Shepard's trajectory in May 1961 was parabolic, the same as a ball thrown into the air, or any other object which is launched upwards with less than orbital velocity "Vo". To enter Earth orbit (as Yuri Gagarin's Vostok spacecraft did three weeks before Shepard's flight), the trajectory must be an ellipse, which requires the speed to be somewhere between "Vo" and escape velocity "VE" = "2"Vo". If the speed is greater than "VE" the object will escape the Earth altogether on a hyperbolic orbit.
The adjective "hyperbolic" can also mean "of exaggerated importance" (from the noun "hyperbole", normally shortened to "hype"). In this sense, Alan Shepard's flight was hyperbolic as well as parabolic!
I don't mean to belittle Shepard personally -- after all, he was just doing a job, and had no control over how that job was presented to the world by NASA or the news media. Arguably, his flight required far more courage than Gagarin's had, since the latter had the benefit of a well-designed, well-engineered spacecraft that virtually flew itself, and was always well within its operational envelope. Soviet cosmonauts were never bothered by Shepard's oft-quoted worry that "every component was built by the lowest bidder"!
The Redstone rocket used for Shepard's mission (and Gus Grissom's similar flight a couple of months later) was designed in the early 1950s as a short-range ballistic missile, and was (in engineering terms if not in visual appearance) only a slight modification on the German V-2 rocket of World War 2. Test flights of captured V-2s in the late 1940s achieved similar altitudes to Shepard's flight, yet no-one at the time described them as "flights into space". Some of these flights even carried monkeys and other animals as passengers, with no great media fanfare. Under normal circumstances, I'm sure that Alan Shepard's mission would have been seen as "just another test flight"... if it hadn't been for the exigencies of Cold War politics, which demanded an instant U.S. response to Gagarin's flight into space!
Eventually, in February 1962, an American did make it into orbit: John Glenn, boosted into space by an Atlas rocket which was far more powerful than the Redstone. As a space-obsessed but scientifically ignorant schoolboy in the 1960s (from which period the postcard above dates), Alan Shepard was one of my great heroes, and I could never understand why grown-ups made such a fuss about John Glenn... after all, he was only the third American in space, wasn't he? And if the Americans really believed that Alan Shepard's flight was on a par with Gagarin's, they wouldn't have made a fuss about John Glenn either!
Reference: mysteries-and-strangeness.blogspot.com
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