Perilune

Author: CislunarSpace
Website: https://cislunarspace.cn

Definition

Perilune is the closest point on a spacecraft's lunar orbit to the Moon's center of mass. In the geometric description of a lunar orbit, perilune and apolune together define the basic shape of the orbit. Perilune altitude is the distance from the Moon's surface to the perilune, and is a critical parameter in orbital design.

Key Elements

Geometric Significance of Perilune

In the two-body problem framework, a lunar orbit is a conic section (ellipse, parabola, or hyperbola). For elliptical orbits, the perilune lies at the end of the semi-major axis closest to the Moon, with the distance from the Moon's center of mass given by:

r_{\text{perilune}} = a(1 - e)

where $a$ is the semi-major axis and $e$ is the orbital eccentricity. For complex orbits like DRO and NRHO in the restricted three-body problem framework, the perilune definition still applies, but the orbits are no longer standard conic sections.

Influence of Perilune Altitude on Gravity Assist

During a lunar gravity assist, perilune altitude is the key factor determining the magnitude of energy change:

Lower perilune (e.g., 100-200 km): Lunar gravity has a stronger effect, producing larger energy change $\Delta E$ , but the trajectory is significantly perturbed by the Moon's non-spherical gravity field ( $J_2$ term, etc.), with collision risk
Higher perilune (e.g., 1000-10000 km): Weaker gravitational effect with smaller energy change, but better orbital safety, suitable for long-duration missions

The velocity deflection angle $\delta$ during the gravity assist relates to perilune distance $r_p$ as:

\sin\frac{\delta}{2} = \frac{1}{1 + \dfrac{r_p \cdot v_\infty^2}{\mu_M}}

where $v_\infty$ is the spacecraft's hyperbolic excess velocity relative to the Moon, and $\mu_M$ is the Moon's gravitational parameter. Lower perilune produces greater deflection.

Perilune Precision Control

In actual missions, perilune precision control faces several challenges:

Lunar non-spherical gravity: Non-uniform mass distribution causes significant perturbations near perilune
Orbit determination errors: Deep-space ranging and velocity measurement accuracy directly affect perilune position prediction
Maneuver timing selection: Perilune maneuver timing and magnitude must be precisely planned to avoid orbit deviation accumulation

Application Value

Perilune parameters have core application value in cislunar missions:

Lunar gravity assist orbit design: Precisely controlling energy and orbital direction changes during gravity assist by adjusting perilune altitude
DRO transfer injection: Wei et al. (2026) showed that when transferring from LEO to DRO via lunar gravity assist, perilune altitude is the core parameter determining transfer efficiency
Safety constraints: Perilune altitude must meet minimum safe distance requirements to avoid collision with lunar terrain
Scientific observation: Low-perilune orbits are suitable for high-resolution lunar surface observation

References

Wei Z et al. Research on lunar gravity-assist injection into cislunar distant retrograde orbit families[J]. 2026.
Vallado D A. Fundamentals of Astrodynamics and Applications[M]. 4th ed. 2013.
Broucke R. Periodic orbits in the restricted three-body problem with Earth-Moon masses[R]. 1968.