduced spacecraft 𝛥V (50-150 m/s depending on the desired launch period, compared to 350-550 m/s for direct transfers)
  • Increased mass delivered to the cislunar environment
  • Reduced operational cadence
  • More launch opportunities
  • The ability to send secondary payloads to anywhere in cislunar space

These benefits require trades including:

  • Increased time of flight (12 to 20 weeks, compared to a few days for direct transfers)
  • Greater maximum distance from the Earth
  • Increased operations duration
  • A higher C3 for some launch options

These benefits and trades are expanded upon in this paper. Further studies will characterize the costs/benefits of navigating BLTs to NRHOs compared to direct transfers.

Figure 1. Deliverd dry mass for SLS Block 1

Figure 1. Delivered dry mass for SLS Block 1.

The analysis presented in this paper finds that BLTs are available with wide launch periods. Transfers to the Moon are highly affected by the inclination of the Moon’s orbit relative to an Earth equator frame, which oscillates between approximately 18o and 28o with a period of approximately 18.6 years. BLTs take advantage of the Sun’s gravity to perform an inclination change, thus offering frequent launch opportunities regardless of the Moon’s inclination.

To learn more, you can read our white paper “Survey of Ballistic Lunar Transfers to Near Rectilinear Halo Orbit.”

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Cover Image for Survey of Ballistic Lunar Transfers to Near Rectilinear Halo Orbit


1Parker, J. S. & Anderson, R. L. Low-Energy Lunar Trajectory Design. (John Wiley and Sons, 2014).
2Hill, B. & Creech, S. NASA’s Space Launch System: A Revolutionary Capability for Science. (2014).
3Ocampo, C. A. An Architecture for a Generalized Trajectory Design and Optimization System. in International Conference on Libration Points and Missions (2002).
4 Folkner, W. M., Williams, J. G., Boggs, D. H., Park, R. S. & Kuchynka, P. The Planetary and Lunar Ephemerides DE430 and DE431. Interplanet. Netw. Prog. Rep 196, (2014).
5Howell, K. C. Three-dimensional, Periodic, ‘Halo’ Orbits. Celest. Mech. 32, 53–71 (1984).
6Zimovan, E. M., Howell, K. C. & Davis, D. C. Near Rectilinear Halo Orbits and Their Application in Cis-Lunar Space. in Advances in the Astronautical Sciences (2017). doi:10.1111/j.1744- 6171.2010.00231.x
7Howell, K. C. & Breakwell, J. V. Almost Rectilinear Halo Orbits. Celest. Mech. (1984). doi:10.1007/BF01358402
8Davis, D. C. et al. Orbit Maintenance and Navigation of Human Spacecraft at Cislunar Near Rectilinear Halo Orbits. in 27th AAS/AIAA Space Flight Mechanics Meeting (2017).
9Howell, K. C. Families of Orbits in the Vicinity of the Collinear Libration Points. 2Journal Astronaut. Sci. 49, 107–125 (2001).
10Newman, C. P., Sieling, R., Davis, D. C. & Whitley, R. J. Attitude Control and Orbit Determination of a Crewed Spacecraft With Lunar Lander in Near Rectilinear Halo Orbit. AAS Astrodyn. Spec. Conf. 1–19 (2019).
11Parker, J. S. Families of low-energy lunar halo transfers. Adv. Astronaut. Sci. AAS 06-132 (2006).
12Whitley, R. J. et al. Earth-Moon Near Rectilinear Halo and Butterfly Orbits for Lunar Surface Exploration. 1–20
13Oberth, H. Ways to Spaceflight. (R. Oldenbourg Publishing House, 1929).
14Davis, D. C., Boudad, K. K., Phillips, S. M. & Howell, K. C. Disposal , Deployment, and Debris in Near Rectilinear Halo Orbits. in AAS/AIAA Astrodynamics Specialist Conference (2019).
15Conley, C. C. Low Energy Transit Orbits in the Restricted Three-Body Problem. SIAM J. Appl. Math. 16, (1968).
16Parker, J. S. Low-Energy Ballistic Lunar Transfers. (University of Colorado Boulder, 2007).
17Topputo, F. Trade-Off Between Cost and Time in Lunar Transfers : a Quantitative Analysis. 24th AAS/AIAA Sp. Flight Mech. Meet. St. Fe, New Mex. 1–15 (2014).
18Folta, D., Woodard, M., Sweetser, T., Broschart, S. B. & Cosgrove, D. Design and Implementation of the ARTEMIS Lunar Transfer Using Multi-Body Dynamics. Adv. Astronaut. Sci. 142, 1647–1665 (2012).
19Sweetser, T. H. et al. ARTEMIS Mission Design. ARTEMIS Mission 9781461495, 61–91 (2014).
20Folta, D. C., Bosanac, N., Cox, A. & Howell, K. C. The Lunar IceCube Mission Design: Construction of Feasible Transfer Trajectories with a Constrained Departure. in AAS 16-285 (2016).
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