Low Prograde Orbit (LoPO)
Author: Tianjiang Says
Website: https://cislunarspace.cn
Definition
A Low Prograde Orbit (LoPO) is a low-altitude prograde periodic orbit near the Moon in the Circular Restricted Three-Body Problem (CR3BP), belonging to the Moon-Centered Orbits family. LoPO revolves counterclockwise around the Moon in the rotating coordinate system (in the same direction as the Moon's orbit around the Earth) and has a relatively low orbital altitude, hence the name "Low Prograde Orbit." Together with DPO (Distant Prograde Orbit) and DRO (Distant Retrograde Orbit), LoPO forms the complete spectrum of lunar-centered periodic orbits in cislunar space.
Core Elements
Dynamical Characteristics of LoPO
LoPO possesses the following properties within the CR3BP framework:
- Low orbital altitude: LoPO operates close to the lunar surface with a relatively low altitude above the Moon, similar to a traditional near-lunar orbit
- Short period: LoPO has relatively short orbital periods, ranging from approximately 0.86 to 11.50 days; low-altitude members have periods close to those of typical near-lunar circular orbits (approximately 2 hours, which appears as approximately 1 day in the rotating coordinate system)
- High energy: LoPO has a high Jacobi constant (approximately 3.18 ~ 3.53), indicating that these orbits are at a high energy level
- Prograde motion: LoPO moves in the same direction as the Moon's orbit, appearing as counterclockwise motion in the rotating coordinate system
Orbital Parameter Characteristics of LoPO
Using the Earth-Moon system as an example, the main parameter ranges for the LoPO orbit family are as follows (based on the dynamic catalog statistics by Guzzetti et al.):
| Parameter | Range |
|---|---|
| Jacobi Constant | 3.1805 ~ 3.5268 (mean 3.2230) |
| Orbital Period | 0.86 ~ 11.50 days (mean approximately 3–5 days) |
| Stability Index | Wide variation range |
The high Jacobi constant of LoPO indicates that transferring from LEO to LoPO requires significant energy injection, but the short period is advantageous for orbital operations and mission planning.
Comparison Between LoPO, DPO, and DRO
LoPO, DPO, and DRO are three important categories within the lunar-centered orbit family:
| Feature | DRO | DPO | LoPO |
|---|---|---|---|
| Motion direction | Retrograde | Prograde | Prograde |
| Orbital altitude | Far from Moon | Moderate | Near Moon |
| Period range | 5.87 ~ 27.38 days | 5.82 ~ 28.00 days | 0.86 ~ 11.50 days |
| Energy level | Low (JC 1.44 ~ 3.02) | Moderate (JC 2.99 ~ 3.18) | High (JC 3.18 ~ 3.53) |
| Stability | Predominantly stable | Highly variable | Highly variable |
Role of LoPO in Lunar Missions
LoPO has the following characteristics in cislunar mission design:
- Lunar parking orbit: LoPO's proximity to the Moon makes it a natural candidate parking orbit for lunar landing missions
- Short-period advantage: LoPO's short period enables rapid orbital adjustments and frequent launch windows
- Communication coverage: Low-altitude members can provide high-resolution lunar surface observation and communication coverage
- Relationship with resonant orbits: Some LoPO members may form simple resonant relationships with the Moon (e.g., 1:1 resonance)
Station-Keeping Challenges
LoPO, as a low-altitude orbit, faces certain unique challenges:
- Proximity to the Moon means that lunar non-spherical gravity (J2, C22, etc.) and terrain perturbations are more significant
- More frequent station-keeping maneuvers may be required to counteract perturbation effects
- In realistic dynamical environments (ephemeris models), the periodicity and closure of LoPO are more severely disrupted
Application Value
LoPO has the following applications in cislunar space missions:
- Lunar landing missions: LoPO can serve as a temporary parking and inspection orbit for crewed or uncrewed lunar landing missions
- Lunar scientific observation: LoPO's proximity to the Moon is suitable for high-resolution lunar surface mapping and scientific exploration
- Communication relay: Some LoPO orbits can provide communication relay services between the lunar surface and Earth
- Orbit comparison and selection: In the dynamic catalog framework proposed by Guzzetti et al., LoPO is an important member of the lunar-centered orbit family, providing near-lunar orbital options for mission design
Related Concepts
- Distant Retrograde Orbit (DRO)
- Distant Prograde Orbit (DPO)
- Prograde
- Retrograde
- Circular Restricted Three-Body Problem (CR3BP)
References
- Guzzetti D, Bosanac N, Howell K C. A framework for efficient trajectory comparisons in the Earth-Moon design space[C]. AAS/AIAA Space Flight Mechanics Meeting, 2014.
- Folta D, Bosanac N, Guzzetti D, et al. An Earth-Moon system trajectory design reference catalog[C]. 2nd IAA Conference on Dynamics and Control of Space Systems, 2014.
- Whitley R, Martinez R. Options for staging orbits in cislunar space[C]. AIAA Space Conference and Exposition, 2016.