Sub-orbital spaceflight

Image:Newton Cannon.svg. Paths A and B depict a sub-orbital trajectory.]]

By definition, a sub-orbital spaceflight reaches an altitude higher than {{convert|100|km|abbr=on}} above sea level. This altitude, known as the Kármán line, was chosen by the Fédération Aéronautique Internationale because it is roughly the point where a vehicle flying fast enough to support itself with aerodynamic lift from the Earth's atmosphere would be flying faster than orbital speed.{{cite web|url=http://www.fai.org/icare-records/100km-altitude-boundary-for-astronautics|title=100 km Altitude Boundary for Astronautics|publisher=Fédération Aéronautique Internationale|archive-url=https://web.archive.org/web/20110809093537/http://www.fai.org/astronautics/100km.asp|archive-date=2011-08-09|url-status=dead|access-date=2017-09-14}} The US military and NASA award astronaut wings to those flying above {{convert|50|mi|abbr=on}},{{cite web|url=http://www.nasa.gov/centers/dryden/news/NewsReleases/2005/05-57.html|title=X-15 Space Pioneers Now Honored as Astronauts|first=Mary|last=Whelan|date=5 June 2013|website=nasa.gov|access-date=4 May 2018|url-status=live|archive-url=https://web.archive.org/web/20170611194526/https://www.nasa.gov/centers/dryden/news/NewsReleases/2005/05-57.html|archive-date=11 June 2017}} although the U.S. State Department does not show a distinct boundary between atmospheric flight and spaceflight.{{cite web|url=https://2009-2017.state.gov/s/l/22718.htm|title=85. U.S. Statement, Definition and Delimitation of Outer Space And The Character And Utilization Of The Geostationary Orbit, Legal Subcommittee of the United Nations Committee on the Peaceful Uses of Outer Space at its 40th Session in Vienna from April|website=state.gov|access-date=4 May 2018}}

During freefall the trajectory is part of an elliptic orbit as given by the orbit equation. The perigee distance is less than the radius of the Earth R including atmosphere, hence the ellipse intersects the Earth, and hence the spacecraft will fail to complete an orbit. The major axis is vertical, the semi-major axis a is more than R/2. The specific orbital energy $\backslash epsilon$ is given by:

$$\backslash varepsilon\; =\; -\{\backslash mu\; \backslash over\; \{2a\}\}\; >\; -\{\backslash mu\; \backslash over\; \{R\}\}\backslash ,\backslash !$$

where $\backslash mu\backslash ,\backslash !$ is the standard gravitational parameter.

Almost always a < R, corresponding to a lower $\backslash epsilon$ than the minimum for a full orbit, which is $-\{\backslash mu\; \backslash over\; \{2R\}\}\backslash ,\backslash !$

Thus the net extra specific energy needed compared to just raising the spacecraft into space is between 0 and $\backslash mu\; \backslash over\{2R\}\backslash ,\backslash !$.

To minimize the required delta-v (an astrodynamical measure which strongly determines the required fuel), the high-altitude part of the flight is made with the rockets off (this is technically called free-fall even for the upward part of the trajectory). (Compare with Oberth effect.) The maximum speed in a flight is attained at the lowest altitude of this free-fall trajectory, both at the start and at the end of it.{{citation needed|date=May 2024}}

If one's goal is simply to "reach space", for example in competing for the Ansari X Prize, horizontal motion is not needed. In this case the lowest required delta-v, to reach 100 km altitude, is about 1.4 km/s. Moving slower, with less free-fall, would require more delta-v.{{citation needed|date=May 2024}}

Compare this with orbital spaceflights: a low Earth orbit (LEO), with an altitude of about 300 km, needs a speed around 7.7 km/s, requiring a delta-v of about 9.2 km/s. (If there were no atmospheric drag the theoretical minimum delta-v would be 8.1 km/s to put a craft into a 300-kilometer high orbit starting from a stationary point like the South Pole. The theoretical minimum can be up to 0.46 km/s less if launching eastward from near the equator.){{citation needed|date=May 2024}}

For sub-orbital spaceflights covering a horizontal distance the maximum speed and required delta-v are in between those of a vertical flight and a LEO. The maximum speed at the lower ends of the trajectory are now composed of a horizontal and a vertical component. The higher the horizontal distance covered, the greater the horizontal speed will be. (The vertical velocity will increase with distance for short distances but will decrease with distance at longer distances.) For the V-2 rocket, just reaching space but with a range of about 330 km, the maximum speed was 1.6 km/s. Scaled Composites SpaceShipTwo which is under development will have a similar free-fall orbit but the announced maximum speed is 1.1 km/s (perhaps because of engine shut-off at a higher altitude).{{citation needed|date=May 2024}}{{update inline|date=June 2024}}

For larger ranges, due to the elliptic orbit the maximum altitude can be much more than for a LEO. On a 10,000-kilometer intercontinental flight, such as that of an intercontinental ballistic missile or possible future commercial spaceflight, the maximum speed is about 7 km/s, and the maximum altitude may be more than 1300 km.

Any spaceflight that returns to the surface, including sub-orbital ones, will undergo atmospheric reentry. The speed at the start of the reentry is basically the maximum speed of the flight. The aerodynamic heating caused will vary accordingly: it is much less for a flight with a maximum speed of only 1 km/s than for one with a maximum speed of 7 or 8 km/s.{{citation needed|date=May 2024}}

The minimum delta-v and the corresponding maximum altitude for a given range can be calculated, d, assuming a spherical Earth of circumference {{val|40000|u=km}} and neglecting the Earth's rotation and atmosphere. Let θ be half the angle that the projectile is to go around the Earth, so in degrees it is 45°×d/{{val|10000|u=km}}. The minimum-delta-v trajectory corresponds to an ellipse with one focus at the centre of the Earth and the other at the point halfway between the launch point and the destination point (somewhere inside the Earth). (This is the orbit that minimizes the semi-major axis, which is equal to the sum of the distances from a point on the orbit to the two foci. Minimizing the semi-major axis minimizes the specific orbital energy and thus the delta-v, which is the speed of launch.) Geometrical arguments lead then to the following (with R being the radius of the Earth, about 6370 km):

$$\backslash text\{major\; axis\}\; =\; (1\; +\; \backslash sin\backslash theta)R$$

$$\backslash text\{minor\; axis\}\; =\; R\backslash sqrt\{2\backslash left(\backslash sin\backslash theta\; +\; \backslash sin^2\backslash theta\backslash right)\}\; =\; \backslash sqrt\{R\backslash sin(\backslash theta)\backslash text\{semi-major\; axis\}\}$$

$$\backslash text\{distance\; of\; apogee\; from\; centre\; of\; Earth\}\; =\; \backslash frac\{R\}\{2\}(1\; +\; \backslash sin\backslash theta\; +\; \backslash cos\backslash theta)$$

$$\backslash text\{altitude\; of\; apogee\; above\; surface\}\; =\; \backslash left(\backslash frac\{\backslash sin\backslash theta\}\{2\}\; -\; \backslash sin^2\backslash frac\{\backslash theta\}\{2\}\backslash right)R\; =\; \backslash left(\backslash frac\{1\}\{\backslash sqrt\{2\}\}\backslash sin\backslash left(\backslash theta\; +\; \backslash frac\{\backslash pi\}\{4\}\backslash right)\; -\; \backslash frac\{1\}\{2\}\backslash right)R$$

The altitude of apogee is maximized (at about 1320 km) for a trajectory going one quarter of the way around the Earth ({{val|10000|u=km}}). Longer ranges will have lower apogees in the minimal-delta-v solution.

$$\backslash text\{specific\; kinetic\; energy\; at\; launch\}\; =\; \backslash frac\{\backslash mu\}\{R\}\; -\; \backslash frac\backslash mu\backslash text\{major\; axis\}\; =\; \backslash frac\{\backslash mu\}\{R\}\backslash frac\{\backslash sin\backslash theta\}\{1\; +\; \backslash sin\backslash theta\}$$

$$\backslash Delta\; v\; =\; \backslash text\{speed\; at\; launch\}\; =\; \backslash sqrt\{2\backslash frac\{\backslash mu\}\{R\}\backslash frac\{\backslash sin\backslash theta\}\{1\; +\; \backslash sin\backslash theta\}\}\; =\; \backslash sqrt\{2gR\backslash frac\{\backslash sin\backslash theta\}\{1\; +\; \backslash sin\backslash theta\}\}$$

(where g is the acceleration of gravity at the Earth's surface). The Δv increases with range, leveling off at 7.9 km/s as the range approaches {{val|20000|u=km}} (halfway around the world). The minimum-delta-v trajectory for going halfway around the world corresponds to a circular orbit just above the surface (of course in reality it would have to be above the atmosphere). See lower for the time of flight.

An intercontinental ballistic missile is defined as a missile that can hit a target at least 5500 km away, and according to the above formula this requires an initial speed of 6.1 km/s. Increasing the speed to 7.9 km/s to attain any point on Earth requires a considerably larger missile because the amount of fuel needed goes up exponentially with delta-v (see Rocket equation).

The initial direction of a minimum-delta-v trajectory points halfway between straight up and straight toward the destination point (which is below the horizon). Again, this is the case if the Earth's rotation is ignored. It is not exactly true for a rotating planet unless the launch takes place at a pole.{{cite journal |last1=Blanco |first1=Philip |title=Modeling ICBM Trajectories Around a Rotating Globe with Systems Tool Kit |journal=The Physics Teacher |date=September 2020 |volume=58 |issue=7 |pages=494–496 |doi=10.1119/10.0002070 |bibcode=2020PhTea..58..494B|s2cid=225017449 }}

In a vertical flight of not too high altitudes, the time of the free-fall is both for the upward and for the downward part the maximum speed divided by the acceleration of gravity, so with a maximum speed of 1 km/s together 3 minutes and 20 seconds. The duration of the flight phases before and after the free-fall can vary.{{citation needed|date=May 2024}}

For an intercontinental flight the boost phase takes 3 to 5 minutes, the free-fall (midcourse phase) about 25 minutes. For an ICBM the atmospheric reentry phase takes about 2 minutes; this will be longer for any soft landing, such as for a possible future commercial flight.{{citation needed|date=May 2024}} Test flight 4 of the SpaceX 'Starship' performed such a flight with a lift off from Texas and a simulated soft touchdown in the Indian Ocean 66 minutes after liftoff.

Sub-orbital flights can last from just seconds to days. Pioneer 1 was NASA's first space probe, intended to reach the Moon. A partial failure caused it to instead follow a sub-orbital trajectory, reentering the Earth's atmosphere 43 hours after launch.{{cite web |url=https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1958-007A |title=Pioneer 1 - NSSDC ID: 1958-007A |publisher=NASA NSSDC}}

To calculate the time of flight for a minimum-delta-v trajectory, according to Kepler's third law, the period for the entire orbit (if it did not go through the Earth) would be:

$$\backslash text\{period\}\; =\; \backslash left(\backslash frac\{\backslash text\{semi-major\; axis\}\}\{R\}\backslash right)^\backslash frac\{3\}\{2\}\; \backslash times\; \backslash text\{period\; of\; low\; Earth\; orbit\}\; =\; \backslash left(\backslash frac\{1\; +\; \backslash sin\backslash theta\}2\backslash right)^\backslash frac\{3\}\{2\}2\backslash pi\backslash sqrt\{\backslash frac\{R\}\{g\}\}$$

Using Kepler's second law, we multiply this by the portion of the area of the ellipse swept by the line from the centre of the Earth to the projectile:

$$\backslash text\{area\; fraction\}\; =\; \backslash frac\{1\}\{\backslash pi\}\backslash arcsin\backslash sqrt\{\backslash frac\{2\backslash sin\backslash theta\}\{1\; +\; \backslash sin\backslash theta\}\}\; +\; \backslash frac\{2\backslash cos\backslash theta\backslash sin\backslash theta\}\{\backslash pi\backslash text\{(major\; axis)(minor\; axis)\}\}$$

$$\backslash begin\{align\}$$

\text{time of flight}

&= \left(\left(\frac{1 + \sin\theta}2\right)^\frac{3}{2}\arcsin\sqrt{\frac{2\sin\theta}{1 + \sin\theta}} + \frac{1}{2}\cos\theta\sqrt{\sin\theta}\right)2\sqrt\frac{R}{g} \\

&= \left(\left(\frac{1 + \sin\theta}2\right)^\frac{3}{2}\arccos\frac{\cos\theta}{1 + \sin\theta} + \frac{1}{2}\cos\theta\sqrt{\sin\theta}\right)2\sqrt\frac{R}{g} \\

\end{align}

This gives about 32 minutes for going a quarter of the way around the Earth, and 42 minutes for going halfway around. For short distances, this expression is asymptotic to $\backslash sqrt\{2d/g\}$.

From the form involving arccosine, the derivative of the time of flight with respect to d (or θ) goes to zero as d approaches {{val|20000|u=km}} (halfway around the world). The derivative of Δv also goes to zero here. So if d = {{val|19000|u=km}}, the length of the minimum-delta-v trajectory will be about {{val|19500|u=km}}, but it will take only a few seconds less time than the trajectory for d = {{val|20000|u=km}} (for which the trajectory is {{val|20000|u=km}} long).

File:Mr3-flight-timeline-simple.png

File:Science and Mechanics Nov 1931 cover.jpg cover of November 1931, showing a proposed sub-orbital spaceship that would reach an altitude {{convert|700|mi|km}} on its one-hour trip from Berlin to New York.]]

While there are a great many possible sub-orbital flight profiles, it is expected that some will be more common than others.

File:X-15.jpg mothership, lifted itself to approximately 100 km, and then glided to the ground.]]

The first sub-orbital vehicles which reached space were ballistic missiles. The first ballistic missile to reach space was the German V-2, the work of the scientists at Peenemünde, on October 3, 1942, which reached an altitude of {{convert|53|mi|km}}.Germany's V-2 Rocket, Kennedy, Gregory P. Then in the late 1940s the US and USSR concurrently developed missiles all of which were based on the V-2 Rocket, and then much longer range Intercontinental Ballistic Missiles (ICBMs). There are now many countries who possess ICBMs and even more with shorter range Intermediate Range Ballistic Missiles (IRBMs).{{citation needed|date=May 2024}}

Sub-orbital tourist flights will initially focus on attaining the altitude required to qualify as reaching space. The flight path will be either vertical or very steep, with the spacecraft landing back at its take-off site.

The spacecraft will shut off its engines well before reaching maximum altitude, and then coast up to its highest point. During a few minutes, from the point when the engines are shut off to the point where the atmosphere begins to slow down the downward acceleration, the passengers will experience weightlessness.

Megaroc had been planned for sub-orbital spaceflight by the British Interplanetary Society in the 1940s.{{cite web|url=http://www.bbc.com/future/story/20150824-how-a-nazi-rocket-could-have-put-a-briton-in-space|title=How a Nazi rocket could have put a Briton in space|first=Richard|last=Hollingham|website=bbc.com|date=25 August 2015 |access-date=4 May 2018|url-status=live|archive-url=https://web.archive.org/web/20161114032515/http://www.bbc.com/future/story/20150824-how-a-nazi-rocket-could-have-put-a-briton-in-space|archive-date=14 November 2016}}{{cite web|url=http://www.bis-space.com/what-we-do/projects/megaroc|title=Megaroc|website=www.bis-space.com|access-date=4 May 2018|url-status=live|archive-url=https://web.archive.org/web/20161030133900/http://www.bis-space.com/what-we-do/projects/megaroc|archive-date=30 October 2016}}

In late 1945, a group led by M. Tikhonravov K. and N. G. Chernysheva at the Soviet NII-4 academy (dedicated to rocket artillery science and technology), began work on a stratospheric rocket project, VR-190, aimed at vertical flight by a crew of two pilots, to an altitude of 200 km (65,000 ft) using captured V-2.{{Cite book |author=Anatoli I. Kiselev |author2=Alexander A. Medvedev| author3=Valery A. Menshikov |title=Astronautics: Summary and Prospects |translator=V. Sherbakov |translator2=N. Novichkov |translator3=A. Nechaev |publisher=Springer Science & Business Media|date=December 2012|pages=1–2|isbn=9783709106488}}

In 2004, a number of companies worked on vehicles in this class as entrants to the Ansari X Prize competition. The Scaled Composites SpaceShipOne was officially declared by Rick Searfoss to have won the competition on October 4, 2004, after completing two flights within a two-week period.

In 2005, Sir Richard Branson of the Virgin Group announced the creation of Virgin Galactic and his plans for a 9-seat capacity SpaceShipTwo named VSS Enterprise. It has since been completed with eight seats (one pilot, one co-pilot and six passengers) and has taken part in captive-carry tests and with the first mother-ship WhiteKnightTwo, or VMS Eve. It has also completed solitary glides, with the movable tail sections in both fixed and "feathered" configurations. The hybrid rocket motor has been fired multiple times in ground-based test stands, and was fired in a powered flight for the second time on 5 September 2013.{{cite web |url=http://www.scaled.com/projects/test_logs/35/model_339_spaceshiptwo |title=Scaled Composites: Projects - Test Logs for SpaceShipTwo |access-date=2013-08-14 |url-status=live |archive-url=https://web.archive.org/web/20130816140953/http://www.scaled.com/projects/test_logs/35/model_339_spaceshiptwo |archive-date=2013-08-16 }} Four additional SpaceShipTwos have been ordered and will operate from the new Spaceport America. Commercial flights carrying passengers were expected in 2014, but became cancelled due to the disaster during SS2 PF04 flight. Branson stated, "[w]e are going to learn from what went wrong, discover how we can improve safety and performance and then move forwards together.""Branson on Virgin Galactic crash: 'Space is hard – but worth it'". CNET. Retrieved August 1, 2015.

A major use of sub-orbital vehicles today is as scientific sounding rockets. Scientific sub-orbital flights began in the 1920s when Robert H. Goddard launched the first liquid fueled rockets, however they did not reach space altitude. In the late 1940s, captured German V-2 ballistic missiles were converted into V-2 sounding rockets which helped lay the foundation for modern sounding rockets.{{Cite web|title = ch2|url = https://history.nasa.gov/SP-4401/ch2.htm|website = history.nasa.gov|access-date = 2015-11-28|url-status = live|archive-url = http://archive.wikiwix.com/cache/20151129091504/https://history.nasa.gov/SP-4401/ch2.htm|archive-date = 2015-11-29}} Today there are dozens of different sounding rockets on the market, from a variety of suppliers in various countries. Typically, researchers wish to conduct experiments in microgravity or above the atmosphere.

Research, such as that done for the X-20 Dyna-Soar project suggests that a semi-ballistic sub-orbital flight could travel from Europe to North America in less than an hour.

However, the size of rocket, relative to the payload, necessary to achieve this, is similar to an ICBM. ICBMs have delta-v's somewhat less than orbital; and therefore would be somewhat cheaper than the costs for reaching orbit, but the difference is not large.{{cite web|url=http://www.thespacereview.com/article/1118/1|title=The Space Review: Point-to-point suborbital transportation: sounds good on paper, but...|website=www.thespacereview.com|access-date=4 May 2018|url-status=live|archive-url=https://web.archive.org/web/20170801074751/http://www.thespacereview.com/article/1118/1|archive-date=1 August 2017}}

Due to the high cost of spaceflight, suborbital flights are likely to be initially limited to high value, very high urgency cargo deliveries such as courier flights, military fast-response operations or space tourism.{{opinion|date=April 2012}}

The SpaceLiner is a hypersonic suborbital spaceplane concept that could transport 50 passengers from Australia to Europe in 90 minutes or 100 passengers from Europe to California in 60 minutes.{{Cite journal|doi=10.1016/j.actaastro.2010.01.020| author = Sippel, M. | title = Promising roadmap alternatives for the SpaceLiner |journal = Acta Astronautica |issue = 11–12 |volume = 66 |date = 2010| pages = 1652–1658 | bibcode = 2010AcAau..66.1652S | url = https://elib.dlr.de/64605/1/AA3731.pdf }} The main challenge lies in increasing the reliability of the different components, particularly the engines, in order to make their use for passenger transportation on a daily basis possible.

SpaceX is potentially considering using their Starship as a sub-orbital point-to-point transportation system.{{cite news |last=Ralph|first=Eric |url=https://www.teslarati.com/spacex-elon-musk-wants-starship-spaceliners/ |title=SpaceX CEO Elon Musk wants to use Starships as Earth-to-Earth transports |work=Teslarati |date=30 May 2019 |access-date=31 May 2019 }}

• The first sub-orbital space flight was on 20 June 1944, when MW 18014, a V-2 test rocket, launched from Peenemünde in Germany and reached 176 kilometres altitude.Walter Dornberger, Moewig, Berlin 1984. {{ISBN|3-8118-4341-9}}.
• Bumper 5, a two-stage rocket launched from the White Sands Proving Grounds. On 24 February 1949 the upper stage reached an altitude of {{convert|248|mi|km}} and a speed of {{convert|7,553|ft/s|m/s Mach}}.

{{cite web | url = http://www.wsmr.army.mil/pao/FactSheets/bump.htm | title = Bumper Project | publisher = White Sands Missile Range | url-status = dead | archive-url = https://web.archive.org/web/20080110163113/http://www.wsmr.army.mil/pao/FactSheets/bump.htm | archive-date = 2008-01-10 }}

• Albert II, a male rhesus macaque, became the first mammal in space on 14 June 1949 in a sub-orbital flight from Holloman Air Force Base in New Mexico to an altitude of 83 miles (134 km) aboard a U.S. V-2 sounding rocket.
• USSR – Energia, 15 May 1987, a Polyus payload which failed to reach orbit
• SpaceX IFT-7, 16 January 2025, a Starship flight test which blew up during ascent, forcing airline flights to alter course to avoid falling debris and setting back Elon Musk's flagship rocket program.{{cite web | url = https://arstechnica.com/space/2025/01/fire-destroys-starship-on-its-seventh-test-flight-raining-debris-from-space/ | title = Fire destroys Starship on its seventh test flight, raining debris from space | date = 17 January 2025 | publisher = Ars Technica }}{{cite web | url = https://www.reuters.com/technology/space/spacex-launches-seventh-starship-mock-satellite-deployment-test-2025-01-16/ | title = SpaceX's Starship explodes in flight test, forcing airlines to divert | publisher = Reuters }} There were also numerous reports of damage on the ground.{{cite web | url = https://edition.cnn.com/2025/01/17/science/spacex-starship-explosion-investigation/index.html | title = Regulators are investigating reports of property damage from SpaceX Starship's explosion | date = 17 January 2025 | publisher = CNN }} It is, to date, the most massive object launched into a sub-orbital trajectory.

Above 100 km (62.14 mi) in altitude.{{efn|Flights exceeding 80km but not 100km, including those flown by SpaceShipTwo, are recognized as spaceflight by the United States.}}

{{suborbital_spaceflight_timeline.svg}}

Most manned rocket flights were either orbital spaceflights or flights of rocket-powered aircraft, which were launched horizontally. Manned vertically launched suborbital flights were before the first launch of New Shepard rare and often the result of a failure of a manned rocket for orbital spaceflight. The following list shows all manned vertically launched suborbital rocket flights.

Private companies such as Virgin Galactic, Armadillo Aerospace (reinvented as Exos Aerospace), Airbus,{{cite news|url=https://www.bbc.co.uk/news/science-environment-27686906|title=Airbus drops model 'space jet'|first=Jonathan|last=Amos|work=BBC News|date=3 June 2014|access-date=4 May 2018|url-status=live|archive-url=https://web.archive.org/web/20180504004642/http://www.bbc.co.uk/news/science-environment-27686906|archive-date=4 May 2018}} Blue Origin and Masten Space Systems are taking an interest in sub-orbital spaceflight, due in part to ventures like the Ansari X Prize. NASA and others are experimenting with scramjet-based hypersonic aircraft which may well be used with flight profiles that qualify as sub-orbital spaceflight. Non-profit entities like ARCASPACE and Copenhagen Suborbitals also attempt rocket-based launches.

• Canadian Arrow
• CORONA
• DH-1 (rocket)
• Interorbital Systems
• Lunar Lander Challenge
• McDonnell Douglas DC-X
• Project Morpheus NASA program to continue developing ALHAT and Q­ landers
• Quad (rocket)
• Reusable Vehicle Testing program by JAXA
• Rocketplane XP
• SpaceX reusable launch system development program
• XCOR Lynx

{{Portal|Spaceflight}}

• Levels of spaceflight: Suborbital, orbital, interplanetary, interstellar and intergalactic
• Near space

{{Notelist}}

{{Reflist}}

{{Spaceflight}}

{{DEFAULTSORT:Sub-orbital spaceflight}}

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