“Parabolic”, suborbital and ballistic trajectories all follow elliptic paths. Is there a generic term for these trajectories?

Question

There are three types of trajectories which produce microgravity but intersect with the surface of the earth:

1. Reduced Gravity Flights in airplanes. These are sometimes called “parabolic” but are really sections of ellipses. They are within the atmosphere but follow a ballistic trajectory.
2. Suborbital flights as in sounding rockets and space tourist flights. These are also elliptic sections when they have sufficient altitude.
3. Intercontinental Ballistic Missiles. Their trajectories are usually described as “ballistic” but are also elliptic sections.

In idealized 2-body mechanics, there are 3 types of orbits :

Open Orbits (hyperbolic and parabolic) never end and never repeat.

Closed Orbits (circles and ellipses) never end and keep repeating

These orbits which never repeat and end in collision.

Is there a generic term for these trajectories to distinguish them from true orbits (Both open and closed)? I’m sure space tourists don’t want to be considered ballistic projectiles

Answer 1

All the analytical orbits I'm aware of are conic sections or conics, including parabolas, ellipses, and hyperbolas. This includes the truncated / terrain-intersecting trajectories you're using as examples.

Answer 2

Having reread the question, I think the correct answer is that there is no natural general term that encompasses all orbital trajectories that intersect the earth. "Suborbital" is logical but only really used in rocketry, and it has a strong connotation that the flight approaches space. Nobody calls a juggler's toss "suborbital". (By the way, those are just as elliptical as any other non-escaping orbit.)

This happens a lot in the ELL and English Usage exchanges. People seek a word where none exists.

So the following paragraph is wrong, since it doesn't answer your question:

Since technically all the paths you are referencing are portions of an ellipse, you can call them all elliptical. You can also call them all ballistic, but that is a more general term, since a hyperbolic or truly parabolic trajectory would also be ballistic in the sense of "behaving like a projectile."

It's worth keeping in mind that the parabolic/elliptical portion of the arc of a reduced-gravity plane only lasts around 30 seconds (see the Wikipedia article). At a ground speed of 600 mph (an overestimate, since the aircraft has a lower airspeed and is not flying in a straight line), 30 seconds of flight time yields 5 miles, or 2.5 miles from the midpoint to one end. That means that the difference in angle between the true vertical at one end of the "parabolic" segment, and what the vertical would be if the earth were flat, is arctan(2.5/4000) = 0.03 degrees. Thus the "flat earth" approximation is very accurate on these scales and the difference between a parabolic arc and an elliptical arc over that distance is negligible. The true path of the plane is neither since it is being flown by hand, but I am confident that a literal parabolic arc would not be noticeably different from a literal elliptical one.

Answer 3

A "wise guy" once said:

A bagel is a bagel, and a donut is a donut, and never the twain shall meet.

Prologue

Just because they could be categorized (along with Cheerios and their cousins Fruit Loops) as "toroidal foodstuffs" doesn't mean we would find any use in coining such a word.

Since both the regimes and the contexts spanned in your question are so different, I do not think one ever tries to group all of these under a single term. It would be too confusing, because the individual words carry a lot of extra helpful information with them.

While a fly ball in baseball could technically be considered to be suborbital, when studying it in science class in high school we'd call it parabolic or ballistic because we'd be studying basic mechanics (e.g. $F=ma$) and friction, and while the high fly is not quite ballistic due to air friction, it's close enough.

In a mechanics class in college we might be taught that that "parabolic" arc is actually elliptical after learning of Keplerian orbits, only then to discover that it's much harder to get the flight time if you treat it as such. We'd also learn to calculate the drag, and terminal velocity of the baseball and learn that it won't really be ballistic after all.

Answer

The closest word for various things which are propulsively launched or boosted like sounding rockets or even a jet aircraft on an arc above the Karman line where its lift peters out as described in

• How did the X-15 control attitude above the Kármán line?

This interesting, archived page https://www.webcitation.org/618QHms8h?url=http://www.fai.org/astronautics/100km.asp which I found in this answer to What would a "Kármán plane" look like, a bird, or a plane?, says:

In the early 1960´s, the U.S. X-15 Aircraft was flown up to 108 km. In that part of the flight it was really a free falling rocket, with no aerodynamic control possible. In fact, it was considered an astronautical flight, and the pilot got, as a consequence, his "astronautical wings", i.e. the recognition of being an astronaut.

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And while we're on the topic of suborbital, ballistic trajectories, note that the Politics SE question What are the exact transgression(s) that Norway is complaining about regarding Sweden's off-course rocket's recovery? links to The BBC's April 26, 2023 Norway criticises Sweden's response after research rocket goes awry which says (in part):

According to the SSC, the rocket reached an altitude of 250km (155 miles) and made it into zero gravity, where it carried out experiments in microgravity into potential carbon-free fuels and creating more efficient solar cells.

You don't need to reach 250 km, or even 20,000 to 60,000 feet to make it into zero gravity. Whether it's suborbital, elliptical, parabolic, a fly ball, or even just jumping up and down; for all those trajectories you can convince you've reached zero gravity by letting go of some object and seeing that it doesn't fall relative to you.

Aw heck, you can even go full orbital and do it on a space station!

For more on the BBC's scientific faux pas see What are "large hadrons"? Are there also "small hadrons"?

Answer 4

Kepler orbit also allows a straight line solution.

This straight line trajectory does not exist; those conics are conveniently describing the two body interaction with amazing precision, yet there is no two body problem in the solar system and those conical trajectories do not exist either.

Second answer to this question says that

The Moon does not orbit the Earth in a neat Kepler orbit because solar tides are significant, making the Moon's elliptical orbit pretty stretched and wobbled. The same sun-tides that affect oceans on earth affect the Lunar orbit around the Earth.

By scaling down, same stretchings exist due to Moon's tides affecting ojects orbiting or suborbiting the Earth.

"Ballistic" better descibes these trajectories since it encompasses what happens to a travelling bullet, either in space or atmosphere, but mostly no interaction is left behind by its definition.

Issue with ballistic is that it does not tell about the shape of the trajectory; once the bullet hits the target it's trajectory is still ballistic, and it's the same trajectory now for bullet and target, and the Earth if this takes place on Earth's surface. Ballistic is too broad of a description to be wrong.

Yet ballistic trajectory excludes Zero-G flights performed by airplanes, since some engine thrust is required to fight drag. Projectiles are not self-propelled.

Elliptical trajectories on the other hand do tell about their shape mathematically considering two bodies in vacuum, which is too much restrictive to be correct when considering other parameters involved.

Other kind of trajectory defining lines are geodesics, that are straight within their curved local geometry of spacetime.

All of these falling objetcs trajectories are geodesics as long as they're not accelerated in another direction, due to atmospheric drag, solar wind, engine thrust or ground encounter.