# How many hours long is Earth's longest possible sub-orbital flight?

This comment below How long will last the Blue Origin New Shepard space flight? says (in part):

The words "suborbital spaceflight" as the first words on Blue Origin's webpage for the New Shepard mean that, yes, the flights will last a few minutes.

Question: How many hours long is Earth's longest possible sub-orbital flight?

• can be an estimate (with justification) or a simple simulation
• neglect atmospheric effects
• don't use the Moon
• it's not "infinite"
• no cheating! It should be non-propulsive
• I suspect it comes down to “what is the time of flight for a vertical launch at escape velocity - 1” – Antzi Dec 14 '19 at 2:32
• @Antzi I don't think that's right, thus the last bulleted item "it's not 'infinite'". – uhoh Dec 14 '19 at 2:34
• If someone with suitable authority were to define an area where a pure parabolic trajectory stops being "in orbit," then it would just be a simple matter of accelerating to that point, then letting gravity do its work to bring us back... Given the average force of gravity, it'd be straightforward to answer. But that implies that we can agree on a definition. Since every non-escape velocity trajectory is an orbit (whether it intercept the surface of the Earth or not), and sub-orbital is just an orbit that intersects the surface, the longest one is infinite... which isn't a reasonable answer. – Ghedipunk Dec 14 '19 at 4:18
• So... can we come up with a satisfying definition of a sub-orbital flight? Say, to LEO and back? To GEO and back? To the Moon's orbit and back? To a distance where the sun's gravitational influence overcomes Earth's influence and back? – Ghedipunk Dec 14 '19 at 4:20
• Imagine a very eccentric elliptical orbit with an apoapsis just slightly smaller than the sphere of influence around the earth whose periapsis is tangent to the earth. That would give you all the parameters you need to find the trajectory and the time of flight would simply be the period. – Paul Dec 14 '19 at 5:26

How many hours long is Earth's longest possible sub-orbital flight?

"Orbit", and thus "orbital" and "sub-orbital" is another one of those words like "rocket" whose definition alters significantly with context. Any trajectory under gravitational influence and not dominated by atmospheric influence can be considered an "orbit", but here at S.SX we usually take "sub-orbital" to mean "a trajectory which does not permit a complete orbit because of unavoidable aerobraking and/or lithobraking effects".

The longest possible coasting-only sub-orbital flight from Earth, then, is an elliptical orbit which goes almost to the edge of Earth's gravitational sphere of influence (itself an extremely fuzzy and context-dependent concept) at apogee and returns to Earth with a perigee low enough to guarantee prompt reentry.

Wikipedia tells me Earth's Hill Sphere goes out to around 1.5 million km; my training and experience in Kerbal Space Program + Realism Overhaul tells me that any Earth-bound orbit going to, say, 45km altitude will reenter promptly.

This orbital calculator informs me that the period of this orbit is 75.3 days. Since we're going at 11 km/s at perigee, we can more or less ignore the time spent on the atmospheric end of it; the period of the complete orbit is almost exactly the same as the period of the suborbital portion of the trajectory. Since we're going out pretty close to the edge of the Hill Sphere and we'll be moseying along at only 50 m/s at apogee, perturbations from other planets might shift this period by a little bit.

If we use the "two-fifths power" definition of sphere of influence (I don't know if this has a better name?) the apogee needs to be closer, around 0.92 Mkm, for a period of 36.3 days.

There is, almost assuredly, some gonzo trajectory which relies on perturbations from Jupiter and Saturn to juggle the spacecraft at the very edge of Earth escape before sending it home a year later, but I'm restricting my solution to the tools available to a poor unfrozen caveman rocket scientist.

• Bingo! If semimajor axis $a$ is half of 1.5 million miles (circa Hill sphere and/or L1, L2; i.e. due to the Sun's gravitational effect), then with $GM=3.986 \times 10^{14} m^3/s^2$, the period is $2 \pi \sqrt{a^3/GM}$ which is 1796 hours or 74.8 days. Any farther than that and your chances of free-returning to the Earth decrease dramatically. It doesn't mean that you're guaranteed to free-return to the Earth just shy of this altitude, three-body effects may still perturb the trajectory, but this is a good estimator of max practical height. – uhoh Dec 14 '19 at 8:45

At least 23,000 km. The Sänger anitpodal bomber concept:

sled launched, boosted to suborbital velocity, 'skips' off upper atmosphere

Eugen Saenger conceived of a winged spaceplane while a doctoral candidate at the Vienna Polytechnic Institute. His 1933 Silverbird concept was for a Mach 10 glider that would cruise at 160 km altitude. ...

It would have a hypersonic L/D ratio of 5.1, reach a top speed of Mach 13 at burnout of its rocket motor, and then enter a 5,000 km long glide, reaching a stable Mach 3.3 cruise at 50 km altitude.

The final refinement to the design was his 1944 report Concerning Rocket Propulsion for Long-Range Bombers, which featured a spaceplane 28 m long with a 15 m wingspan and 100 tone take-off mass. The glider would reach a top speed of 21,800 kph and have a range of 23,400 km.

• Wow, quite a piece of space history! – uhoh Dec 14 '19 at 8:39

According to Wikipedia's list of Flight Endurance Records, the longest continuous flight of an airplane thus far has been 623:57:00, recorded July 11 – August 8, 2018, flown by an unmanned Airbus Zephyr 8 drone.

It was a flight, and it did not achieve orbit, thus a suborbital flight.

This is of course not the theoretical maximum, it is the publicly known practical maximum that has been achieved so far as of the writing of this answer.

• My second bulleted item is "neglect atmospheric effects" so I'm going to say that airplanes don't count. Considering that this site is about Space Exploration it's safe to assume I'm asking about spaceflight. I will however add "non-propulsive" to the question to avoid any further ambiguities. – uhoh Dec 14 '19 at 4:25
• @uhoh How do you leave the Earth's surface without propulsion? It has to be propulsive at the very start of the flight – LeoS Dec 14 '19 at 4:36
• @uhoh: You explicitly distinguish between the term "sub-orbital spaceflight" when talking about New Shepard and "sub-orbital flight" (without "space") when phrasing your question. What, then, is the difference between the two if not the "space" part? – Jörg W Mittag Dec 14 '19 at 8:44
• @uhoh: What do you mean by "neglect atmospheric effects"? You used New Shepard as example, yet both the New Shepard booster and the Crew Capsule crucially depend on aerodynamics for at least a portion of their flight: the booster has grid fins and the capsule lands under parachutes. – Jörg W Mittag Dec 14 '19 at 8:46
• @uhoh: Can you clarify what you mean by "non-propulsive"? You used New Shepard as an example, yet both the booster and the capsule have a propulsion system. – Jörg W Mittag Dec 14 '19 at 8:47