Shepard is amazing in the film, which paints in him as a true pioneer and the best of the best. So much so that it's almost to the detriment of the other pilots who later participated in the space programme - despite his skills, Yeager's lack of a university degree rendered him unappealing to the NASA (then NACA) recruiters.
The "flyboy" camaraderie and brinksmanship that infuses this section is fantastic, and lends the events a mythic quality befitting their historical status.
For the second two-thirds of the film's three hour running time, we focus on the build up and execution of the Mercury missions themselves.
The seven astronauts are played by one of the most appealing collection of actors ever assembled - Scott Glenn (The Keep, Silence of the Lambs) projects unmitigated coolness as Alan Shepard, the first American in space. His performance demonstrates once again that he has been underutilised as a leading man.
Ed Harris gives the most heartfelt performance in the film as John Glenn, the most PR-friendly of the seven. The great Fred Ward (Tremors, Henry & June) does stellar work as the doomed Gus Grissom, and there's solid back-up from a very young Dennis Quaid and genre-stalwart Lance Henriksen (The Terminator, Aliens)
Jeff Goldblum and Harry Shearer (Spinal Tap, The Simpsons) are great as two bumbling government recruiters attempting to find the best men for the job of going into space. One hilarious scene has them with screening footage of various types of experts - surfers, trapeze artists, stock car racers - with President Eisenhower, trying to determine who might be best suited to the demands of space flight.
The film's broad scope is offset by its commitment to portraying the human cost of the events - the first scene is the death of a test pilot. The pressures on the astronauts and their families come through loud and clear, and the significance of their actions is palpable.
Kaufman's film is far from simplistic, but some of the more jingoistic elements haven't dated so well. The flying scenes were impressive at the time, but were soon blown out of the water by those in 1986's Top Gun - although Top Gun owes a lot to The Right Stuff, especially in its portrayal of alpha male pilots.
Watching The Right Stuff, I felt an overwhelming sense of pride in humanity I haven't felt since viewing the 2007 feature documentary In The Shadow of the Moon, which is very much worth seeing if you haven't.
It features interviews with surviving Apollo astronauts over amazing footage taken from the shuttles during the missions. Naturally, the press-shy Armstrong declined to participate, but he comes across as almost super-human when discussed by his colleagues.
So what about other movies that highlight NASA's efforts?
The most famous example since The Right Stuff is of course Ron Howard's 1995 hit Apollo 13. This film takes a lot of inspiration from Kaufman's in how it portrays the domestic lives of the astronauts and their families, and builds considerably on the brotherly astronaut bond of the earlier film.
The nascent digital revolution allowed the film to present much more realistic footage of the shuttles in action, and the special effects hold up pretty well today. Apollo 13 also paints a much more generous picture of the NASA engineers, who barely got a look-in in The Right Stuff and were portrayed as stuffy, out-of-touch scientists when they did appear. This was an aspect of the 1983 film that apparently irked Mercury astronaut Wally Schirra.
A more detailed exploration of the Apollo missions occurs in the 1998 HBO mini-series From The Earth To The Moon, produced by Apollo 13 star Tom Hanks. There also exist innumerable documentaries on the subject.
My favourite fictional (or is it?) film about the space programme is the 1977 cult classic Capricorn One in which three astronauts go on the run from the government after they participate in a faked Mars landing.
Lending amusing credence to the persistent theory that NASA faked the moon-landings, Capricorn One is one of the most entertaining conspiracy films of the '70s.
1986's Spacecamp attempted to marry NASA authenticity with the youthful populism of the Star Wars films. There is some nice hardware in the film, but it's flop-tastic fate was sealed when the Challenger exploded mere months before its release.
The 2000 Clint Eastwood film Space Cowboys told a fictional story about four pilots who were passed over for the space programme but get a second chance to go into space late in life. The mostly enjoyable film borrows a lot from The Right Stuff, especially in its portrayal of the "flyboy" culture of test pilots.
The spectre of The Right Stuff also hangs over 1998's duelling meteor films Armageddon and Deep Impact. Both films strive for NASA-realism (to a degree) and the former directly lifts its iconic "astronauts walking to the shuttle" shot from Kaufman's film.
You can also spot its influence in 2000's duelling Mars films Red Planet and Mission To Mars, which both at least attempt something approaching a realistic portrayal of future space programmes. The latter in particular recalls certain sections of The Right Stuff.
Richard Kelly's inexplicably derided 2009 mind-bender The Box mined a huge amount of drama out of the fact that it's main character worked for NASA (as Kelly's father did).
Last year a film called Apollo 18 was released. It told the story of a fictional eighteenth Apollo mission, and the nasty things it encounters on the moon. I haven't seen it, but by all accounts it's terrible.
Other films of note that touch upon the space programme in some sort of tangible way include 2001: A Space Odyssey (for which NASA artist Robert McCall provided concept designs), the sequel 2010 (directed by Capricorn One's Peter Hyams), Bond films You Only Live Twice and Moonraker, and er, Transformers: Dark of the Moon.
While Armstrong doesn't feature in the events covered by The Right Stuff, the film remains a fantastic tribute to what he represented, and is very much worth a watch.
* Have you seen The Right Stuff? Thoughts? Do you prefer Apollo 13? What are your favourite movies that touch on the space programme? Can you think of other examples? Comment below!
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