Robert A. Braeunig
The following is an animated graphical representation of a computer simulated circumlunar trajectory with free return to Earth. 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 red 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.
Below the animation is a table giving the elapsed time since translunar injection, the geocentric distance to Earth, the lunar centric distance to the Moon, the spacecraft velocity relative to Earth, and the velocity relative to the Moon. Each four-hour increment is included as well as a few other important points in the trajectory.
The following simplifying assumptions have be made:
|Distance to Earth
|Distance to Moon
|Velocity, Earth relative
|Velocity, Moon relative
|000:00:00||6,563||388,677||10,943||11,629||Translunar Injection, Note 1|
|060:17:41||346,089||64,374||829||1,074||Equigravisphere, Note 2|
|075:32:51||387,587||3,184||998||2,021||Pericynthion, Note 3|
|090:32:27||347,042||64,374||823||1,075||Equigravisphere, Note 2|
|151:10:03||6,500||387,407||10,998||11,595||Entry Interface, Note 4|
1) Translunar Injection, or TLI, is a propulsive maneuver used to set a spacecraft on a trajectory that will arrive at the Moon. Prior to TLI the spacecraft is in a low circular parking orbit around Earth. In this example, we have assumed a parking orbit altitude of 185 kilometers and a TLI delta-v of 3,150 m/s.
2) The Equigravisphere, or "sphere of influence", is the boundary where the spacecraft trajectory is considered to transition from earth-centered to moon-centered, which NASA defines as being 40,000 statute miles (64,374 kilometers) from the center of the Moon. This arbitrary definition is not to be confused with the commonly held definition of the equigravisphere being all points in space where Earth and lunar gravity are equal, the so-called "neutral point."
3) Pericynthion is the point in the spacecraft's trajectory that is nearest the Moon. For a free return trajectory, the altitude at pericynthion is typically about 100 to 1,500 nautical miles (185 to 2,800 km) - see diagram. The pericynthion altitude in this example is 1,446 kilometers.
4) Entry Interface is the point at which the first effects of Earth's atmosphere are encountered, defined as an altitude of 400,000 feet (121,920 meters). An entry flight path angle of -5.3 to -7.7 degrees is required for a survivable reentry. In this example, the entry angle is -6.46 degrees.
Here is an illustration of the same circumlunar free return trajectory as seen from a Moon-centered perspective: Lunar-Centric View.
Also see the following simulation: Lunar Hybrid Profile with LOI and TEI.