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st full orbit are not considered sub orbital examples of this include flights of the fractional orbital bombardment system a flight that does not reach space is still sometimes called sub orbital but cannot officially be classified as a sub orbital spaceflight usually a rocket is used but some experimental sub orbital spaceflights have also been achieved via the use of space guns 3 altitude requirement edit isaac newton s cannonball paths a and b depict a sub orbital trajectory by definition a sub orbital spaceflight reaches an altitude higher than 100 km 62 mi 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 4 the us military and nasa award astronaut wings to those flying above 50 mi 80 km 5 although the u s state department does not show a distinct boundary between atmospheric flight and spaceflight 6 orbit edit 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 ϵ displaystyle epsilon is given by ε μ 2 a μ r displaystyle varepsilon mu over 2a mu over r where μ displaystyle mu is the standard gravitational parameter almost always a r corresponding to a lower ϵ displaystyle epsilon than the minimum for a full orbit which is μ 2 r displaystyle mu over 2r thus the net extra specific energy needed compared to just raising the spacecraft into space is between 0 and μ 2 r displaystyle mu over 2r speed range and altitude edit 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 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 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 spacecraft 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 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 needs update 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 the minimum delta v and the corresponding maximum altitude for a given range can be calculated d assuming a spherical earth of circumference 40 000 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 10 000 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 major axis 1 sin θ r displaystyle text major axis 1 sin theta r minor axis r 2 sin θ sin 2 θ r sin θ semi major axis displaystyle text minor axis r sqrt 2 left sin theta sin 2 theta right sqrt r sin theta text semi major axis distance of apogee from centre of earth r 2 1 sin θ cos θ displaystyle text distance of apogee from centre of earth frac r 2 1 sin theta cos theta altitude of apogee above surface sin θ 2 sin 2 θ 2 r 1 2 sin θ π 4 1 2 r displaystyle text altitude of apogee above surface left frac sin theta 2 sin 2 frac theta 2 right r left frac 1 sqrt 2 sin left theta frac pi 4 right frac 1 2 right r the altitude of apogee is maximized at about 1320 km for a trajectory going one quarter of the way around the earth 10 000 km longer ranges will have lower apogees in the minimal delta v solution specific kinetic energy at launch μ r μ major axis μ r sin θ 1 sin θ displaystyle text specific kinetic energy at launch frac mu r frac mu text major axis frac mu r frac sin theta 1 sin theta δ v speed at launch 2 μ r sin θ 1 sin θ 2 g r sin θ 1 sin θ displaystyle delta v text speed at launch sqrt 2 frac mu r frac sin theta 1 sin theta sqrt 2gr frac sin theta 1 sin theta where g is the acceleration of gravity at the earth s surface the δ v increases with range leveling off at 7 9 km s as the range approaches 20 000 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 7 flight duration edit 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 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 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 8 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 period semi major axis r 3 2 period of low earth orbit 1 sin θ 2 3 2 2 π r g displaystyle text period left frac text semi major axis r right frac 3 2 times text period of low earth orbit left frac 1 sin theta 2 right frac 3 2 2 pi sqrt 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 area fraction 1 π arcsin 2 sin θ 1 sin θ 2 cos θ sin θ π major axis minor axis displaystyle text area fraction frac 1 pi arcsin sqrt frac 2 sin theta 1 sin theta frac 2 cos theta sin theta pi text major axis minor axis time of flight 1 sin θ 2 3 2 arcsin 2 sin θ 1 sin θ 1 2 cos θ sin θ 2 r g 1 sin θ 2 3 2 arccos cos θ 1 sin θ 1 2 cos θ sin θ 2 r g displaystyle begin aligned 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 aligned 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 2 d g displaystyle 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 20 000 km halfway around the world the derivative of δ v also goes to zero here so if d 19 000 km the length of the minimum delta v trajectory will be about 19 500 km but it will take only a few seconds less time than the trajectory for d 20 000 km for which the trajectory is 20 000 km long flight profiles edit profile for the first crewed american sub orbital flight 1961 launch rocket lifts the spacecraft for the first 2 22 minutes dashed line zero gravity science and mechanics cover of november 1931 showing a proposed sub orbital spaceship that would reach an altitude 700 miles 1 100 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 the x 15 1958 1968 was launched to an altitude of 13 7 km by a b 52 mothership lifted itself to approximately 100 km and then glided to the ground ballistic missiles edit 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 53 miles 85 km 9 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 tourist flights edit 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 10 11 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 12 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 13 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 14 scientific experiments edit 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 15 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 sub orbital transportation edit 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 t...
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