Six decades ago was a very special time for America. I’m not talking about the fact that you could buy a Mercury Comet for $1,898 at the North Florida Motor Company, or that slacks at Pennys sold for a $1.33 a pair. I am referring to big steps in America’s space race.
Six decades ago, on February 20, 1962, John H. Glenn became the first American to orbit the earth. He was launched atop an Atlas rocket in his Mercury capsule, called Friendship 7. To everyone's relief, it survived reentry into the atmosphere – disintegration on reentry was a "real concern" to the Project Mercury team. The event was a huge milestone in America's race to conquer space, warranting three banner headlines in The New York Times. Glenn wasn't the first man in space, of course: the Soviets had put one man in orbit the previous April, 1961, and two men in orbit the previous August. But from the American perspective, it was the culmination of years of cautious efforts, most visible the year before with several suborbital launches. I missed talking about those warm-up trials last year. They were important confidence-builders to a nation groping its way into the next frontier, to a nation deeply anxious to catch up with, and beat, the Soviets. I want to give some credit here to some of the previous year's events and to convey a sense of the tensions simmering at dawn of the space race. It will help put Glenn's feat into a little historical perspective.
The real start of getting an American into space was not with a man but with a cousin to man. It began January 31, 1961, by tucking a little monkey named Ham into a U.S. Army Redstone rocket and launching him as a projectile, on a ballistic path like an artillery shell, and collecting the poor guy in the Atlantic Ocean. In my book, the bewildered, stalwart chimpanzee was technically the first American in space. Ham splashed down in fine shape and was hailed as a hero. His mission gave confidence to put Alan Shepard on top of another Redstone rocket on May 5th of that year.
But before Shepard flew, the Soviets again were first out of the gate: on April 12th they launched Yuri Gagarin into an orbit. He completed a single revolution around the earth aboard the Vostok capsule, and he too was hailed as a hero when he returned. From the point of view of the history of man and civilization, it was a landmark feat of technology that mankind had for the first time put a man in an actual orbit around the Earth. Yet this was rather grating to American politicians. It was the era of high-stakes international competition for the big prizes, and the Soviets were stealing the show: first earth satellite in space (Sputnik); first man in space (Gagarin); first man in orbit (Gagarin). All the United States had to show for it at the time was a little suborbital monkey. Something had to be done.
The obvious strategy was to engineer a giant, long-shot leapfrog and go for … the moon. So, a mere three weeks after Alan Shepard’s 15 ½ minute suborbital ballistic flight, watched by millions of anxious Americans, President John F. Kennedy told the nation that the United States should “commit itself to achieve the goal, before this decade is out, of landing a man on the Moon and returning him safely to Earth.” Given our track record at the time of his speech was one monkey and one man in one ballistic toss that landed a few hundred miles offshore, it was a hefty commitment, a rather gasping leap of faith.
Other events early that year in man’s conquest of the air and space included a record for a manned balloon. Navy Cmdr. Malcolm Ross and Lieut. Cmdr. Victor Prather boarded their balloon on the aircraft carrier Antietam on May 4, 1961. Their balloon, with the lofty name ONR STRATO-LAB HIGH V, reached an altitude of 103,740 feet (21.5 miles), a record ascent for a manned balloon. They broke the record set the previous August by Air Force Capt. J. Kittinger. Kittinger rather spectacularly bailed out of his balloon at 102,800 feet, setting a parachute descent record. Ross and Prather’s feat was hardly noticed in the hoopla over Alan Shepard’s flight the very next day.
Given the Cold War context, the Shepard springtime flight in a Mercury capsule called Freedom 7 was a very big deal. Banner headlines in The Florida Times Union for Saturday, May 6, 1961: “Perfect Flight Gives the U.S. Big Boost in Space Race.”
“Cape Canaveral, May 5 (AP) – Beaming “Boy what a ride!” Astronaut Alan B. Shepard returned safely to earth today after blasting 115 miles into space – a perfect flight that gave the United States a mighty stride forward in the space race with Russia.
“What a beautiful sight,” the 37-year-old test pilot exalted at the top of his 15-minute hop into space and back.
His 6-by-9-foot space capsule reached speeds of 5,100 mph before plunging back down into the Atlantic 302 miles southeast, where was plucked from the waves by a helicopter.
Shepherd was flown immediately to the carrier Lake Champlain, the physicians checked them over for any ill effects.”
Also on the front page: “redouble efforts, U.S. told – Kennedy Tempers Joy over Success of Shepard Exploit.” “All America rejoices in the successful flight – but it also should provide an incentive for redoubled efforts in this vital field,” said Kennedy. A few days after Freedom 7 landed President Kennedy presented Alan Shepard with NASA’s highest award, the Distinguished Service Medal. Shepherd and his wife then rode Vice President Johnson’s limousine in a motorcade to the Capitol for a reception with lawmakers. Various other parades and honors followed for the hero. But in a follow-up news conference– that incidentally also touched upon “the matter of sending U.S. troops to help South Vietnam ward off Communist thrusts” – Kennedy had made it clear that there was much work to do: “We have a long way to go in the field of space. We are behind but we are working hard and are going to increase our efforts.”
The Soviets, feeling smug, taunted. Just below the fold on the front page of that Saturday’s Florida Times Union was the following report from the Soviet news agency, Tass:
“MOSCOW, May 5, (AP) – The official Soviet news agency Tass tonight belittled the American man-in-space feat.
Said Tass: ‘The launching carried out in the United States of America today of a rocket with a man aboard cannot be compared with the flight of the Soviet spaceship Vostok which carried the world’s first cosmonaut Yuri Gagarin.
During Shepard’s training for the flight, the American press itself acknowledged that from the point of view of technical complexity and scientific value, this flight would be very inferior to the flight of Gagarin.’ ”
The Americans had every reason to feel sober about the challenge, even after Shepard’s trip. The only other vehicle capable of duplicating the Soviet orbital success with Yuri Gagarin was the Atlas rocket. But its resume was looking rather spotty. During a test a week earlier, the mighty Atlas had veered off course and was destroyed in spectacular a ball of fire 40 seconds after launch. Yet progress comes in small steps. In his short flight Shepard was able to manually turn the Mercury capsule around so that the heat shield faced forward, and successfully tested the braking rockets that would be necessary for reentry on orbital flights.
Interesting to me, but not at all emphasized in the media coverage was that his flight was parabolic – as I mentioned, a ballistic uncontrolled flight on a parabolic path traveling through the upper atmosphere just like an artillery shell and sailing back for its splashdown. This of course is a radically different path than an orbit such as Glenn achieved the next year. And different physics with a rich history. I always wish they would give a little more technical detail and historical context in popular accounts, but they rarely do. Below is my own personal footnote to the Florida Times Union article.
Parabolas Are Cool
I like parabolas for the reason that they, like circles, always have the same shape. People are sometimes surprised by this. There are many (technically infinite) varieties of ellipses and hyperbolas, but only one kind of parabola. It is one of the small wonders of physics that, apart from wind and friction, a randomly thrown ball will describe a precise mathematical curve known as the parabola. No matter how many times it is thrown, high, low, fast or slow, it will always follow this one type of path. A baseball, bullet, cannonball, catapult, or ballistic missile – no matter what, will always describe this unique curve. And this curve, one of the so-called conic sections, is slipped in between the ellipse and hyperbola, and is exactly described by a simple mathematical equation [1].
It was a profound moment in the history of science when in the early 1600s a brilliant and curious Italian thinker discovered that the path of such a baseball or cannonball can be described simply as the combination of its forward, projected motion and the downward motion due to the pull of gravity, at each moment of time. One can describe the motions and forces acting on them, as Galileo did, completely in independent of one another. This was a new thing. The first component was a horizontal quantity, and the second, a vertical quantity. We can call the first our “x equation” and the second, our “y equation”. (You may remember from your math class that these are called parametric equations, and they greatly simplify such problems.) Think of each motion as completely independent of the other – that was Galileo’s unproven hypothesis – but both changing with each tick of the clock.
Let’s say we tell one person, “Make a table of values of distance x for each second of time.” (Distance in this direction will vary directly in proportion to time.) To the other, we say, “Write down in the table the values of y for each second of time.” (Distance in this direction will vary in proportion to the square of time – Galileo’s discovery of the law of freefall.) Then we plot the positions (x, y) at each second. The result will be a parabola. Galileo was the first person to grasp significance of the independence of forces and the true path of a ballistic projectile. Before him in the Middle Ages it was thought that projectiles leaving a gun had a certain energy or impetus, and they would fall to the ground once that impetus had run out. The path was presumed to be a rising arc with a sudden drop-off to the target.
One can see these odd paths in military books written before 1600. On a sabbatical trip to Spain, my wife and I visited the Alcázar of Segovia, an iconic medieval castle-fortress built in the early 12th century high on a rock between a confluence of two rivers; it was established soon after the Christians reconquered the city from the Muslims. On display near the armory was a late 16th century book opened to a picture of a cannon and the path of its shot. Its path was assuredly not a parabola! It depicted the cannonball’s trajectory rising steadily up at an angle from the cannon, then at some good distance from it dropping vertically downward to the ground, as if when reaching the top it lost its will to travel any more and gave up all forward motion.
Galileo’s purpose was to verify the underlying principle of the independence of forces, not to find that the path was parabolic, per se – it could have been anything – but to find whether motions in a curve can be analyzed as the combination of forces each acting independently. That is a weightier and more far-reaching principle of physics: the evidence of that independence being a parabolic path if the motions were indeed independent. And of course, the knowledge that the path is parabolic had huge practical implications in applied mathematics, engineering, physics, astronomy, and other fields.
Shepard’s Parabola
We can easily approximate Shepard’s parabola. We know that his launch speed was 2,290 m/s, at an angle of 57° (units are in kilometers). Surprisingly, that data (and the measure of gravity's pull) is all we need to know to plot its path. We take the sine of that angle to find the vertical component of the speed and the cosine of it to find the horizontal speed.
What Galileo (or anyone else) didn’t know, is that in the parabola, the kinetic energy and the gravitational potential energy are always equal. Knowing the launch speed times the sine of the launch angle tells us the kinetic energy of the y component off the launchpad: it is proportional to half the vertical velocity squared. We also know the vertical component kinetic energy at the very top, which is zero. And we know that the gravitational potential energy, proportional to g times height, can be assigned zero at the launchpad and a value equal to the launch kinetic energy at the top, because total mechanical energy is conserved. [2] Graph it and you have the beautiful parabola shown in the diagram.
Far Out Parabolas
This reminds me of one other thing that I hope isn't too far off topic from Soviets, monkeys, and motorcades. You may know that Comet Leonard C/2021 A1, which recently passed us in the inner solar system, is another of those far-distant visitors skittering just along the edge of a purely parabolic path. Its orbit’s eccentricity is 1.0001004 with some uncertainty in that last digit. Not many comets come so close to my ideal of "parabolic perfection." Some try hard, and maybe I'll do a post on those, but they're rare. Of recent ones, Comet ISON C/2012 S1 of course beats Leonard hands-down in the parabolic sweepstakes, with a winning eccentricity of about 1.000005091. Both trajectories (technically not orbits) are ever so slightly hyperbolic.
You may know that parabolic velocity is called the velocity of escape. [3] That means it has enough energy to slip the bonds of gravity that would otherwise hold it into an elliptical orbit. This also means that any object with a parabolic or greater (i.e., hyperbolic) velocity will never return unless between now and whenever something perturbs it by the lightest breath of some planet’s gravitational pull into an elliptical, bound orbit.
Shepard's capsule of course wasn’t launched with anywhere near enough velocity to escape the earth's gravity. That kind of power was not yet available in the U.S. space program. To do that, he’d have to have been traveling about 11.2 km/s. He was launched at only about 1/5th of that speed, at 2.29 km/s.
NOTES [1] You may recall in our earlier posts (including about Interstellar Object ‘Oumuamua), the eccentricity of the parabola (at a perfect e = 1.0000) lies between the ellipse (with eccentricity e <1) and the hyperbola (e >1).
[2] The actual equations can be found in any high school or college physics book. The value of g at the Earth's surface is 9.8 m/s^2. It diminishes with height but here for simplicity we are using it as a constant in this approximate model. The mass of the projectile cancels out on each side of the energy equation.
[3] The escape velocity of an object is the square root of two times the circular velocity of the object at the applicable distance from the center of the sun, or earth if earth-orbiting.
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