Lunar Halo Orbits
Problem
Importance: Back to the Moon

No human being has set foot on the moon since Apollo 17 in December 1972. However, the moon may still have much to tell us. Ian Crawford of Birkbeck College in London states that the lunar geological record has much to tell us about the earliest history of the Solar System, the origin and evolution of the Earth-Moon system, and the geological evolution of rocky planets. The moon soil is also rich in helium, an important and increasingly depleted earth resource (2). Also, in the 2009 Lunar CRater Observation and Sensing Satellite (LCROSS) mission, water was discovered on the moon. These deposites of ice contain vast amounts of hydrogen. Moreover, the moon could also be a source for rare earth elements such as europium and tantalam, which are important for electronics and green energy products such as solar panels and hybrid cars (7). Crawford also argues that the lunar surface is ideal for astronomical observations in the ultra-low-frequency regime, a regime un-viewable from earth due to interference with the ionosphere. Radio waves at low frequencies are of interest to many astronomers because they could shed light on the universe’s “Dark Age”: that period when the universe was just a few million years old, before the formation of stars and galaxies (2).

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Figure 7: Apollo 17 Lunar Expedition (click for cite)

Finally, sending humans back to the moon will provide more insight into the long-term effects of microgravity on the human body, and will inspire advances in many types of lunar life support systems (7).

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Figure 8: Moon Base Concept Art (click for cite)



The Problem

Before radio telescopes, mining operations, geological studies, and human ventures can begin on the moon, an infrastructure must exist that can support it. One major problem with lunar missions is that no radio communication is available on the back side of the moon, the likely site of future moon endeavors. This means that operations will have no contact with earth for long periods of time leading to mission inefficiency and risk.



The Solution: Halo Communication Orbits

A potential solution to this problem, made available by the three-body dynamics of the Earth-Moon system, is a halo orbit near the L1 and L2 Lagrange points. With just two spacecraft (one at L1 and one at L2), the moon could be covered on both sides with full visibility to the Earth. Dr. Robert W. Farquhar proposed a communication satellite for the back side of the moon using an L2 halo orbit in 1968 (4).

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Figure 9: Farquhar's Lunar Relay Satellite (4)

The real benefit of this set-up is its simultaneous view of the backside of the moon and of Earth at all times.

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Figure 10: Communication with a Halo Satellite from Earth (4)

Farquhar says that the ideal halo orbiter could perform activities such as (4):

  • Control rendezvous and docking operations for Earth and Moon bound vehicles
  • Monitor and control the ascent and descent trajectories at the moon
  • Provide navigation and control of surface vehicles
  • Provide relay communication to the Earth


Lunar Halo Orbit Analysis

Orbit selection is very important when designing a lunar communications cluster. Hamera and Mosher suggest the following 3-spacecraft set-up (5).

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Figure 11: Example Lunar Communication Cluster (5)

Two orbits of the same energy are placed around the L1 and L2 points in order to provide total lunar coverage. The smaller L2 orbit has line of sight to the South Pole for 95% of its orbit.

Halo orbits do present problems because of their instability. This means that station keeping will need to be done to ensure that the spacecraft does not wander of its selected path. Farquhar argues that “the control techniques are extremely simple and the annual fuel expenditure is quite reasonable (ΔV   400fps per year)” (4). Moreover, the instability of these orbits can also be exploited to aid in orbit reconfigurability. In Hamera’s cluster, above, the spacecraft with the larger two orbits have the same energy allowing for low energy transfers between them. A low energy transfer is based on halo orbit manifolds. A set of stable (approaching) and unstable (departing) halo orbit manifolds shown below in the moon rotating frame (5).

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Figure 12: Halo Manifolds (5)

The red trajectories represent objects exponentially departing an unstable halo orbit. The green trajectories show objects that will exponentially approach a halo orbit. The intersection of the arriving and departing trajectories represent low earth transfers that exist within the system. An example transfer from L1 to L2 halo is shown below (5).

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Figure 13: Low Energy Transfer Between Two Halo Orbits (5)

The orbiter departs the L1 orbit on an unstable manifold, and approaches L2 on a stable manifold. The cost of such a drastic maneuver are only 10 m∕s. The total transfer time is about 72 days. These types of maneuvers give mission designers the ability to cost effectively reconfigure halo orbits to meet changing mission needs. This will increase the flexibility of lunar expeditions, increasing science and exploration, and providing opportunities for multi-agency collaboration on lunar communication systems (5).

A summary of halo orbit advantages are listed below (5):

  • Constant communication with the lunar surface
  • Slower apparent motion relative to ground stations
  • 100% Earth visibility
  • Halo orbit launches require less fuel than Geostationary launches
  • Autonomous navigation can be used to eliminate extensive Earth-based tracking
  • Fewer orbiters are needed to provide global coverage
  • Reconfigurability via low energy transfers