The 352-page document bears the annotations made by all three crew members recording in detail the actions they had to take after an explosion ripped off part of their space ship.
The mission notes include the crucial changes made to the flight plan that ensured the stricken craft defied the odds and returned to Earth rather than float out to space.
It was presented by mission commander Jim Lovell, who was played by Tom Hanks in the 1995 movie Apollo 13, and fellow astronauts Fred Haise and Jack Swigert to the lead flight planner Robert ‘Bob’ Lindsey following their return.
The front page of the plan carries a touching personal message from the trio, thanking Lindsey for putting together the ‘perfect’ flight plan.
It reads: “To Bob – a truly perfect flight plan as far as we got. We know it would have led us by the hand the rest of the way also.
“Thanks for this remarkable document which we carried to the moon on Odyssey 11 – 17 April 1970.”
The flight plan has remained in the Lindsey family for the last 47 years and they have now decided to put it up for auction with an estimate price of £30,000.
The Apollo 13 mission which set off on April 11, 1970 was meant to culminate in a third moon landing, with Lovell and Haise voyaging to the lunar surface while Swigert orbited in the command module Odyssey.
But just under 56 hours into the mission, an oxygen tank explosion resulted in a major loss of electrical power to the command and service module, forcing the crew to cancel the lunar landing and move into the Aquarius lunar module.
They used it as a lifeboat in order to survive a four day journey around the moon and return back to Earth.
With NASA experts working around the clock and under tremendous pressure, an alternate flight plan had to be rapidly developed which resulted in the safe return of the crew despite seemingly insurmountable obstacles.
The flight plan, which measures 8.5in by 10in, is divided into seven sections consisting of timelines, consumables and food logs.
The notations in black felt-tip pen were by Lovell, in blue ball-point pen by Swigert and in pencil by Haise.
There is an element of foreshadowing as a problem with the tank gauge is noted nine hours before the oxygen tank exploded.
The pre-ordained flight plan for hours 55 to 56 – the time of the explosion – has been crossed out with annotations made in haste as alternative plans were developed in light of the disastrous event.
The meal log at the back of the flight plan was altered because the loss of power caused by the explosion meant they could not boil water to rehydrate food.
Cassandra Hatton, vice president of the books and manuscripts department of auctioneers Sotheby’s, said: “It has really been exciting for me going through the flight plan page by page to see how much of the mission had to be scrapped since they didn’t land.
“You can see all the new calculations, the new plans and the new procedures they had to follow to make it back alive.
“When you go through the flight plan you can foreshadow the explosion since there are references to a problem with the oxygen tank in the hours before the explosion.
“When you look at the meal log at the back of the flight plan you can see how big a problem it was when they lost power because they could not boil water to rehydrate their food.
“They had no food, no water, no power. It’s incredible that they made it back to the earth with the on the fly procedures.
“Going through the flight plan you realise how well trained and prepared the astronauts and ground control were to survive despite all the obstacles.
“Page by page you live the mission with them. I was very tense reading it.
“This is an incredible primary document of the most dramatic and harrowing mission of the Apollo program.
“The importance of this document can not be overstated.” The drama that unfolded during the Apollo 13 mission was re-told in the Hollywood film starring Tom Hanks, Kevin Bacon as Swigert and the late Bill Paxton as Haise.
However, the film is inaccurate when it shows the astronauts ripping off the front cover of the flight plan to clean a filter as the actual flight plan’s front cover is still intact.
Instead a lunar module cue card was used to do the job.
The auction takes place on July 20.