Free-return

Even before Kennedy’s challenge, the lunar Tree-return trajectory had been recognised as a safe and efficient means by which a spacecraft could make the journey. The idea is attributed to Yuri Kondratyuk of the Soviet Union, who realised its possibilities for lunar flight in the early twentieth century. A major crater on the far side of the Moon is named after him. It was a wonderful solution to the problem, and one whose propellant needs were within the capabilities of the Saturn V. It could get a crew’ to the Moon within three days and allow the entire mission to be carried out within 14 days, well within the duration for which the Apollo spacecraft was being designed. Furthermore, if a fault arose in the SPS on the way to the Moon to prevent major manoeuvres, the free-return trajectory would bring the crew back towards Earth, and any fine tuning on the homeward leg would be within the capability of their RCS thrusters. This was an inherently attractive option for an agency that had a presidential directive to preserve the life of its human crews.

The free-return trajectory relied on using the Moon’s gravity as a steering device for the spacecraft. It is one of a range of techniques that have been used by interplanetary probes for decades to move around the solar system much more quickly than w’ould be possible with rockets alone. If a spacecraft coasts towards a planet from beyond that planet’s sphere of gravitational influence, it must have the same speed on both the incoming and outgoing legs when measured with respect to that body. However, the planet is moving with respect to the Sun so there is an opportunity for some exchange of momentum between the planet and spacecraft. If it passes by the planet’s trailing hemisphere, its heliocentric (or Sun-centred) velocity is increased as it gets a little gravitational tug like a skater holding onto a car. The result is that its orbit is made larger; speed has been gained without so much as a squirt of rocket propellant. This is often characterised as a slingshot effect.

Conversely, if the spacecraft passes the /^Mo°n

leading hemisphere of the body, the ex­change is away from the spacecraft. It gets a tug from the planet against its orbital motion so heliocentric velocity is reduced and its orbit gets smaller.

With the lunar free-return trajectory, the leading-edge case is taken to an extreme in which the spacecraft is made to swing all the way around the far side of the Moon and onto a path back to Earth, in the process tracing out an immense figure-of-eight.

Such a trajectory also affords a slower approach velocity with respect to the Moon, thereby minimising the amount of propel­lant required to achieve lunar orbit. A win – win scenario.

Once the free-return trajectory was factored into the TLI calculation, there were very few solutions remaining to the equations that calculated the burn for the S-IVB. Such equations took into account the motions of Earth, the Moon and the spacecraft as well as the other major bodies in the solar system whose gravity would to some degree influence the spacecraft’s path. They also accounted for the trajec­tory that the lunar module would take during its descent to the surface, particu­larly when Apollos 15 and 17 had to approach through mountain ranges. One

particular flight controller in mission control was responsible for procuring the details of a TLI burn that would achieve as many of the desired conditions as possible. The flight dynamics officer (FIDO) worked with a backroom team and a room full of mainframe computers to calculate a range of possible solutions whose starting point was the orbit that had been achieved around Earth. These could be optimised for fuel efficiency, duration of flight, suitability for entering lunar orbit, and flight safety in terms of their return-to-Earth characteristics. From these, he picked one which, by his judgement, was the best compromise; one that required the Saturn’s third stage to fire along its flight path in order to change the speed of the spacecraft by a certain amount at a certain time. It was then up to the J-2 engine of the S-IVB to supply that change in velocity.

Over the course of the Apollo lunar flights, the manner in which planners used free-return altered as NASA’s operational confidence increased. A pure version of the trajectory, one that would set the spacecraft on a path directly to Earth without

intervention, would fly around the far side of the Moon at an altitude of roughly 500 kilometres, depending on the precise Hanh/Moon/Sun geometry. Up to and including Apollo 11, the spacecraft was sent on a trajectory that was a near approximation to this and which, if lunar orbit insertion were to be impracticable, would require only minor burns of the RCS thrusters to steer to the desired splashdown site. Since the free-return trick only worked if the flight was kept within the plane of the Moon’s orbit around Harth, it limited the potential landing sites to those that lay along the track of the resulting lunar orbit. Since the Moon’s equator is within a few degrees of the plane of its orbit around Earth, the ground tracks for missions which flew a free-return trajectory were all near-equatorial.

Later missions evolved the trajectory to hybrid versions. The H-missions of Apollos 12, 13 and 14 started out from Harth on a free-return trajectory, but once safely on their way they performed a small burn to improve their approach characteristics, knowing that a corrective burn from either the SPS engine on the CSM or the large engines on the LM would be sufficient to re-establish a safe coast home. The latter contingency had to be used on Apollo 13 to restore a free-return after the SPS engine was disabled. The J-missions were injected directly into a non – free-return trajectory, one that would not bring them home directly. Again, they relied on either the SPS engine to effect a safe return or. if that was out of action, one or both of the large LM engines.