Free return path

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A free return path (engl. Free return trajectory) is a trajectory which a spacecraft without further drive from a first celestial body (for. Example, the ground ) to a second celestial body (e.g., as the moon ) and then returns. The term "free" is intended to make it clear that no further drive (thrust pulse) is necessary for this.

theory

Sketch of a circumlunar free return path (not to scale).

In the case of a free return path, the changes in the flight direction are brought about exclusively by gravity. The spacecraft will not enter a permanent orbit around the second body on a free return path (unless it ignites its engines, reduces its speed and leaves the original trajectory).

Using the example of a flight around the moon, two cases can be distinguished:

  • Circumlunar free return orbit around the moon. The point of closest approach to the moon, the periapsis (also known as periseles or perilune in English), is behind the moon when viewed from the earth . The spacecraft moves in the opposite direction of the moon's orbit ; the overall trajectory has the shape of an 8 (see sketch on the right).
  • Cislunar free return orbit around the moon. The spacecraft moves behind the lunar orbit as seen from the earth, then returns to the area within the lunar orbit, moves in front of the moon, is then diverted to a path outside of the lunar orbit by the lunar gravity, and then finally back from gravity to be directed to earth. The periapsis is on the earth- facing side of the moon, the spacecraft moves in the same direction as the moon on its orbit around the earth.

The flight time for a cislunar free return orbit is longer than that for a circumlunar return orbit, especially for orbits with a strong approach to the moon (periapsis): the flight time for a cislunar free return orbit decreases with increasing radius of the periapsis, while the flight time for a circumlunar free return path increases with increasing radius of the periapsis.

If one simply assumes that the moon's orbit around the earth is circular, there are even periodic orbits for the special case of the free return orbits that lie in the plane of the moon's orbit: after they have passed the earth, they would return to the moon return etc. The same is true for similar three-body problems (two bodies of high mass and one body of small mass in one plane).

While a “theoretical” free return path does not require a drive, in reality several (albeit small) course corrections are often necessary due to disruptions and inaccuracies.

Application in the Apollo program

Free return paths to Apollo 11

A free return path, for example, was flown for the initial path to the moon in order to be able to guarantee a safe return to earth in the event of a failure of the drive system. This was used in the Apollo 8 , Apollo 10 , and Apollo 11 missions . The orbit was chosen in such a way that the spaceship would have circled the moon without the use of the propulsion system and then would have flown straight back to earth without the use of the engines. For a re-entry only minimal changes of path would have been necessary. Since there were no problems with these three Apollo flights, the free return path did not have to be used. The spacecraft maneuvered themselves into lunar orbit when they reached the moon.

Hybrid orbits from Apollo 12

Since the free return path restricted the choice of possible landing points, the subsequent Apollo missions, such as Apollo 12 and Apollo 13 , which was accompanied by technical problems , flew on a so-called hybrid orbit. This orbit initially consisted of a highly elliptical orbit around the earth, the apogee of which was shortly before the moon and which offered an unpowered (free) return to a reentry. On the way to the moon, a maneuver (“mid-course maneuver”) was then carried out in order to switch to a trans-lunar orbit. This then no longer offered a free return. This procedure allowed the security of a free return at the start; the spacecraft left this "safe" path only after the functionality of the relevant systems had been verified and the lunar module had been coupled with the command module ( redundancy of the drive systems). For example, after the technical incident at Apollo 13, the lunar module was used within a few hours to maneuver the team from the intended trans-lunar path into a free return path. Apollo 13 was the only Apollo mission that actually used the free return orbit around the moon (although two hours after the periselenum, activation of the drive shortened the return to earth by 10 hours and the landing point was moved from the Indian Ocean to the Pacific ).

swell

  1. ↑ a b c d Arthur J. Schwaninger: Trajectories in the Earth-Moon Space with Symmetrical Free Return Properties  (= Technical Note D-1833). NASA / Marshall Space Flight Center , Huntsville, Alabama 1963.
  2. ↑ Diagram of the free return ( Memento from January 13, 2013 in the Internet Archive )
  3. ↑ Hybrid trajectory diagram ( Memento from January 18, 2013 in the Internet Archive )
  4. ^ Robin Wheeler: Apollo lunar landing launch window: The controlling factors and constraints. In: NASA . 2009, accessed May 10, 2016 .
  5. ↑ Stephen Cass: Apollo 13, We Have a Solution. In: IEEE Spectrum. April 1, 2005, accessed May 10, 2016 .