Author: CislunarSpace

Source: CislunarSpace

TLI Overview

Definition

TLI (Trans-Lunar Injection) is the first major maneuver in a lunar transfer mission, delivering a spacecraft from a low-Earth parking orbit into a trans-lunar trajectory. The TLI maneuver is typically executed from a Earth parking orbit (LEO or high elliptical orbit) using an upper stage or the spacecraft's main engine to provide the required ΔV\Delta V.

Historically, missions that have performed TLI maneuvers include: Apollo crewed lunar missions, the Chang'e series lunar probes, the SLIM lunar lander, and several deep space exploration missions.

Launch Windows

TLI launch windows are determined by the Earth-Moon geometry, with the main considerations including:

Lunar Phase

The optimal TLI launch window occurs when the Moon is near perigee, when the Moon is closest to Earth and the transfer requires the least energy. Lunar phase (the angle relative to the Sun) is also an important parameter — the ideal launch timing is when the Moon's position in the sky favors observation and communication.

Launch Opportunity Frequency

Due to the orbital period relationship of the Earth-Moon system, suitable TLI launch windows occur approximately every 14-15 days (half a synodic month). This is because after each launch, one must wait for the Moon to move to the appropriate position for optimal-energy arrival.

Cost of Window Deviation

If the launch timing deviates from the optimal window:

  • Transfer energy C3C_3 increases (possibly reaching -0.3 km2^2/s2^2 or higher)
  • Transfer time varies (may lengthen or shorten)
  • Arrival phase at the Moon is unfavorable, affecting rendezvous/docking or landing

Energy Budget

TLI energy requirements are characterized by hyperbolic excess velocity C3C_3:

C3=v2−2μErC_3 = v^2 - \frac{2\mu_E}{r}

The velocity increment needed to go from LEO (185 km circular orbit, v≈7.8v \approx 7.8 km/s) to escape velocity (vescape=2μE/r≈11.0v_{escape} = \sqrt{2\mu_E/r} \approx 11.0 km/s):

ΔVTLI=vescape−vLEO≈3.1−3.3 km/s\Delta V_{TLI} = v_{escape} - v_{LEO} \approx 3.1-3.3 \text{ km/s}

MissionLEO Parking OrbitTLI ΔVNotes
Apollo 11185 km~3.05 km/sSaturn V S-IVB
Chang'e 5190 km~3.0 km/sOrbiter+Return
SLIM190 km~3.1 km/sSmall lander

Post-Launch Trajectory

A typical TLI launch sequence:

  1. LEO Insertion: Launch vehicle delivers spacecraft to parking orbit
  2. Checkout and Wait: Perform system checks in LEO, await suitable launch window
  3. TLI Maneuver: Upper stage or main engine ignition, providing ΔV≈3.1\Delta V \approx 3.1 km/s
  4. Upper Stage Separation: Transfer stage separates from spacecraft
  5. Mid-Course Correction (optional): 1-2 trajectory correction maneuvers (ΔV∼1−50\Delta V \sim 1-50 m/s)
  6. Lunar Arrival: Enter Moon's sphere of influence (~64,000 km), prepare for orbit insertion

Launch Window Planning Tools

Modern mission planning uses tools such as GMAT and STK for TLI launch window optimization:

  • GMAT: NASA's open-source orbit design tool, supporting TLI optimization and pork-chop plot generation
  • STK (Satellite Tool Kit): AGI's professional orbit analysis software, providing high-precision window calculations

Simulation Experiments

Design TLI maneuvers in the Satellite Orbit Simulation Lab to observe transfer trajectory profiles under different launch windows.