Translunar Injection

Translunar injection (TLI) is an orbital manoeuvre employed to send a spacecraft from Earth orbit onto a trajectory that will carry it to the Moon. It represents a critical phase in lunar missions, determining both the path and the timing of a spacecraft’s journey. TLI raises the spacecraft from a low Earth parking orbit into a highly elongated trajectory whose apogee intersects the Moon’s orbit. Depending on mission requirements, this transfer may approximate a classical Hohmann transfer, or it may follow a low-energy pathway that trades time for reduced propellant consumption.

Purpose and Fundamental Principles

A spacecraft typically begins a lunar mission in a stable, circular low Earth orbit. The TLI manoeuvre is then executed, usually via a powerful chemical rocket burn, to increase the spacecraft’s velocity by the necessary delta-v to escape this circular orbit. The new trajectory becomes a highly elliptical orbit about the Earth, carrying the spacecraft outward until it nears the lunar orbital radius.
The TLI burn must be precisely timed. As the spacecraft coasts toward apogee, the Moon must be approaching the same point of space, allowing the spacecraft to enter the Moon’s sphere of influence on an intercept path. The accuracy of this burn is crucial; even minor deviations can significantly alter the spacecraft’s arrival conditions at the Moon.

Free-Return Trajectories

Some lunar missions employ free-return trajectories, in which the spacecraft naturally loops around the far side of the Moon and returns to Earth without further propulsion. This path is particularly valued for human missions due to its inherent safety margin. Apollo 8, 10 and 11 used such trajectories initially, while later missions adopted similar hybrid paths that incorporated mid-course corrections for improved targeting.

Trajectory Modelling

Analysing and designing translunar trajectories involves several modelling approaches of increasing complexity.
Patched Conics ApproximationThis simplified method treats the spacecraft’s path as a series of two-body interactions. The craft is assumed to move under Earth’s gravity until it encounters the Moon’s sphere of influence, at which point calculations switch to lunar gravity. This approach is sufficiently accurate for preliminary mission planning and conceptual studies.
Restricted Circular Three-Body ApproximationA more accurate model treats the Earth, Moon and spacecraft as a three-body system, in which the spacecraft’s negligible mass permits simplification. In this model the gravitational influence of both major bodies acts concurrently, creating libration points and complex dynamical pathways. The resulting three-body problem cannot be solved analytically and requires numerical computation.
High-Fidelity Numerical ModellingFor final mission design, full simulations incorporate non-uniform gravitational fields of both Earth and Moon, perturbations from the Sun and other bodies, and effects such as solar radiation pressure. These models allow accurate propagation of spacecraft motion over long durations.

History of Translunar Injection

The first attempt at a TLI occurred on 2 January 1959 with the Soviet Luna 1 spacecraft. Due to an inaccurately executed burn, the probe missed the Moon and entered heliocentric orbit. Success followed later that year with Luna 2, which became the first spacecraft to impact the Moon after a correctly calculated TLI.
Between 1959 and 1976 the Soviet Union conducted numerous lunar missions under the Luna and Zond programmes. In parallel, the United States began its lunar efforts with Ranger 3 in 1962, followed by successful impact and reconnaissance missions including Ranger 4, the Surveyor landers and the Lunar Orbiter programme.
The most famous use of TLI came during the Apollo programme. For these missions, a restartable J-2 engine in the third stage of the Saturn V rocket performed the TLI burn, typically lasting about 350 seconds and imparting a delta-v of approximately 3.05–3.25 kilometres per second. Following TLI, the spacecraft travelled at roughly 10.4 kilometres per second relative to the Earth. Several TLI burns were visible from the ground, including the dramatic predawn Apollo 8 burn observed from Hawaii and the Apollo 10 injection seen from Australia.

Later Missions and Low-Energy Transfers

After the Apollo era, TLI remained a standard procedure in lunar exploration, with several missions experimenting with alternative low-energy pathways.

• Hiten (1990): Japan’s first lunar mission used a low delta-v transfer taking six months instead of the three days typical of Apollo missions.
• Clementine (1994): Employed an extended transfer involving two Earth flybys before lunar orbit insertion.
• Asiasat-3 (1997): Became the first commercial satellite to reach the Moon’s sphere of influence after a launch failure; it used lunar swingbys as a low-delta-v route to geostationary orbit.
• SMART-1 (2003): ESA’s first lunar orbiter used solar-electric propulsion, taking thirteen months to reach lunar orbit.
• Chang’e 1 (2007) and Chandrayaan-1 (2008): China and India incrementally raised spacecraft apogees through multiple burns before heading to the Moon.
• Beresheet (2019): Used a similar method but crashed during descent.
• GRAIL (2011): NASA twin spacecraft used a low-energy trajectory passing near the Sun–Earth L1 point, requiring over three months to reach lunar orbit.

Analytical and Mission Design Considerations

Several key factors determine the design of a translunar injection:

• Delta-v requirements: Classical TLI demands around 3.2 kilometres per second from low Earth orbit, though low-energy methods greatly reduce this at the expense of time.
• Timing: The relative positions of Earth, Moon and spacecraft determine the allowable launch windows and TLI burn epoch.
• Perturbations: Gravitational influences, solar radiation pressure and non-uniform fields must be considered for long-duration missions.
• Safety margins: Free-return profiles remain an important design option for human missions.