Arthur John Schwaniger may have saved Apollo 13

I recently stumbled upon a web link to a documentary article.  The text is copied in English below.  The original link appears in Italian.

https://www.astrospace.it/2020/04/19/arthur-schwaniger-il-fisico-che-salvo-la-missione-apollo-13/

Arthur Schwaniger, the Physicist Who Saved the Apollo 13 Mission
The Apollo 13 mission was paradoxically one of NASA's greatest successes and this is also due to the calculations of a young physicist from Kentucky.

Fifty years ago, at 18:07:41 on April 17, 1970, the Apollo 13 mission had just concluded with a happy ending, splashing down in the Pacific with the astronauts safe and sound inside. One aspect, often forgotten, had contributed substantially to their survival. It was as important as the technical solutions produced in record time by NASA engineers: gravity.

Three and a half days earlier, while the Command and Service Module (CSM) Odyssey and the Lunar Module (LM) Aquarius were traveling coupled toward the Moon , a violent explosion had interrupted the crew's daily routine. " Okay, Houston, we've had a problem here ," Command Module Pilot John Swigert had said immediately afterward. One of the Service Module's liquid oxygen tanks had just exploded, ruining any chance of a lunar landing for the Jim Lovell-Fred Haise duo.

From that moment on, the priority was only one: to bring the crew safely back to Earth. Failure? An option not even to be considered.

It was precisely gravity that was used to transform Apollo 13, a potential tragedy, into NASA's most successful failure. To fully understand what we are talking about, we need to rewind the tape to the afternoon of April 11, exactly 2 hours and 30 minutes after launch from Cape Canaveral.

At that moment, the mission was going swimmingly: the third stage of the Saturn V was orbiting 190 km above the eastern coast of Australia. A handful of minutes later, the powerful J2 engine, with its 100 tons of thrust, had ignited one last time to perform the  Trans Lunar Injection , or TLI for short.

For over five minutes, the capsule had accelerated, reaching a speed of about 11 km/s. This was enough for the apogee – the point of the orbit farthest from the Earth – to “rise” until it crossed the orbit of the Moon. At the end of the TLI, the Lunar Module and the Service and Command Module had positioned themselves on a highly elliptical orbit. This would lead them to a close encounter with our satellite three days later.

The TLI had been planned down to the smallest detail and executed to perfection. A few more seconds would have led to Apollo 13's fatal crash on the lunar surface; a few less seconds would have caused it to miss its rendezvous, with the probable consequence of being "launched" into deep space by a gravitational slingshot with the Moon. As the hours and days passed, the force of lunar gravity had taken over the reins of the game.

If everything had gone according to plan, at the point of minimum distance from the satellite, the Service Module's engine would have ignited to slow the spacecraft and allow it to be captured in a circular orbit. A few hours later, Jim Lovell and Fred Haise would have fulfilled their dream of walking on the Moon.

But that wasn't the case. Things had taken a turn for the worse after the explosion, and the Service Module was no longer usable. There was fuel available, but Mission Control Center in Houston wasn't about to ignite it and risk a second detonation.

Salvation in a well-studied trajectory
NASA, for the Apollo 8-10-11 missions, had deployed every ounce of its knowledge, planning trajectories that would minimize risks for the astronauts. In particular, seven years earlier, a physicist named Arthur J. Schwaniger had provided the first mathematical treatment of Free Return Trajectories.

Born in 1933 in Louisville, Kentucky, Arthur Schwaniger graduated in Physics from the University of the same name, and then began a career in aerospace, dedicating himself in particular to the study of trajectories for human space flight. He began collaborating with NASA in 1960, shortly after its foundation, and would remain there until 1993, the year of his retirement. It was on his studies that NASA astrodynamicists had laid the foundations of the lunar missions.

When an object in space follows a Free Return Trajectory away from a celestial body, if it is influenced by the gravitational field of a second body, this causes it to return to its origin without the need for any means of propulsion. In short, once they left Earth, the Moon's gravity alone would have been able to send the three astronauts back home, even in the absence of a propulsion system.

A Free Return Trajectory in the Earth-Moon system.
The trajectory is illustrated in the image above. The curve at the bottom represents the outward journey. As you can see, the spacecraft precedes the Moon along its orbit, so that it is in front of it at the rendezvous. This relative position causes the Moon's gravity to act like a giant magnet. The spacecraft initially rotates around it, and then is sent back in the direction of Earth. In this way, the spacecraft's path is modified without firing the engine, and therefore without consuming propellant. Hence the term "free".

What better way to bring three astronauts home without a reliable engine? Although Apollo 13 was not on a free-return trajectory at the time of the explosion, NASA engineers used one of the planned orbital corrections, or Midcourse Corrections, to bring the spacecraft back on a free-return trajectory. Schwaniger's studies had signed a life insurance policy for many of the Apollo astronauts, ready to be used in case of emergency, as happened with Apollo 13.

That thirty-year-old from Kentucky, with a degree in physics and an unbridled passion for space, had allowed them to set foot on Earth again and hug their families again. Half a century later, Arthur's contribution may not be over yet. The Artemis missions , planned by NASA for the second half of this decade and aimed at a second and more lasting exploration of the Moon, may require dusting off those studies that, although sixty years old, are still fully applicable.