Apolune

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

Definition

Apolune is the farthest point on a spacecraft's lunar orbit from the Moon's center of mass. Together with perilune (the closest point), it describes the basic geometric characteristics of a lunar orbit. Apolune and perilune correspond to the two endpoints of the semi-major axis of an elliptical orbit.

Key Elements

Geometric Significance of Apolune

In the two-body problem framework, the distance from apolune to the Moon's center of mass for an elliptical lunar orbit is:

r_{\text{apolune}} = a(1 + e)

where $a$ is the semi-major axis and $e$ is the orbital eccentricity. Apolune altitude $h_a$ is the distance from apolune to the Moon's surface:

h_a = r_{\text{apolune}} - R_M

where $R_M$ is the Moon's radius (approximately 1737.4 km).

The relationship between apolune and perilune can be expressed through orbital eccentricity:

e = \frac{r_{\text{apolune}} - r_{\text{perilune}}}{r_{\text{apolune}} + r_{\text{perilune}}}

Apolune in Different Orbit Types

Near-circular orbits: Apolune and perilune altitudes are similar, with eccentricity $e \approx 0$
Highly elliptical orbits: Apolune is much higher than perilune, with eccentricity $e$ approaching 1, suitable for high lunar orbit observation
DRO orbits: In the synodic reference frame, the apolune of a DRO lies on the Earth-Moon line on the side away from the Moon, with its position varying with resonance ratio
NRHO orbits: The apolune altitude of a near-rectilinear halo orbit is much greater than the perilune altitude, forming an extremely elongated elliptical shape, with perilune near the lunar north polar region

Influence of Apolune Altitude on Orbital Period

According to Kepler's third law, the relationship between orbital period $T$ and semi-major axis $a$ is:

T = 2\pi\sqrt{\frac{a^3}{\mu_M}}

where $\mu_M$ is the Moon's gravitational parameter. Higher apolune altitude means larger semi-major axis and longer orbital period. This relationship is particularly important in DRO resonance design -- by adjusting the apolune position, specific resonance ratios with the Moon's orbital period can be achieved.

Application Value

Apolune parameters have important applications in orbital design:

Orbital configuration design: Apolune altitude together with perilune altitude determines orbit shape, serving as the basic parameter for describing target orbits like DRO and NRHO
Communication relay planning: When apolune is on the lunar far side, it can provide communication coverage for regions not visible from Earth
Orbit transfer design: During transfers from highly elliptical orbits to DRO, the apolune evolution trajectory directly affects transfer efficiency
Orbital stability analysis: Changes in apolune position are an important indicator for assessing long-term orbital stability

References

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