Hybrid Lunar Profile with LOI and TEI

Robert A. Braeunig
© September-2008

The following is an animated graphical representation of a computer simulated hybrid lunar profile with lunar orbit insertion and transearth injection. Spacecraft position is shown relative to a fixed Earth, with Earth being located at the origin of the axes and represented by the blue disc. Location of the spacecraft is shown in four-hour increments with the path traversed since translunar injection represented by the trailing line. The yellow line is the Moon's orbit and the Moon is shown as a gray disc. The distances shown are in units of kilometers and the illustration is drawn to scale. The time scale is one second equals four hours.

A hybrid profile begins as a free return trajectory and transitions to a non-free return following a midcourse transfer maneuver (see diagram). The red line represents the free return portion of the trajectory (this is the same trajectory as modeled here). After completion of the transfer maneuver, the trajectory line changes to blue. As the spacecraft swings behind the Moon, a lunar orbit insertion (LOI) maneuver is performed. For this demonstration four lunar orbits are completed*, which are represented by the magenta line. To set the spacecraft on a trajectory that will return it to Earth, a transearth injection (TEI) maneuver is performed. The green line represents the transearth trajectory.

The following simplifying assumptions have be made:

(* Four orbits is an arbitrary selection; any other number could just as easily been used.)



Event Timeline and Propulsive Maneuvers

Event Time
Distance to Earth
Distance to Moon
Velocity, Earth relative Velocity, Moon relative
before after before after
Translunar Injection 000:00:00 6,563
altitude = 185 km
388,677 +3,150 7,793 10,943 8,489 11,629
Midcourse Transfer 028:00:00 226,380 189,041 -9.74 1,367 1,357 1,170 1,164
Equigravisphere 060:26:14 345,293 64,374 n/a 816 1,068
Lunar Orbit Insertion
075:33:27 386,224 1,849
altitude = 111 km
-880.0 1,511 646 2,508 1,628
Transearth Injection 083:24:22 386,252 1,849
altitude = 111 km
+923.9 605 1,529 1,628 2,552
Equigravisphere 097:23:49 339,598 64,374 n/a 970 1,172
Entry Interface 152:06:16 6,500
altitude = 122 km
387,651 n/a 11,007
Entry angle = -6.50o

Compare this simulation's delta-V figures to Apollo 12:

Maneuver Delta-V (ft/s)
Apollo 12 Simulation
TLI 10,515 10,335
MCC 61.8 32.0
LOI 2,889.5 2,887.2
TEI 3,042.0 3,031.3


Also see the following simulation: Circumlunar Free Return Trajectory.