Multistage rocket - Knowledge

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assumption may not be the ideal approach to yielding an efficient or optimal system, it greatly simplifies the equations for determining the burnout velocities, burnout times, burnout altitudes, and mass of each stage. This would make for a better approach to a conceptual design in a situation where a basic understanding of the system behavior is preferential to a detailed, accurate design. One important concept to understand when undergoing restricted rocket staging, is how the burnout velocity is affected by the number of stages that split up the rocket system. Increasing the number of stages for a rocket while keeping the specific impulse, payload ratios and structural ratios constant will always yield a higher burnout velocity than the same systems that use fewer stages. However, the law of diminishing returns is evident in that each increment in number of stages gives less of an improvement in burnout velocity than the previous increment. The burnout velocity gradually converges towards an asymptotic value as the number of stages increases towards a very high number. In addition to diminishing returns in burnout velocity improvement, the main reason why real world rockets seldom use more than three stages is because of increase of weight and complexity in the system for each added stage, ultimately yielding a higher cost for deployment.

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density. Asides from the fuel required, the mass of the rocket structure itself must also be determined, which requires taking into account the mass of the required thrusters, electronics, instruments, power equipment, etc. These are known quantities for typical off the shelf hardware that should be considered in the mid to late stages of the design, but for preliminary and conceptual design, a simpler approach can be taken. Assuming one engine for a rocket stage provides all of the total impulse for that particular segment, a mass fraction can be used to determine the mass of the system. The mass of the stage transfer hardware such as initiators and safe-and-arm devices are very small by comparison and can be considered negligible.

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oxidizer combination being used. For example, a mixture ratio of a bipropellant could be adjusted such that it may not have the optimal specific impulse, but will result in fuel tanks of equal size. This would yield simpler and cheaper manufacturing, packing, configuring, and integrating of the fuel systems with the rest of the rocket, and can become a benefit that could outweigh the drawbacks of a less efficient specific impulse rating. But suppose the defining constraint for the launch system is volume, and a low density fuel is required such as hydrogen. This example would be solved by using an oxidizer-rich mixture ratio, reducing efficiency and specific impulse rating, but will meet a smaller tank volume requirement.

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consideration when determining amount of fuel for the rocket. A common initial estimate for this residual propellant is five percent. With this ratio and the mass of the propellant calculated, the mass of the empty rocket weight can be determined. Sizing rockets using a liquid bipropellant requires a slightly more involved approach because there are two separate tanks that are required: one for the fuel, and one for the oxidizer. The ratio of these two quantities is known as the mixture ratio, and is defined by the equation:

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from above. Two common methods of determining this perfect ΔV partition between stages are either a technical algorithm that generates an analytical solution that can be implemented by a program, or simple trial and error. For the trial and error approach, it is best to begin with the final stage, calculating the initial mass which becomes the payload for the previous stage. From there it is easy to progress all the way down to the initial stage in the same manner, sizing all the stages of the rocket system.

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the previous example, the end of the first stage which is sometimes referred to as 'stage 0', can be defined as when the side boosters separate from the main rocket. From there, the final mass of stage one can be considered the sum of the empty mass of stage one, the mass of stage two (the main rocket and the remaining unburned fuel) and the mass of the payload.

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is kept for another stage. Most quantitative approaches to the design of the rocket system's performance are focused on tandem staging, but the approach can be easily modified to include parallel staging. To begin with, the different stages of the rocket should be clearly defined. Continuing with

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for the "stage-0" with two core stages. In these designs, the boosters and first stage fire simultaneously instead of consecutively, providing extra initial thrust to lift the full launcher weight and overcome gravity losses and atmospheric drag. The boosters are jettisoned a few minutes into flight

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A rocket system that implements tandem staging means that each individual stage runs in order one after the other. The rocket breaks free from the previous stage, then begins burning through the next stage in straight succession. On the other hand, a rocket that implements parallel staging has two

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The ultimate goal of optimal staging is to maximize the payload ratio (see ratios under performance), meaning the largest amount of payload is carried up to the required burnout velocity using the least amount of non-payload mass, which comprises everything else. This goal assumes that the cost of a

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The burnout time does not define the end of the rocket stage's motion, as the vehicle will still have a velocity that will allow it to coast upward for a brief amount of time until the acceleration of the planet's gravity gradually changes it to a downward direction. The velocity and altitude of the

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and developed by the Firearms Bureau (火㷁道監) during the 14th century. The rocket had the length of 15 cm and 13 cm; the diameter was 2.2 cm. It was attached to an arrow 110 cm long; experimental records show that the first results were around 200m in range. There are records that

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Hot-staging is a type of rocket staging in which the next stage fires its engines before separation instead of after. During hot-staging, the earlier stage throttles down its engines. Hot-staging may reduce the complexity of stage separation, and gives a small extra payload capacity to the booster.

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Restricted rocket staging is based on the simplified assumption that each of the stages of the rocket system have the same specific impulse, structural ratio, and payload ratio, the only difference being the total mass of each increasing stage is less than that of the previous stage. Although this

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Where n is the number of stages the rocket system comprises. Similar stages yielding the same payload ratio simplify this equation, however that is seldom the ideal solution for maximizing payload ratio, and ΔV requirements may have to be partitioned unevenly as suggested in guideline tips 1 and 2

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The payload ratio can be calculated for each individual stage, and when multiplied together in sequence, will yield the overall payload ratio of the entire system. It is important to note that when computing payload ratio for individual stages, the payload includes the mass of all the stages after

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The common thrust-to-weight ratio of a launch vehicle is within the range of 1.3 to 2.0. Another performance metric to keep in mind when designing each rocket stage in a mission is the burn time, which is the amount of time the rocket engine will last before it has exhausted all of its propellant.

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A further advantage is that each stage can use a different type of rocket engine, each tuned for its particular operating conditions. Thus the lower-stage engines are designed for use at atmospheric pressure, while the upper stages can use engines suited to near vacuum conditions. Lower stages tend

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When comparing one rocket with another, it is impractical to directly compare the rocket's certain trait with the same trait of another because their individual attributes are often not independent of one another. For this reason, dimensionless ratios have been designed to enable a more meaningful

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These equations show that a higher specific impulse means a more efficient rocket engine, capable of burning for longer periods of time. In terms of staging, the initial rocket stages usually have a lower specific impulse rating, trading efficiency for superior thrust in order to quickly push the

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For modern day solid rocket motors, it is a safe and reasonable assumption to say that 91 to 94 percent of the total mass is fuel. It is also important to note there is a small percentage of "residual" propellant that will be left stuck and unusable inside the tank, and should also be taken into

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The advantage of staging comes at the cost of the lower stages lifting engines which are not yet being used, as well as making the entire rocket more complex and harder to build than a single stage. In addition, each staging event is a possible point of launch failure, due to separation failure,

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for the "stage-0" with three core stages. In these designs, the boosters and first stage fire simultaneously instead of consecutively, providing extra initial thrust to lift the full launcher weight and overcome gravity losses and atmospheric drag. The boosters are jettisoned a few minutes into

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is the mass of the fuel. This mixture ratio not only governs the size of each tank, but also the specific impulse of the rocket. Determining the ideal mixture ratio is a balance of compromises between various aspects of the rocket being designed, and can vary depending on the type of fuel and

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where g is the gravity constant of Earth. This also enables the volume of storage required for the fuel to be calculated if the density of the fuel is known, which is almost always the case when designing the rocket stage. The volume is yielded when dividing the mass of the propellant by its

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are used to assist with launch. These are sometimes referred to as "stage 0". In the typical case, the first-stage and booster engines fire to propel the entire rocket upwards. When the boosters run out of fuel, they are detached from the rest of the rocket (usually with some kind of small

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that would eventually burn out, yet before they did they automatically ignited a number of smaller rocket arrows that were shot out of the front end of the missile, which was shaped like a dragon's head with an open mouth. The British scientist and historian

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Multi-stage rockets overcome a limitation imposed by the laws of physics on the velocity change achievable by a rocket stage. The limit depends on the fueled-to-dry mass ratio and on the effective exhaust velocity of the engine. This relation is given by the

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stage is attached alongside another stage. The result is effectively two or more rockets stacked on top of or attached next to each other. Two-stage rockets are quite common, but rockets with as many as five separate stages have been successfully launched.

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By jettisoning stages when they run out of propellant, the mass of the remaining rocket is decreased. Each successive stage can also be optimized for its specific operating conditions, such as decreased atmospheric pressure at higher altitudes. This

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launch vehicles, arranged in a row, used parallel staging in a similar way: the outer pair of booster engines existed as a jettisonable pair which would, after they shut down, drop away with the lowermost outer skirt structure, leaving the central

1251:{\displaystyle v_{\mathrm {bo} }=I_{\mathrm {sp} }g_{\mathrm {0} }\ln({\frac {m_{\mathrm {0} }}{m_{\mathrm {f} }}})-g_{\mathrm {0} }{\frac {m_{\mathrm {0} }-m_{\mathrm {f} }}{\frac {\operatorname {d} \!m}{\operatorname {d} \!t}}}+v_{\mathrm {0} }} 1284:

comparison between rockets. The first is the initial to final mass ratio, which is the ratio between the rocket stage's full initial mass and the rocket stage's final mass once all of its fuel has been consumed. The equation for this ratio is:

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After comparing the three equations for the dimensionless quantities, it is easy to see that they are not independent of each other, and in fact, the initial to final mass ratio can be rewritten in terms of structural ratio and payload ratio:

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rocket into higher altitudes. Later stages of the rocket usually have a higher specific impulse rating because the vehicle is further outside the atmosphere and the exhaust gas does not need to expand against as much atmospheric pressure.

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is the mass of the payload. The second dimensionless performance quantity is the structural ratio, which is the ratio between the empty mass of the stage, and the combined empty mass and propellant mass as shown in this equation:

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to require more structure than upper as they need to bear their own weight plus that of the stages above them. Optimizing the structure of each stage decreases the weight of the total vehicle and provides further advantage.

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Calculate the burnout velocity, and sum it with the initial velocity for each individual stage. Assuming each stage occurs immediately after the previous, the burnout velocity becomes the initial velocity for the following

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are the initial and final masses of the rocket stage respectively. In conjunction with the burnout time, the burnout height and velocity are obtained using the same values, and are found by these two equations:

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For initial sizing, the rocket equations can be used to derive the amount of propellant needed for the rocket based on the specific impulse of the engine and the total impulse required in N·s. The equation is:

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rocket launch is proportional to the total liftoff mass of the rocket, which is a rule of thumb in rocket engineering. Here are a few quick rules and guidelines to follow in order to reach optimal staging:

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is a commonly used rocket system to attain Earth orbit. The spacecraft uses three distinct stages to provide propulsion consecutively in order to achieve orbital velocity. It is intermediate between a

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When selecting the ideal rocket engine to use as an initial stage for a launch vehicle, a useful performance metric to examine is the thrust-to-weight ratio, and is calculated by the equation:

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is a rocket system used to attain Earth orbit. The spacecraft uses four distinct stages to provide propulsion consecutively in order to achieve orbital velocity. It is intermediate between a

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The last major dimensionless performance quantity is the payload ratio, which is the ratio between the payload mass and the combined mass of the empty rocket stage and the propellant:

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space programs, were not passivated after mission completion. During the initial attempts to characterize the space debris problem, it became evident that a good proportion of all

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These performance ratios can also be used as references for how efficient a rocket system will be when performing optimizations and comparing varying configurations for a mission.

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One of the most common measures of rocket efficiency is its specific impulse, which is defined as the thrust per flow rate (per second) of propellant consumption:

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When dealing with the problem of calculating the total burnout velocity or time for the entire rocket system, the general procedure for doing so is as follows:

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carried out a pioneering engineering study of general sequential and parallel staging, with and without the pumping of fuel between stages. The design of the

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This is generally not practical for larger space vehicles, which are assembled off the pad and moved into place on the launch site by various methods. NASA's

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Other designs (in fact, most modern medium- to heavy-lift designs) do not have all three stages inline on the main stack, instead having strap-on

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is a spacecraft in which two distinct stages provide propulsion consecutively in order to achieve orbital velocity. It is intermediate between a

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High-altitude and space-bound upper stages are designed to operate with little or no atmospheric pressure. This allows the use of lower pressure

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For most non-final stages, thrust and specific impulse can be assumed constant, which allows the equation for burn time to be written as:

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was designed to use hot staging, however none of the test flights lasted long enough for this to occur. Starting with the Titan II, the

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the separation—the interstage ring is designed with this in mind, and the thrust is used to help positively separate the two vehicles.

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that burn simultaneously. Upon launch, the boosters ignite, and at the end of the stage, the two boosters are discarded while the

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ignition failure, or stage collision. Nevertheless, the savings are so great that every rocket ever used to deliver a payload into

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for many years after use, and occasionally, large debris fields created from the breakup of a single upper stage while in orbit.

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developed a theory of parallel stages, which he called "packet rockets". In his scheme, three parallel stages were fired from

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sounding rocket. The greatest altitude ever reached was 393 km, attained on February 24, 1949, at White Sands.

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moved the entire vehicle stack to the launch pad in an upright position. In contrast, vehicles such as the Russian

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points out that the written material and depicted illustration of this rocket come from the oldest stratum of the

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are assembled horizontally in a processing hangar, transported horizontally, and then brought upright at the pad.

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Each individual stage is generally assembled at its manufacturing site and shipped to the launch site; the term

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Repeat the previous two steps until the burnout time and/or velocity has been calculated for the final stage.

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into the success of the launch mission. Reducing the number of separation events results in a reduction in

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refers to the mating of all rocket stage(s) and the spacecraft payload into a single assembly known as a

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When rearranging the equation such that thrust is calculated as a result of the other factors, we have:

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emerged from that study. The trio of rocket engines used in the first stage of the American

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Other designs do not have all four stages inline on the main stack, instead having strap-on

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of Korean development. It was proposed by medieval Korean engineer, scientist and inventor

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after their use as a launch vehicle is complete in order to minimize risks while the stage

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rocket after burnout can be easily modeled using the basic physics equations of motion.

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Partition the problem calculations into however many stages the rocket system comprises.

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of the vehicle (change of velocity plus losses due to gravity and atmospheric drag);

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or more different stages that are active at the same time. For example, the

4149: 4012: 3675: 3458:"SpaceX Starship Never Stops Thrusting With Hot Staging | NextBigFuture.com" 3166: 2944: 2884: 2539: 2506: 2268: 2220: 301:{\displaystyle \Delta v=v_{\text{e}}\ln \left({\frac {m_{0}}{m_{f}}}\right)} 156: 17: 3433:"Proton-M flyout continues with launch of Angosat-2 - NASASpaceFlight.com" 218: 4074: 3048: 2989: 2949: 2938: 2927: 2843: 2838: 2832: 2822: 2651: 2436: 2409: 2240: 2212: 2146: 211: 2667:

Separation of each portion of a multistage rocket introduces additional

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show Korea kept developing this technology until it came to produce the

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A diagram of the second stage and how it fits into the complete rocket

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are above it, usually decreasing in size. In parallel staging schemes

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to complete the first stage's engine burn towards apogee or orbit.

653:{\displaystyle T=I_{\mathrm {sp} }g_{\mathrm {0} }{\frac {dm}{dt}}} 4139: 4124: 4109: 2974: 2970: 2447:

Spent upper stages of launch vehicles are a significant source of

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launcher, most often used with solid-propellant launch systems.

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was due to the breaking up of rocket upper stages, particularly

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The next stage is always a smaller size than the previous stage.

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is the initial total (wet) mass, equal to final (dry) mass plus

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Calculate the initial and final mass for each individual stage.

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family of rockets used hot staging. SpaceX retrofitted their

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is the effective exhaust velocity (determined by propellant,

3701:"VIENO EKSPONATO PARODA: KNYGA "DIDYSIS ARTILERIJOS MENAS"!" 3404:"SpaceX Achieves New Milestones With Second Starship Flight" 1772:{\displaystyle m_{\text{p}}=I_{\text{tot}}/gI_{\text{sp}}} 406:

is the final (dry) mass, after the propellant is expended;

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from 1948 to 1950. These consisted of a V-2 rocket and a

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The second stage being lowered onto the first stage of a

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shows the oldest known multistage rocket; this was the "

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designs are sought, but have not yet been demonstrated.

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separates prior to orbital insertion, or when used, a

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Another example of an early multistaged rocket is the

2108:{\displaystyle \lambda =\prod _{i=1}^{n}\lambda _{i}} 2067: 2023: 1990: 1960: 1903: 1871: 1796: 1727: 1648: 1570: 1496: 1460: 1431: 1402: 1293: 1079: 901: 868: 839: 736: 676: 596: 529: 497: 447: 414: 385: 352: 320: 240: 27:

Most common type of rocket, used to launch satellites

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An illustration and description in the 14th century

4047: 4021: 3952: 2683:which separates after the early phase of a launch. 30:"Second stage" redirects here. For other uses, see 2630:In 1947, the Soviet rocket engineer and scientist 2457:After the 1990s, spent upper stages are generally 2107: 2039: 2006: 1976: 1927: 1889: 1854: 1771: 1683: 1627: 1550: 1478: 1446: 1417: 1385: 1250: 1064: 883: 854: 822: 716:{\displaystyle TWR={\frac {T}{mg_{\mathrm {0} }}}} 715: 652: 576: 515: 453: 427: 398: 365: 332: 300: 194:Cutaway drawings showing three multi-stage rockets 2687:, or in some cases pneumatic systems like on the 2611:The first high-speed multistage rockets were the 1225: 1216: 138:is at the bottom and is usually the largest, the 2691:, are typically used to separate rocket stages. 2058:the current one. The overall payload ratio is: 2546:(1509–1576), the arsenal master of the town of 3307:. 2nd ed. Daytona Beach: Elsevier, 2010. Print 2961:Geosynchronous Satellite Launch Vehicle Mk III 3930: 3510: 3508: 2452:remaining in orbit in a non-operational state 127:allows the thrust of the remaining stages to 8: 3111:(optional boosters and optional third stage) 2871:(optional boosters and optional third stage) 2420:with attached launch umbilical towers, in a 2203:. Some upper stages, especially those using 1984:, and later/final stages should have higher 114:stage is mounted on top of another stage; a 3303:Curtis, Howard. "Rocket Vehicle Dynamics." 2313:. Unsourced material may be challenged and 3937: 3923: 3915: 3797:"Saturn V Rockets & Apollo Spacecraft" 3337:"Here's What's Next for SpaceX's Starship" 3305:Orbital Mechanics for Engineering Students 3766:"Falcon 1 – Stage Separation Reliability" 2786:Learn how and when to remove this message 2377:Learn how and when to remove this message 2099: 2089: 2078: 2066: 2053:Similar stages should provide similar ΔV. 2028: 2022: 1995: 1989: 1965: 1959: 1909: 1908: 1902: 1877: 1876: 1870: 1836: 1835: 1826: 1816: 1815: 1800: 1795: 1763: 1751: 1745: 1732: 1726: 1655: 1647: 1615: 1614: 1600: 1599: 1584: 1583: 1577: 1569: 1538: 1537: 1523: 1522: 1510: 1509: 1503: 1495: 1466: 1465: 1459: 1437: 1436: 1430: 1408: 1407: 1401: 1370: 1369: 1355: 1354: 1338: 1337: 1323: 1322: 1308: 1307: 1300: 1292: 1241: 1240: 1203: 1202: 1188: 1187: 1180: 1173: 1172: 1153: 1152: 1141: 1140: 1134: 1118: 1117: 1103: 1102: 1085: 1084: 1078: 1052: 1051: 1037: 1036: 1019: 1018: 1009: 1002: 1001: 986: 976: 975: 956: 955: 943: 942: 928: 927: 920: 907: 906: 900: 874: 873: 867: 845: 844: 838: 810: 809: 795: 794: 771: 770: 756: 755: 748: 740: 735: 703: 702: 689: 675: 630: 623: 622: 608: 607: 595: 564: 563: 539: 533: 528: 503: 502: 496: 446: 419: 413: 390: 384: 357: 351: 319: 286: 276: 270: 254: 239: 202:Apollo 11 Saturn V first-stage separation 134:In serial or tandem staging schemes, the 3299: 3297: 3295: 3293: 3291: 3289: 3287: 3285: 3283: 3281: 2817:Examples of three-stage-to-orbit systems 2219:, which eliminates the need for complex 3518:Orbital Debris from Upper-stage Breakup 3319: 3317: 3315: 3313: 3198: 3032:Examples of four-stage-to-orbit systems 3855:"Atlas V Launch Services User's Guide" 3083:Examples of three stages with boosters 1940:Optimal staging and restricted staging 3867:from the original on 14 December 2020 3330: 3328: 3326: 2468:Many early upper stages, in both the 174:Only multistage rockets have reached 7: 2901:Examples of two stages with boosters 2311:adding citations to reliable sources 2161:rocket to use hot staging after its 3899:from the original on 22 August 2021 3709:Lithuanian Museum of Ethnocosmology 3233:"Learning about rockets, in stages" 1928:{\displaystyle m_{\mathrm {fuel} }} 1454:is the mass of the propellant, and 3586:. 星辰在线. 2003-12-26. Archived from 3493:from the original on June 19, 2014 2511:fire-dragon issuing from the water 2223:. Other upper stages, such as the 1919: 1916: 1913: 1910: 1881: 1878: 1846: 1843: 1840: 1837: 1820: 1817: 1616: 1601: 1588: 1585: 1539: 1524: 1511: 1470: 1467: 1438: 1409: 1374: 1371: 1356: 1342: 1339: 1324: 1309: 1222: 1213: 1204: 1154: 1107: 1104: 1089: 1086: 1053: 1003: 990: 987: 977: 957: 932: 929: 911: 908: 875: 811: 760: 757: 737: 612: 609: 507: 504: 321: 241: 131:to its final velocity and height. 25: 3375:"One Web 2 | Soyuz 2.1b/Fregat-M" 2416:, were assembled vertically onto 2412:crewed Moon landing vehicle, and 2169:Tandem vs parallel staging design 1954:Initial stages should have lower 1890:{\displaystyle m_{\mathrm {ox} }} 1479:{\displaystyle m_{\mathrm {PL} }} 516:{\displaystyle I_{\mathrm {sp} }} 129:more easily accelerate the rocket 98:, each of which contains its own 4029:Advanced Cryogenic Evolved Stage 3561:. The Space Show. Archived from 3553:Johnson, Nicholas (2011-12-05). 2740: 2283: 2199:and engine nozzles with optimal 2137:It also eliminates the need for 1897:is the mass of the oxidizer and 1447:{\displaystyle m_{\mathrm {p} }} 1425:is the empty mass of the stage, 1418:{\displaystyle m_{\mathrm {E} }} 884:{\displaystyle m_{\mathrm {f} }} 855:{\displaystyle m_{\mathrm {0} }} 3807:from the original on 2022-02-11 3746:from the original on 2018-02-05 3652:from the original on 2024-02-24 3613:Needham, Volume 5, Part 7, 510. 3535:from the original on 2024-02-24 3439:from the original on 2023-06-05 3414:from the original on 2023-11-28 3385:from the original on 2023-12-01 3355:from the original on 2023-11-25 3213:from the original on 2019-12-20 1710:of multistage rockets carrying 439:design and throttle condition); 2484:upper-stage propulsion units. 1698:Component selection and sizing 1162: 1131: 1059: 1026: 994: 968: 817: 787: 485:has had staging of some sort. 469:The delta v required to reach 1: 3373:Sesnic, Trevor (2020-02-04). 63:has its own set of tail fins. 3559:audio file, @1:03:05-1:06:20 3460:. 2023-06-24. Archived from 2724:launcher and a hypothetical 2443:Passivation and space debris 428:{\displaystyle v_{\text{e}}} 3795:Sharp, Tim (October 2018). 3736:"Lietuvos kariuomenei - 95" 2852:(three stages and boosters) 2766:the claims made and adding 4202: 3515:Loftus, Joseph P. (1989). 3207:"Brief History of Rockets" 2698: 2617:White Sands Proving Ground 2047:should contribute less ΔV. 2017:The stages with the lower 333:{\displaystyle \Delta v\ } 44: 29: 3648:. 한국민족문화대백과. 1999-09-25. 3103:flight to reduce weight. 2463:remains derelict in orbit 2422:Vehicle Assembly Building 2418:mobile launcher platforms 2397:. Single-stage vehicles ( 229:classical rocket equation 3705:www.etnokosmomuziejus.lt 3257:10.1088/1361-6552/ac6928 3124:Mars Ascent Vehicle(MAV) 3117:Extraterrestrial Rockets 2263:. Upper stages, such as 4034:Exploration Upper Stage 3231:Blanco, Philip (2022). 3066:(optional fourth stage) 2864:(optional fourth stage) 2562:Kazimieras Simonavičius 2488:History and development 2239:cycle engines like the 2201:vacuum expansion ratios 3734:Simonaitis, Ričardas. 3670:Ulrich Walter (2008). 3162:Reusable launch system 2615:rockets tested at the 2571:Konstantin Tsiolkovsky 2231:, use liquid hydrogen 2109: 2094: 2041: 2040:{\displaystyle I_{sp}} 2008: 2007:{\displaystyle I_{sp}} 1978: 1977:{\displaystyle I_{sp}} 1929: 1891: 1856: 1773: 1714: 1685: 1629: 1552: 1480: 1448: 1419: 1387: 1252: 1066: 885: 856: 824: 717: 654: 578: 517: 455: 429: 400: 367: 334: 302: 223: 215: 203: 195: 152:liquid rocket boosters 91:that uses two or more 76: 71:The second stage of a 64: 4186:Space launch vehicles 4171:Aerospace engineering 4130:Payload Assist Module 3887:"Falcon User's Guide" 3555:"Space debris issues" 3521:. AIAA. p. 227. 3150:Single-stage-to-orbit 2726:single-stage-to-orbit 2685:Pyrotechnic fasteners 2424:, and then a special 2180:Solid Rocket Boosters 2110: 2074: 2042: 2009: 1979: 1930: 1892: 1857: 1774: 1705: 1686: 1630: 1553: 1481: 1449: 1420: 1388: 1253: 1067: 886: 857: 825: 718: 655: 579: 518: 456: 430: 401: 399:{\displaystyle m_{f}} 368: 366:{\displaystyle m_{0}} 335: 303: 221: 209: 201: 193: 180:Single-stage-to-orbit 70: 55: 36:reading (legislature) 4145:Transfer Orbit Stage 4120:Inertial Upper Stage 3140:Three-stage-to-orbit 3026:three-stage-to-orbit 2800:three-stage-to-orbit 2732:Three-stage-to-orbit 2722:three-stage-to-orbit 2689:Falcon 9 Full Thrust 2681:launch escape system 2307:improve this section 2065: 2021: 1988: 1958: 1901: 1869: 1794: 1725: 1646: 1568: 1494: 1458: 1429: 1400: 1291: 1077: 899: 866: 837: 734: 674: 594: 527: 495: 454:{\displaystyle \ln } 445: 412: 383: 350: 318: 238: 40:Second Stage Theatre 3830:www.astronautix.com 3699:Balčiūnienė, Irma. 3487:RussianSpaceWeb.com 3249:2022PhyEd..57d5035B 3022:five-stage-to-orbit 3015:four-stage-to-orbit 3009:Four-stage-to-orbit 2985:Space Launch System 2963:(However, like the 2952:-Medium+ and -Heavy 2835:(optional boosters) 2807:four-stage-to-orbit 2632:Mikhail Tikhonravov 2426:crawler-transporter 2326:"Multistage rocket" 2197:combustion chambers 3836:on August 20, 2016 3715:on 5 February 2018 3379:Everyday Astronaut 3145:Two-stage-to-orbit 3136:Multistage rocket 2910:to reduce weight. 2811:two-stage-to-orbit 2751:possibly contains 2707:two-stage-to-orbit 2701:Two-stage-to-orbit 2695:Two-stage-to-orbit 2640:Dmitry Okhotsimsky 2215:second stage, are 2184:external fuel tank 2105: 2037: 2004: 1974: 1925: 1887: 1852: 1769: 1715: 1681: 1625: 1548: 1476: 1444: 1415: 1383: 1248: 1062: 881: 852: 820: 713: 650: 574: 513: 451: 425: 396: 363: 330: 298: 224: 216: 204: 196: 77: 73:Minuteman III 65: 56:Each stage of the 4176:Rocket propulsion 4158: 4157: 3707:(in Lithuanian). 3685:978-3-527-40685-2 3237:Physics Education 3172:Apogee kick motor 2796: 2795: 2788: 2753:original research 2728:(SSTO) launcher. 2663:Separation events 2559:Polish–Lithuanian 2387: 2386: 2379: 2361: 2207:propellants like 1766: 1748: 1735: 1712:Apollo spacecraft 1679: 1623: 1546: 1381: 1231: 1230: 1160: 985: 963: 782: 711: 648: 572: 557: 532: 463:natural logarithm 422: 329: 292: 257: 81:multistage rocket 16:(Redirected from 4193: 3939: 3932: 3925: 3916: 3909: 3908: 3906: 3904: 3898: 3891: 3883: 3877: 3876: 3874: 3872: 3866: 3859: 3851: 3845: 3844: 3842: 3841: 3832:. 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2589:Hermann Oberth 2583: 2580:Robert Goddard 2574: 2565: 2520:Joseph Needham 2489: 2486: 2444: 2441: 2385: 2384: 2367:September 2024 2291: 2289: 2282: 2276: 2273: 2233:expander cycle 2192: 2189: 2170: 2167: 2133: 2130: 2124: 2121: 2116: 2115: 2102: 2098: 2092: 2087: 2084: 2081: 2077: 2073: 2070: 2055: 2054: 2051: 2048: 2034: 2031: 2027: 2015: 2001: 1998: 1994: 1971: 1968: 1964: 1946: 1943: 1941: 1938: 1921: 1918: 1915: 1912: 1907: 1883: 1880: 1875: 1863: 1862: 1848: 1845: 1842: 1839: 1834: 1829: 1822: 1819: 1814: 1810: 1807: 1803: 1799: 1780: 1779: 1762: 1758: 1754: 1744: 1740: 1731: 1699: 1696: 1692: 1691: 1677: 1674: 1671: 1666: 1663: 1660: 1654: 1651: 1636: 1635: 1618: 1613: 1609: 1603: 1598: 1590: 1587: 1582: 1576: 1573: 1559: 1558: 1541: 1536: 1532: 1526: 1521: 1513: 1508: 1502: 1499: 1472: 1469: 1464: 1440: 1435: 1411: 1406: 1394: 1393: 1376: 1373: 1368: 1364: 1358: 1353: 1344: 1341: 1336: 1332: 1326: 1321: 1317: 1311: 1306: 1299: 1296: 1277: 1276: 1273: 1269: 1266: 1259: 1258: 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2917: 2916:Space Shuttle 2913: 2912: 2911: 2908: 2900: 2896: 2895:KSLV-2 "Nuri" 2893: 2891: 2888: 2886: 2883: 2881: 2880:Long March 1D 2877: 2874: 2872: 2870: 2866: 2863: 2860: 2858:(four stages) 2857: 2854: 2851: 2848: 2846:(four stages) 2845: 2842: 2840: 2837: 2834: 2831: 2829: 2826: 2824: 2821: 2820: 2816: 2814: 2812: 2808: 2804: 2803:launch system 2801: 2790: 2787: 2779: 2769: 2765: 2761: 2755: 2754: 2749:This section 2747: 2738: 2737: 2731: 2729: 2727: 2723: 2719: 2716: 2712: 2708: 2702: 2694: 2692: 2690: 2686: 2682: 2678: 2674: 2670: 2662: 2660: 2658: 2653: 2649: 2645: 2641: 2637: 2633: 2628: 2626: 2622: 2619:and later at 2618: 2614: 2604: 2599: 2596: 2593: 2590: 2587: 2584: 2581: 2578: 2575: 2572: 2569: 2566: 2563: 2560: 2557: 2556: 2555: 2553: 2549: 2545: 2541: 2536: 2532: 2527: 2525: 2521: 2516: 2512: 2508: 2504: 2500: 2499: 2495: 2487: 2485: 2483: 2479: 2475: 2471: 2466: 2464: 2460: 2455: 2453: 2450: 2442: 2440: 2438: 2435: 2431: 2427: 2423: 2419: 2415: 2414:Space Shuttle 2411: 2407: 2402: 2400: 2396: 2395:space vehicle 2392: 2381: 2378: 2370: 2359: 2356: 2352: 2349: 2345: 2342: 2338: 2335: 2331: 2328: – 2327: 2323: 2322:Find sources: 2316: 2312: 2308: 2302: 2301: 2297: 2292:This section 2290: 2286: 2281: 2280: 2274: 2272: 2270: 2266: 2262: 2258: 2254: 2250: 2246: 2242: 2238: 2237:gas generator 2234: 2230: 2226: 2222: 2218: 2214: 2210: 2206: 2202: 2198: 2190: 2188: 2185: 2181: 2177: 2176:Space Shuttle 2168: 2166: 2164: 2160: 2156: 2152: 2148: 2144: 2140: 2139:ullage motors 2131: 2129: 2122: 2120: 2100: 2096: 2090: 2085: 2082: 2079: 2075: 2071: 2068: 2061: 2060: 2059: 2052: 2049: 2032: 2029: 2025: 2016: 1999: 1996: 1992: 1969: 1966: 1962: 1953: 1952: 1951: 1944: 1939: 1937: 1905: 1873: 1832: 1827: 1812: 1808: 1805: 1801: 1797: 1790: 1789: 1788: 1784: 1760: 1756: 1752: 1742: 1738: 1729: 1721: 1720: 1719: 1713: 1709: 1708:Saturn family 1704: 1697: 1695: 1675: 1672: 1669: 1664: 1661: 1658: 1652: 1649: 1642: 1641: 1640: 1611: 1607: 1596: 1580: 1574: 1571: 1564: 1563: 1562: 1534: 1530: 1519: 1506: 1500: 1497: 1490: 1489: 1488: 1462: 1433: 1404: 1366: 1362: 1351: 1334: 1330: 1319: 1315: 1304: 1297: 1294: 1287: 1286: 1285: 1281: 1274: 1270: 1267: 1264: 1263: 1262: 1242: 1237: 1233: 1226: 1217: 1199: 1195: 1189: 1184: 1174: 1169: 1165: 1149: 1142: 1137: 1128: 1125: 1119: 1114: 1099: 1095: 1081: 1073: 1048: 1044: 1038: 1033: 1029: 1020: 1015: 1010: 998: 972: 965: 952: 944: 939: 924: 917: 903: 895: 894: 893: 870: 846: 841: 806: 802: 796: 791: 784: 779: 772: 767: 752: 745: 741: 730: 729: 728: 704: 699: 695: 691: 686: 683: 680: 677: 670: 669: 668: 665: 644: 641: 636: 633: 624: 619: 604: 600: 597: 590: 589: 588: 565: 560: 553: 550: 545: 542: 535: 499: 491: 490: 489: 486: 484: 478: 474: 472: 464: 448: 441: 438: 416: 408: 391: 387: 379: 376: 358: 354: 346: 343: 324: 314: 313: 312: 294: 287: 283: 277: 273: 267: 263: 260: 251: 247: 244: 234: 233: 232: 230: 220: 213: 208: 200: 192: 185: 183: 181: 177: 176:orbital speed 172: 170: 166: 162: 158: 153: 149: 145: 141: 137: 132: 130: 126: 120: 117: 113: 109: 105: 101: 97: 94: 90: 86: 82: 74: 69: 62: 59: 54: 48: 41: 37: 33: 19: 4181:Space access 4000:Star 27 / 37 3946:Upper stages 3903:20 September 3901:. Retrieved 3881: 3871:20 September 3869:. Retrieved 3849: 3838:. Retrieved 3834:the original 3829: 3820: 3809:. Retrieved 3800: 3790: 3778:. Retrieved 3774:the original 3760: 3748:. Retrieved 3739: 3729: 3717:. Retrieved 3713:the original 3704: 3694: 3672:Astronautics 3671: 3665: 3654:. Retrieved 3640: 3629: 3618: 3592:. Retrieved 3588:the original 3578: 3567:. Retrieved 3563:the original 3558: 3548: 3537:. Retrieved 3517: 3495:. Retrieved 3486: 3477: 3466:. Retrieved 3462:the original 3452: 3441:. Retrieved 3427: 3416:. Retrieved 3408:Supercluster 3407: 3398: 3387:. Retrieved 3378: 3368: 3357:. Retrieved 3340: 3268:. Retrieved 3240: 3236: 3226: 3215:. Retrieved 3201: 3109:Long March 5 3107: 3097: 3014: 3012: 2956:Falcon Heavy 2941:third stage) 2904: 2876:Long March 1 2869:Long March 5 2867: 2799: 2797: 2782: 2773: 2750: 2714: 2710: 2706: 2704: 2666: 2644:R-7 Semyorka 2629: 2625:WAC Corporal 2610: 2552:Transylvania 2548:Hermannstadt 2535:Ch'oe Mu-sŏn 2530: 2528: 2523: 2496: 2491: 2482:unpassivated 2467: 2456: 2449:space debris 2446: 2430:Soyuz rocket 2403: 2390: 2388: 2373: 2364: 2354: 2347: 2340: 2333: 2321: 2305:Please help 2293: 2235:engines, or 2217:pressure fed 2194: 2191:Upper stages 2172: 2163:first flight 2135: 2126: 2117: 2056: 1948: 1864: 1785: 1781: 1716: 1693: 1637: 1560: 1395: 1282: 1278: 1260: 832: 725: 666: 662: 586: 487: 479: 475: 468: 310: 225: 173: 168: 164: 144:upper stages 143: 140:second stage 139: 135: 133: 124: 121: 115: 111: 107: 95: 84: 80: 78: 3584:"火龙出水（明）简介" 3177:Conrad Haas 3059:Minotaur IV 2607:(1889–1969) 2601: [ 2591:(1894–1989) 2582:(1882–1945) 2573:(1857–1935) 2564:(1600–1651) 2544:Conrad Haas 2524:Huolongjing 2498:Huolongjing 2213:Ariane 5 ES 2132:Hot-staging 186:Performance 136:first stage 85:step rocket 47:Third Stage 18:Third stage 4165:Categories 4140:Saturn IVB 3840:2021-02-07 3826:"Vanguard" 3811:2021-02-07 3750:5 February 3719:5 February 3656:2013-04-18 3623:ko:주화 (무기) 3569:2011-12-08 3539:2020-05-10 3468:2023-11-22 3443:2023-11-25 3418:2023-11-27 3389:2023-11-27 3359:2023-11-25 3217:2021-05-04 3193:References 3070:Minotaur V 2965:Titan IIIC 2813:launcher. 2760:improve it 2673:complexity 2531:Juhwa (走火) 2459:passivated 2399:suborbital 2337:newspapers 2269:space tugs 2221:turbopumps 2205:hypergolic 2123:Restricted 375:propellant 159:charge or 104:propellant 4150:Transtage 4135:Saturn IV 4013:Yuanzheng 3980:CTS / SMA 3970:Castor 30 3801:Space.com 3780:8 January 3676:Wiley-VCH 3646:"주화 (走火)" 3349:1059-1028 3265:249535749 3167:Space tug 3122:NASA-ESA 2945:Delta III 2885:Zenit-3SL 2776:July 2021 2764:verifying 2540:Singijeon 2507:Liu Bowen 2294:does not 2151:N1 rocket 2097:λ 2076:∏ 2069:λ 1676:λ 1670:ϵ 1665:λ 1650:η 1572:λ 1498:ϵ 1295:η 1196:− 1166:− 1129:⁡ 1045:− 966:× 803:− 785:× 738:Δ 465:function. 322:Δ 264:⁡ 242:Δ 157:explosive 4075:Blok 2BL 3894:Archived 3862:Archived 3805:Archived 3744:Archived 3740:aidas.lt 3650:Archived 3594:July 17, 3533:Archived 3497:July 25, 3491:Archived 3483:"Fregat" 3437:Archived 3412:Archived 3383:Archived 3353:Archived 3211:Archived 3131:See also 3100:boosters 3049:Ariane 1 2990:Titan IV 2950:Delta IV 2939:Delta II 2928:Ariane 5 2907:boosters 2844:Ariane 1 2839:Ariane 2 2833:Ariane 4 2828:Vanguard 2823:Saturn V 2652:Atlas II 2577:American 2437:Falcon 9 2432:and the 2410:Saturn V 2275:Assembly 2241:Ariane 5 2178:has two 2159:Starship 2147:Proton-M 212:Saturn V 116:parallel 4100:Delta-P 4095:Delta-K 4090:Delta-D 4048:Retired 4022:Planned 3975:Centaur 3634:ko:화통도감 3270:17 June 3245:Bibcode 3157:Adapter 2933:Atlas V 2758:Please 2648:Atlas I 2636:liftoff 2568:Russian 2503:Jiao Yu 2494:Chinese 2351:scholar 2315:removed 2300:sources 2247:or the 2225:Centaur 2209:Delta-K 1945:Optimal 461:is the 342:delta-v 311:where: 165:staging 125:staging 100:engines 4085:Burner 4080:Blok D 4070:Astris 4065:Altair 3995:Fregat 3953:Active 3770:SpaceX 3682: 3525: 3347: 3263: 3087:": --> 3064:Proton 3036:": --> 2922:Angara 2890:Unha-3 2862:Proton 2595:French 2586:German 2478:debris 2470:Soviet 2434:SpaceX 2406:Apollo 2353: 2346: 2339: 2332: 2324: 2265:Fregat 2259:or to 2243:ECA's 2149:. The 1865:Where 1396:Where 1272:stage. 984: 833:Where 531: 437:engine 328: 214:rocket 169:before 112:serial 108:tandem 96:stages 93:rocket 75:rocket 38:, and 4125:KVD-1 4110:FG-02 4055:Agena 4008:Volga 3990:DM-03 3897:(PDF) 3890:(PDF) 3865:(PDF) 3858:(PDF) 3341:Wired 3261:S2CID 2980:Soyuz 2975:H-IIB 2971:H-IIA 2713:) or 2605:] 2358:JSTOR 2344:books 2249:S-IVB 2155:Titan 2143:Soyuz 483:orbit 148:solid 87:is a 4115:Ikar 4105:EPKM 4060:Able 4039:KVTK 4003:/ 48 3985:DCSS 3965:Briz 3960:AVUM 3905:2021 3873:2021 3782:2011 3752:2018 3721:2018 3680:ISBN 3596:2008 3523:ISBN 3499:2014 3345:ISSN 3272:2022 3089:edit 3076:ASLV 3054:PSLV 3038:edit 3013:The 2856:PSLV 2850:GSLV 2798:The 2711:TSTO 2669:risk 2650:and 2505:and 2474:U.S. 2472:and 2330:news 2298:any 2296:cite 2245:HM7B 2229:DCSS 2145:and 1706:The 862:and 106:. A 102:and 3253:doi 2935:551 2914:US 2762:by 2501:by 2309:by 2257:GTO 2253:J-2 2251:'s 2227:or 2211:or 1747:tot 340:is 150:or 110:or 83:or 4167:: 3892:. 3860:. 3828:. 3803:. 3799:. 3768:. 3742:. 3738:. 3703:. 3674:. 3604:^ 3557:. 3531:. 3507:^ 3489:. 3485:. 3410:. 3406:. 3381:. 3377:. 3351:. 3343:. 3339:. 3325:^ 3312:^ 3280:^ 3259:. 3251:. 3241:57 3239:. 3235:. 3209:. 3001:, 2997:, 2973:, 2924:A5 2878:, 2705:A 2603:fr 2550:, 2271:. 1765:sp 1126:ln 523:= 449:ln 261:ln 231:: 178:. 79:A 34:, 3938:e 3931:t 3924:v 3907:. 3875:. 3843:. 3814:. 3784:. 3754:. 3723:. 3688:. 3659:. 3598:. 3572:. 3542:. 3501:. 3471:. 3446:. 3421:. 3392:. 3362:. 3274:. 3255:: 3247:: 3220:. 3093:] 3042:] 2789:) 2783:( 2778:) 2774:( 2756:. 2709:( 2408:/ 2380:) 2374:( 2369:) 2365:( 2355:· 2348:· 2341:· 2334:· 2317:. 2303:. 2101:i 2091:n 2086:1 2083:= 2080:i 2072:= 2033:p 2030:s 2026:I 2014:. 2000:p 1997:s 1993:I 1970:p 1967:s 1963:I 1920:l 1917:e 1914:u 1911:f 1906:m 1882:x 1879:o 1874:m 1847:l 1844:e 1841:u 1838:f 1833:m 1828:/ 1821:x 1818:o 1813:m 1809:= 1806:F 1802:/ 1798:O 1761:I 1757:g 1753:/ 1743:I 1739:= 1734:p 1730:m 1673:+ 1662:+ 1659:1 1653:= 1617:P 1612:m 1608:+ 1602:E 1597:m 1589:L 1586:P 1581:m 1575:= 1540:P 1535:m 1531:+ 1525:E 1520:m 1512:E 1507:m 1501:= 1471:L 1468:P 1463:m 1439:p 1434:m 1410:E 1405:m 1375:L 1372:P 1367:m 1363:+ 1357:E 1352:m 1343:L 1340:P 1335:m 1331:+ 1325:p 1320:m 1316:+ 1310:E 1305:m 1298:= 1243:0 1238:v 1234:+ 1227:t 1223:d 1218:m 1214:d 1205:f 1200:m 1190:0 1185:m 1175:0 1170:g 1163:) 1155:f 1150:m 1143:0 1138:m 1132:( 1120:0 1115:g 1108:p 1105:s 1100:I 1096:= 1090:o 1087:b 1082:v 1060:) 1054:f 1049:m 1039:0 1034:m 1030:+ 1027:) 1021:0 1016:m 1011:/ 1004:f 999:m 995:( 991:n 988:l 978:f 973:m 969:( 958:e 953:m 945:0 940:g 933:p 930:s 925:I 918:= 912:o 909:b 904:h 876:f 871:m 847:0 842:m 818:) 812:f 807:m 797:0 792:m 788:( 780:T 773:0 768:g 761:p 758:s 753:I 746:= 742:t 705:0 700:g 696:m 692:T 687:= 684:R 681:W 678:T 645:t 642:d 637:m 634:d 625:0 620:g 613:p 610:s 605:I 601:= 598:T 566:0 561:g 554:t 551:d 546:m 543:d 536:T 508:p 505:s 500:I 421:e 417:v 392:f 388:m 377:; 359:0 355:m 325:v 295:) 288:f 284:m 278:0 274:m 268:( 256:e 252:v 248:= 245:v 49:. 42:. 20:)

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