Talk:Delta-v - Knowledge (XXG)

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other measurements like "pounds of thrust", or "kilonewtons". There are some articles that pretty much require an assumption that the person reading it will have a working knowledge of the subject, but I think "delta-V" is basic enough that the concept ought to be within the grasp of mere humans, if it was written right. I note above in the comments that someone once advocated re-writing the entire article basically as a series of formulas interspersed with lines of text leading from one formula to the next. While I'm sure this is ideal for people who know what they are looking at, to many people, complex formulas, with their strange symbols and terms, are about as clear as Greek, or a fraternity cipher. And it would seem unfair to write an

127: 341: 320: 236: 215: 117: 93: 351: 2184: 2147:) caused by the thruster force is just an additional acceleration to be added to the other accelerations (force per unit mass) affecting the spacecraft and the orbit can easily be propagated with a numerical algorithm including also this thruster force. But for many purposes, typically for studies or for maneuver optimization, they are approximated by impulsive maneuvers having the 246: 62: 2358:"reducing the total delta-v needed for a given spaceflight" is mission design, not propulsion system design and this has nothing to do with "modern", this has always been the target for mission design! "designing spacecraft that are capable of producing a large delta-v"? Should rather say "sufficent delta-v with a reaction control system as light as possible" 21: 429: 3448:

is no excuse for performing an unthinking reversion of all the copyedit changes I made to the lead, the most significant of which is removing the lame phrase "amount of effort". You could have very easily just changed "vector" back to "scalar" without reverting. And a scalar quantity (which never had

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I haven't been able to find a cleanup template that precisely says this, but this article suffers greatly from a lack of direction. The term "delta-v" is in fact rather generic; it is a fundamental parameter in kinematics, and means simply a change in velocity of any object or particle. It happens to

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and als not wage any "editing war". What should be said about the article as it stands in this moment has already been said! The Knowledge (XXG) system has in it advantages and its disadvantages! Some articles get good but the system does not always work! Actually, it is wonder that it works well

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in Knowledge (XXG). But this article does not (and should not) contain any discussion about the state budget of US although such a text necessarily would contain many numbers with the dimension $ ! Nor should it contain any comparison of the cost of living in different cities just because dollars,

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When rocket thrust is applied in short bursts the other sources of acceleration may be negligible, and the magnitude of the velocity change of one burst may be simply approximated by the delta-v. The total delta-v to be applied can then simply be found by addition of each of the delta-vs needed at

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Could we get like a section that contains a laymans summary for people who don't have a degree in physics or mathematics? People who don't know what the difference is between a "scalar" and a "vector" is, and don't really care, but are interested to know what "delta-v" is , and how it compares to

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Articles are supposed to cover the whole subject, but you seem to have just removed things arbitrarily, so I've reintroduced them. You should really only take things out if they are off-topic or completely not neutral to include them, but clearly delta-v budgets (for example) are notable, and on

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Text says "the figure of 30 for LEO to the sun is also too high." but the reference looks like an OR calculation and seems wrong. Perhaps that comment should go on the image talk page so it can be discussed ? (perhaps it would be better if the line went from the Sun to "earth C3=0" ?) -

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What you guys think of deleting this part of the article: "Delta-v is produced by the use of propellant by reaction engines to produce a thrust that accelerates the vehicle." It is only a orbital manouver, it can be by an explosion or something like that, not only by propellant.

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article in such a fashion that it is inaccessible to those who haven't passed the initiation and joined the club. There should be at least a nod towards those who haven't got more than a high school education, but are curious to learn what they can. Even if you find such things

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could a list of approximate Delta-v's between various locations (planetary surfaces, important planetary orbits (low orbit, rotationally synchronous orbits, etc.), Lagrange points for various planets, moons of the gas giants, etc.) be given? Or is there already one somewhere?

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For example, most spacecraft are launched in an orbit with inclination fairly near to the latitude at the launch site, to take advantage of the Earth's rotational surface speed. If it is necessary, for mission-based reasons, to put the spacecraft in an orbit of different

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Please could someone write a sentence or two explaining how delta-v is different from acceleration. "For a typical debris avoidance maneuver, the station will be subjected to delta V of between 0.5 and 1 meter per second." -- is this not an acceleration? (from

1014:"Delta-v budgets" is (in my opinion!) not very good and is anyway misplaced in this article. And the statement "Additionally raising thrust levels (when close to a gravitating body) can sometimes improve delta-v" is nonsens, the Delta-V is the same but the 3615:

A spacecraft hovering against gravity doesn't change this; as the text said, simplifying assumptions are made (no gravity). If it is hovering against gravity, then that term (negative) must be added, and the delta-v balances against gravity (for a net

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The existing definition of delta-v in the article does not ignore gravity. Your changes give the wrong answers. A rocket hovering against gravity uses enormous delta-v if maintained for any length of time, whereas what you wrote defines it as

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systems, this approximation is less accurate. But even for geostationary spacecraft using electrical propulsion for out-of-plane control with thruster burn periods extending over several hours around the nodes this approximation is fair.

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I recently heard of an audiobook reader who pronounced it "Delta-Five". I'm going to insert a comment in the leading paragraph about this. If you feel it needs to be moved, so be it; but please don't discard or delete it as being too

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Articles are not on terms, they are on topics. The topic here is the scalar delta-v that is used in rocketry. You can see from the equation it's a scalar, it's the integral of a scalar, the magnitude operator turns the vector into a

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I'm not entirely convinced you understand the topic well enough to be editing here if you don't know it's a scalar. Some of your comments above seem to be implicitly assuming it's a vector, but it makes no sense considered in that

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with the fact I thought the topic scope wasn't general enough back in December. I accept the fact that the scope of this article is limited to rocket calculations. The existence of other articles is completely irrelevant to

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There's another article on the vector quantity, and nothing links to it and that article has no references either, basically because it's unimportant. Whereas the topic this article is on, is critical to astrodynamics; high

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One should rather say what is true rather than to list all what not is true. But is there some special reason to think that the reader should belive that "conservation of energy" has anything to do with the matter?

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Ignoring your personal attack, that's not ever referred to in rocketry as delta-v, nor is the delta-v they use in rocketry the integral of the change in velocity as you wrote, nor have your changes been based on any

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Many things are roughly equivalent to delta-v, but real delta-v follows the rocket equation (tank venting forms a reaction engine, but many types of aerobraking don't follow the rocket equation and can have infinite

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know at the start. This is determined by methods outside of the scope of this article; you can't start talking about rocket calculations until you know the direction in which the rocket fires. Once you know that,

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be applied to astrodynamics of space vehicles, and the introduction rather arbitrarily usurps that single definition. You don't have to be talking about rockets or spacecraft necessarily, to use the term delta-v.

2653: 2736: 2939: 1899: 2339:, i.e., the thrust per total vehicle mass. The actual acceleration vector would be found by adding thrust per mass on to the gravity vector and the vectors representing any other forces acting on the object. 981:

Doesn't the bar notation either side of the T mean that the magnitude of the force is taken, and hence wouldn't the magnitude of the force being generated be the same in a rotating spacecraft at all times?-

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Although the page's is more detailed and makes perfect sense, There is a much simpler derivation of the rocket equation, which goes as follows. By representing the Delta-v equation as the following:

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I agree that the section does not belong in this article at all. I'll be removing the section and request temporary protection as the article is currently on the front page of the KSP subreddit.

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Absolutely twisted text! Does the author wants to say that the "impulsive manoeuvre approximation" using one impulse can cover the effect of several burns if these burns are in rapid sequence?

2379:"When designing a trajectory, delta-v budget is used as a good indicator of how much propellant will be required. Propellant usage is an exponential function of delta-v in accordance with the 3634:

Pot calling the kettle black: what I wrote is as much based on references, as what you reverted it to (which is, not at all). Where are the reliable sources which support (your?) version?

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For rockets the 'absence of external forces' usually is taken to mean the absence of atmospheric drag as well as the absence of aerostatic back pressure on the nozzle and hence the

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attempt to understand your reactions.) You have demonstrated a tendency to "shoot from the hip" and have made several incorrect assumptions about what I wrote and why I wrote it.

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systems considerable study is put into reducing the total delta-v needed for a given spaceflight, as well as designing spacecraft that are capable of producing a large delta-v.

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we nearly always only have one reference section in Knowledge (XXG)'s articles, and it goes at the end (it is possible to have more than one, but not the way you've done it).

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should be explained. Texts that for example discuss strategies to reach planets ("Porkchop plot") does not belong here although they necessarily refer to this concept

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Knowledge (XXG) articles are supposed to cover all aspects of the topic as much as possible, removing other sections like delta-v budget in particular, that's wrong.

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Your wholesale reversion, while easy, also took out other improvements I made, such as calling it the measure of "effort", and the confusing change of symbol from

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wrote "delta-v is the integral of the change in velocity"; where exactly do you see that? Do you have trouble interpreting what you read objectively? (And that is

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I now update the article! If somebody feels that the "Porkchop plot" is useful and should be a separate article, please go ahead! I personally do not think so!

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If the direction of thrust is constant this is more or less the same thing but for a rotating spacecraft operating radial thrusters in pulsed mode it is not.

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How about ""Delta-v is typically produced in spacecraft by the use of propellant in reaction engines to produce a thrust that accelerates the vehicle."? --

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Realising that Impulse over the change in mass is equivalent to Force over propellant mass flow rate (p), which is itself equivalent to exhaust velocity,

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This approximation with impulsive maneuvers is in most cases very accurate, at least when chemical propulsion is used. For low thrust systems, typically

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Delta-v doesn't always involve propellant, there is aerobreaking, tank venting, etc. I think "typically" covers the situations you are concerned with.--

1024:"Porkchop plot" could possibly be made a separate article but this has little to do with the definition of "Delta-V" and is misplaced in this article. 4423: 4413: 397: 524: 268: 4393: 3747: 3603:

it's based on the velocity change required (including direction, which is often not in the same direction as current or final velocity), which they

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Anyway, somebody interested in the topics will also read this "Discussion"! That is what I always do myself to see if an article is disputed or not!

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The article can certainly be improved greatly, please just make sure that it's unarguable that that's what you're actually doing with your edits.

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by considering only the total energy of the vehicle in the initial and final orbits since energy is carried away in the exhaust (see also below).

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Well, this topic quite literally is rocket science, so many people will find it confusing, at least initially. I'd recommend playing with

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for a while and it may start to come into focus for you. Once you understand it, feel free to make suggestions on how it may be improved.

2571: 4230: 3372: 2948:. However, this relation does not hold in the general case: If, for instance, a constant, unidirectional acceleration is reversed after 2666: 4418: 4270:

http://webarchive.loc.gov/all/20011128074814/http://science.nas.nasa.gov/services/education/spacesettlement/75summerstudy/s.s.doc.html

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it becomes a "scalar" to calculate how much fuel is required, and this is becasuse the thrust is in the same direction as the delta v.

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The rocket equation shows that the required amount of propellant dramatically increases, with increasing delta-v. Therefore in modern

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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

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Is the section "Simulation" actually needed? I feel that it's simply a plug for the game instead of giving any actual information.

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the discrete burns, even though between bursts the magnitude and direction of the velocity changes due to gravity, e.g. in an

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and realising that the Integral of a resultant force over time is Total Impulse, assuming thrust is the only force involved,

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I repeat what I said about not wanting you to navigate a spacecraft on which I would fly; you would surely get us lost.

2335:, but can be created by other reaction engines. The time-rate of change of delta-v is the magnitude of the acceleration 4197: 3524:. If a craft is traveling in one direction, and its desired velocity is at, say a 60 degree angle from this, then you 2187:

Figure 1:Approximation of a finite thrust maneuver with an impulsive change in velocity having the Delta-V given by (

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During the burn the mass of the spacecraft will decrease due to use of fuel, the time derivative of the mass being

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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the

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A screwed-up statement! Yes, the "rocket equation" links delta-v with propellant use in terms of kg propellant

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And as the article already points out delta-v is the integral of the magnitude of the acceleration over time.

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Can be the case for a "blow-down" system for which the pressure in the tank gets lower when less fuel is left

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The "Delta-V" is not really a "scalar" but rather a "vector quantity" with the dimension "velocity" defined

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In the absence of external forces, and when thrust is applied in a constant direction this simplifies to:

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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with

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http://arstechnica.com/science/2013/07/how-nasa-steers-the-international-space-station-around-space-junk

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on Knowledge (XXG). If you would like to participate, please visit the project page, where you can join

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on Knowledge (XXG). If you would like to participate, please visit the project page, where you can join

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on Knowledge (XXG). If you would like to participate, please visit the project page, where you can join

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on 17 September 2024. For the contribution history and old versions of the redirected page, please see

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That is obviously completely wrong! The delta-v is the same but its effect on the orbit is stronger!

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Additionally raising thrust levels (when close to a gravitating body) can sometimes improve delta-v.

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before doing mass systematic removals. This message is updated dynamically through the template

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I don't think that's a good idea, delta-v is something to work out how much propellant you need.

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As I already pointed out in the section above, I think the introduction should be re-written!

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Please help fix the broken anchors. You can remove this template after fixing the problems. |

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sorry I did the last edit while not logged in (the need for delta-v to change inclination).

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https://science.nas.nasa.gov/Services/Education/SpaceSettlement/75SummerStudy/s.s.doc.html

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This covers the old "Introduction" and "Producing Delta-V" leaving out the misplaced text

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to be a constant not depending on the amount of fuel left this relation is integrated to

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If you found an error with any archives or the URLs themselves, you can fix them with

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to produce a reaction force acting on the spacecraft. The size of this force will be

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It's not an acceleration. A metre per second has units of velocity not acceleration.

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Ok, I close this matter now. I am not going to continue the argumentation with Mr

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introductions in Knowledge (XXG) articles are supposed to be just a few paragraphs

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himself as it so much stresses "scalar" which seems to be his favourite thesis!

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that often considering that absolutly everybody is allowed to edit everything!

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a vector, I certainly wouldn't want you to navigate any spaceflight I made!)

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This is now clearly said in the introduction! This is now just a repetition!

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is of interest as a measure of the fuel usage only, from the rocket equation

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simply subtract the new velocity from the old one, and the rocket thrust is

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the above thread on "Scope of this article". And your objection to the word

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Also please include a formula connecting delta-v and acceleration. Thanks.

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add and subtract linearly. This doesn't do that; you can only add delta-v.

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and potential energies in the final orbit and the initial orbit are equal.

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the capacity of the reaction control system is computed by the integral (

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This article links to one or more target anchors that no longer exist.

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do the vector calculation to get the proper magnitude of the delta-v.

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And that is it! Why discuss "g-force" as a concept here? Pointless!

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because the thrust and the delta-v are both in the same direction.

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It is unclear why delta-v is used at all instead of acceleration.

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I don't think it's a good idea for the same reason I already gave.

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You are quite wrong about spacecraft delta-v not being a vector;

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Your response to my recent edit doesn't have anything to do with

2934:{\displaystyle =\int _{t_{0}}^{t_{1}}{|a|}\,dt=|{v}_{1}-{v}_{0}|} 1894:{\displaystyle \Delta {V}=V_{exh}\ \ln({\frac {m_{0}}{m_{1}}})\,} 3545:

Read what I have written; I went to great pains to explain this.

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If for example 20% of the launch mass is fuel giving a constant

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any direction asociated with it) is not really the same as the

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is used for calculating the vehicle's delta-v capacity via the

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in the banner shell. Please resolve this conflict if possible.

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This article has been given a rating which conflicts with the

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If now the direction of the force, i.e. the direction of the

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of the Delta-V is larger (in terms of energy, hello Oberth!)

1011:"Producing Delta-V" seems rather pointless (little contents) 4100:{\displaystyle {\frac {J}{\Delta m}}={\frac {F}{p}}=V_{exh}} 4186:{\displaystyle \Delta v=V_{exh}~ln({\frac {m_{0}}{m_{1}}})} 2808:

than gravity, this is the integral of the magnitude of the

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for additional information. I made the following changes:

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It is not possible to determine delta-v requirements from

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A simpler derivation of the Rocket Equation from Delta V

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is a non-constant function of the amount of fuel left

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Start-Class articles with conflicting quality ratings

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pointed in either the new nor the old direction; you

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when dealing with launches from a planetary surface.

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Superflous (and somewhat ridiculos!) discussion, skip

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is the propellant flow rate to the combustion chamber

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I would propose to reduce the "Delta-V" article to:

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LEO to Sun calculation looks like original research

4296:using the archive tool instructions below. Editors 4203:I added this to the Rocket equation page instead. 4185: 4099: 4029: 3936: 3893: 3870: 3840: 3044: 2994: 2933: 2786: 2761: 2730: 2647: 2166: 2121: 2055: 2016: 1948: 1893: 1801: 1747: 1642: 1620: 1582: 1469: 1440: 1390: 1339: 1301: 1218: 1182: 1158: 1103: 950: 927: 898: 868: 839: 805: 729: 638: 604: 3901:is the initial mass minus the final (dry) mass, 3486:Formally, this isn't a vector quantity, vectors 2405:, a substantial delta-v is required, though the 1226:of the spacecraft caused by this force will be 4399:Start-Class physics articles of Mid-importance 4282:This message was posted before February 2018. 2383:, it will also depend on the exhaust velocity" 453:] The anchor (#Powered slingshots) has been 8: 3400:Scope of this article is very poorly defined 2525:I guess this introduction was written by Mr 1606:Changing the integration variable from time 646:is the force caused by the thrust (vector) 46:; for the discussion at that location, see 4252:I have just modified one external link on 4224: 4204: 1918:which is the well known "rocket equation" 314: 209: 87: 4172: 4162: 4156: 4133: 4118: 4085: 4068: 4050: 4048: 4006: 4001: 3979: 3974: 3962: 3955: 3912: 3883: 3862: 3856: 3822: 3817: 3804: 3799: 3792: 3784: 3781: 3772: 3764: 3749: 3030: 3025: 3015: 3010: 3007: 2984: 2975: 2962: 2953: 2926: 2920: 2915: 2905: 2900: 2894: 2877: 2869: 2868: 2860: 2855: 2848: 2843: 2834: 2779: 2754: 2710: 2702: 2697: 2690: 2685: 2673: 2668: 2626: 2618: 2615: 2607: 2602: 2595: 2590: 2578: 2573: 2157: 2152: 2096: 2077: 2071: 2039: 2033: 1999: 1977: 1972: 1932: 1926: 1878: 1868: 1862: 1839: 1827: 1822: 1785: 1779: 1727: 1713: 1708: 1700: 1695: 1688: 1683: 1668: 1663: 1633: 1611: 1556: 1554: 1540: 1535: 1527: 1522: 1515: 1510: 1495: 1490: 1459: 1453: 1430: 1424: 1366: 1365: 1363: 1330: 1287: 1273: 1256: 1242: 1241: 1239: 1203: 1202: 1200: 1173: 1142: 1136: 1082: 1070: 941: 917: 911: 888: 882: 858: 852: 829: 823: 783: 779: 767: 754: 748: 708: 700: 697: 689: 684: 677: 672: 660: 623: 622: 620: 579: 577: 569: 564: 557: 552: 529: 528: 526: 3086:Strange and superflous discussion, skip 2883: 2720: 2637: 2205: 2162: 2117: 2051: 2012: 1944: 1889: 1797: 1743: 1638: 1616: 1572: 1465: 1436: 1386: 1335: 1297: 1214: 1178: 1154: 1099: 946: 923: 894: 864: 835: 795: 719: 634: 594: 316: 277:Knowledge (XXG):WikiProject Spaceflight 211: 89: 59: 3522:spacecraft do not fly in one dimension 3453:. (And if you really think delta-v is 2944:which is simply the magnitude of the 2327:Delta-v is typically provided by the 2318:Explicit reasons to delete sections: 2299:euros, pound and yens are mentioned! 1053:Orbit maneuvers are made by firing a 7: 4409:High-importance spaceflight articles 2122:{\displaystyle V_{exh}=V_{exh}(m)\,} 1814: 1655: 1482: 1355: 1231: 1062: 1030:+++++++++++++++++++++++++++++++++++ 382:Knowledge (XXG):WikiProject Rocketry 362:This article is within the scope of 257:This article is within the scope of 138:This article is within the scope of 1391:{\displaystyle {\dot {m}}=-\rho \,} 158:Knowledge (XXG):WikiProject Physics 78:It is of interest to the following 4120: 4056: 4018: 3885: 3814: 3751: 2670: 2575: 2302:That should be separate articles! 2154: 1974: 1824: 1665: 1492: 1166:is the velocity of the exhaust gas 1104:{\displaystyle f=V_{exh}\ \rho \,} 532: 180:project-independent quality rating 14: 4256:. Please take a moment to review 3514:absolutely nothing whatever to do 3045:{\displaystyle {v}_{1}-{v}_{0}=0} 2515:"if you don't know it's a scalar" 2451:delta-v is a scalar, not a vector 1956:of 2100 m/s (typical value for a 1046:in velocity"), is a term used in 500:Ah! I found a partial list under 4424:Mid-importance Rocketry articles 4414:WikiProject Spaceflight articles 4110:you can equate your integral to 3420:Is delta-v a vector or a scalar? 3002:then the velocity difference is 2460:this isn't an article about the 2294:There is for example an article 427: 349: 339: 318: 280:Template:WikiProject Spaceflight 244: 234: 213: 125: 115: 91: 60: 19: 4394:Mid-importance physics articles 2995:{\displaystyle (t_{1}-t_{0})/2} 2804:If there are no other external 2564:Critics of section "Definition" 402:This article has been rated as 297:This article has been rated as 192:This article has been rated as 4180: 4153: 4013: 3998: 3986: 3971: 3878:is the initial (wet) mass and 3793: 3785: 3540:it becomes a scalar quantity, 2981: 2955: 2927: 2895: 2878: 2870: 2819:Pointless to mention "g-force" 2627: 2619: 2114: 2108: 2009: 1996: 1960:thruster) the capacity of the 1886: 1859: 1347:is the mass of the spacecraft 709: 701: 628: 584: 539: 1: 4429:WikiProject Rocketry articles 4350:09:11, 8 September 2017 (UTC) 3947:The Integral is found to be: 3731:11:29, 6 September 2015 (UTC) 3712:00:15, 6 September 2015 (UTC) 3681:21:39, 18 February 2015 (UTC) 3644:21:10, 18 February 2015 (UTC) 3574:20:41, 18 February 2015 (UTC) 3559:20:34, 18 February 2015 (UTC) 3500:20:12, 18 February 2015 (UTC) 3482:20:05, 18 February 2015 (UTC) 3467:18:57, 18 February 2015 (UTC) 3435:16:17, 17 February 2015 (UTC) 3415:18:42, 15 December 2014 (UTC) 3394:01:22, 2 September 2014 (UTC) 3377:19:50, 1 September 2014 (UTC) 2280:is precisely the right word! 2180:) as illustrated in figure 1 385:Template:WikiProject Rocketry 376:and see a list of open tasks. 271:and see a list of open tasks. 152:and see a list of open tasks. 4404:C-Class spaceflight articles 4389:Start-Class physics articles 4239:20:21, 3 February 2016 (UTC) 4219:22:14, 3 February 2016 (UTC) 2167:{\displaystyle \Delta {V}\,} 1219:{\displaystyle {\dot {V}}\,} 639:{\displaystyle {\bar {T}}\,} 481:05:04, 23 January 2006 (UTC) 161:Template:WikiProject Physics 4198:Tsiolkovsky rocket equation 3937:{\displaystyle \int F~dt=J} 3588:a "personal attack", but a 2189: 2176: 2143: 2134: 4445: 4313:(last update: 5 June 2024) 4249:Hello fellow Wikipedians, 3260:02:46, 25 March 2013 (UTC) 3225:23:07, 24 March 2013 (UTC) 3195:18:30, 24 March 2013 (UTC) 3169:17:43, 24 March 2013 (UTC) 3155:16:01, 24 March 2013 (UTC) 3137:04:18, 24 March 2013 (UTC) 3122:03:12, 24 March 2013 (UTC) 3102:20:35, 9 August 2011 (UTC) 2556:16:44, 2 August 2011 (UTC) 2493:14:41, 2 August 2011 (UTC) 2439:09:53, 2 August 2011 (UTC) 2314:06:34, 2 August 2011 (UTC) 2271:15:53, 1 August 2011 (UTC) 2252:13:52, 1 August 2011 (UTC) 995:15:56, 1 August 2011 (UTC) 509:03:27, 19 March 2006 (UTC) 496:03:25, 19 March 2006 (UTC) 408:project's importance scale 303:project's importance scale 198:project's importance scale 4419:C-Class Rocketry articles 3697:Section for stupid people 3347:15:22, 29 July 2014 (UTC) 2490:Now with added dubiosity! 2283:Here the very concept of 2268:Now with added dubiosity! 2236:16:17, 31 July 2011 (UTC) 2056:{\displaystyle V_{exh}\,} 1949:{\displaystyle V_{exh}\,} 1802:{\displaystyle V_{exh}\,} 1159:{\displaystyle V_{exh}\,} 992:Now with added dubiosity! 976:15:53, 27 July 2011 (UTC) 401: 334: 296: 229: 191: 177: 110: 86: 4370:13:51, 29 May 2018 (UTC) 3894:{\displaystyle \Delta m} 3321:19:34, 5 July 2013 (UTC) 3301:19:06, 5 July 2013 (UTC) 3276:delta-v and acceleration 958:is the exhaust velocity 4245:External links modified 2801:+++++ stop here ++++++ 1962:reaction control system 1628:to the spacecraft mass 1470:{\displaystyle t_{1}\,} 1441:{\displaystyle t_{0}\,} 1183:{\displaystyle \rho \,} 928:{\displaystyle t_{0}\,} 899:{\displaystyle M_{0}\,} 869:{\displaystyle t_{1}\,} 840:{\displaystyle M_{1}\,} 514:Critics of introduction 260:WikiProject Spaceflight 4187: 4101: 4031: 3938: 3895: 3872: 3842: 3595:The whole reason they 3442:this particular thread 3046: 2996: 2935: 2788: 2763: 2732: 2649: 2393:conservation of energy 2194: 2168: 2123: 2057: 2018: 1950: 1895: 1803: 1749: 1644: 1622: 1584: 1471: 1442: 1392: 1341: 1303: 1220: 1184: 1160: 1105: 952: 929: 900: 870: 841: 807: 731: 640: 606: 455:deleted by other users 68:This article is rated 4188: 4102: 4032: 3939: 3896: 3873: 3871:{\displaystyle m_{0}} 3843: 3451:magnitude of a vector 3047: 2997: 2936: 2794:is the instantaneous 2789: 2769:is the instantaneous 2764: 2733: 2650: 2352:spacecraft propulsion 2337:caused by the engines 2199:electrical propulsion 2186: 2169: 2124: 2058: 2019: 1951: 1896: 1804: 1750: 1645: 1623: 1585: 1472: 1443: 1393: 1342: 1304: 1221: 1185: 1161: 1106: 953: 930: 901: 871: 842: 808: 732: 641: 607: 72:on Knowledge (XXG)'s 26:The contents of the 4294:regular verification 4117: 4047: 3954: 3911: 3882: 3855: 3748: 3719:Kerbal Space Program 3006: 2952: 2833: 2778: 2753: 2667: 2572: 2151: 2070: 2032: 1971: 1925: 1821: 1778: 1662: 1632: 1610: 1489: 1452: 1423: 1362: 1329: 1238: 1199: 1172: 1135: 1069: 940: 910: 906:is the mass at time 881: 851: 847:is the mass at time 822: 747: 659: 619: 525: 365:WikiProject Rocketry 283:spaceflight articles 4284:After February 2018 3780: 2867: 2709: 2614: 1707: 1643:{\displaystyle m\,} 1621:{\displaystyle t\,} 1534: 1340:{\displaystyle m\,} 951:{\displaystyle V\,} 696: 576: 141:WikiProject Physics 4338:InternetArchiveBot 4289:InternetArchiveBot 4183: 4097: 4027: 3934: 3891: 3868: 3838: 3760: 3042: 2992: 2946:change in velocity 2931: 2884: 2839: 2784: 2759: 2728: 2721: 2681: 2645: 2638: 2586: 2482:Sheer Incompetence 2480:Hope this helps.- 2260:Sheer Incompetence 2195: 2164: 2163: 2141:The acceleration ( 2119: 2118: 2053: 2052: 2014: 2013: 1946: 1945: 1891: 1890: 1799: 1798: 1745: 1744: 1679: 1640: 1639: 1618: 1617: 1580: 1573: 1506: 1467: 1466: 1438: 1437: 1388: 1387: 1337: 1336: 1299: 1298: 1216: 1215: 1180: 1179: 1156: 1155: 1101: 1100: 984:Sheer Incompetence 948: 947: 925: 924: 896: 895: 866: 865: 837: 836: 803: 796: 727: 720: 668: 636: 635: 602: 595: 548: 252:Spaceflight portal 74:content assessment 4314: 4241: 4229:comment added by 4221: 4209:comment added by 4178: 4146: 4076: 4063: 4025: 3961: 3921: 3831: 3828: 3618:delta-v (physics) 3380: 3363:comment added by 2787:{\displaystyle m} 2762:{\displaystyle T} 2718: 2635: 2444:OK, a few points: 2374:"Delta-v budgets" 2322:Producing Delta-v 2007: 1989: 1915: 1914: 1884: 1852: 1769: 1768: 1740: 1726: 1604: 1603: 1569: 1564: 1553: 1412: 1411: 1374: 1323: 1322: 1295: 1286: 1264: 1250: 1211: 1195:The acceleration 1125: 1124: 1095: 1001:Complete re-write 791: 774: 717: 631: 592: 587: 542: 469: 468: 444:in most browsers. 422: 421: 418: 417: 414: 413: 388:Rocketry articles 313: 312: 309: 308: 208: 207: 204: 203: 54: 53: 29:Delta-v (physics) 4436: 4348: 4339: 4312: 4311: 4290: 4192: 4190: 4189: 4184: 4179: 4177: 4176: 4167: 4166: 4157: 4145: 4144: 4143: 4106: 4104: 4103: 4098: 4096: 4095: 4077: 4069: 4064: 4062: 4051: 4036: 4034: 4033: 4028: 4026: 4024: 4016: 4012: 4011: 4010: 3985: 3984: 3983: 3963: 3960: 3943: 3941: 3940: 3935: 3920: 3900: 3898: 3897: 3892: 3877: 3875: 3874: 3869: 3867: 3866: 3847: 3845: 3844: 3839: 3830: 3829: 3827: 3826: 3821: 3810: 3809: 3808: 3797: 3796: 3788: 3782: 3779: 3771: 3599:it "delta-v" is 3379: 3357: 3051: 3049: 3048: 3043: 3035: 3034: 3029: 3020: 3019: 3014: 3001: 2999: 2998: 2993: 2988: 2980: 2979: 2967: 2966: 2940: 2938: 2937: 2932: 2930: 2925: 2924: 2919: 2910: 2909: 2904: 2898: 2882: 2881: 2873: 2866: 2865: 2864: 2854: 2853: 2852: 2793: 2791: 2790: 2785: 2768: 2766: 2765: 2760: 2737: 2735: 2734: 2729: 2719: 2711: 2708: 2707: 2706: 2696: 2695: 2694: 2677: 2654: 2652: 2651: 2646: 2636: 2631: 2630: 2622: 2616: 2613: 2612: 2611: 2601: 2600: 2599: 2582: 2407:specific kinetic 2224:Any objections? 2213: 2210: 2173: 2171: 2170: 2165: 2161: 2128: 2126: 2125: 2120: 2107: 2106: 2088: 2087: 2062: 2060: 2059: 2054: 2050: 2049: 2023: 2021: 2020: 2015: 2008: 2000: 1988: 1981: 1955: 1953: 1952: 1947: 1943: 1942: 1909: 1900: 1898: 1897: 1892: 1885: 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2686: 2665: 2664: 2617: 2603: 2591: 2570: 2569: 2566: 2462:rocket equation 2381:rocket equation 2216: 2211: 2207: 2149: 2148: 2092: 2073: 2068: 2067: 2035: 2030: 2029: 1969: 1968: 1928: 1923: 1922: 1907: 1874: 1864: 1835: 1819: 1818: 1781: 1776: 1775: 1761: 1729: 1709: 1696: 1684: 1660: 1659: 1630: 1629: 1608: 1607: 1596: 1536: 1523: 1511: 1487: 1486: 1455: 1450: 1449: 1426: 1421: 1420: 1404: 1360: 1359: 1327: 1326: 1315: 1269: 1236: 1235: 1197: 1196: 1170: 1169: 1138: 1133: 1132: 1117: 1078: 1067: 1066: 1003: 938: 937: 913: 908: 907: 884: 879: 878: 854: 849: 848: 825: 820: 819: 775: 763: 750: 745: 744: 699: 685: 673: 657: 656: 617: 616: 565: 553: 531: 523: 522: 516: 488: 474: 465: 447: 446: 445: 428: 387: 384: 381: 378: 377: 357:Rocketry portal 355: 350: 348: 328: 299:High-importance 282: 279: 276: 273: 272: 250: 245: 243: 224:High‑importance 223: 163: 160: 157: 154: 153: 131: 124: 104: 101: 69: 41: 20: 12: 11: 5: 4442: 4440: 4432: 4431: 4426: 4421: 4416: 4411: 4406: 4401: 4396: 4391: 4386: 4376: 4375: 4356: 4353: 4332: 4331: 4324: 4277: 4276: 4268:Added archive 4246: 4243: 4194: 4193: 4182: 4175: 4171: 4165: 4161: 4155: 4152: 4149: 4142: 4139: 4136: 4132: 4128: 4125: 4122: 4108: 4107: 4094: 4091: 4088: 4084: 4080: 4075: 4072: 4067: 4061: 4058: 4054: 4038: 4037: 4023: 4020: 4015: 4009: 4005: 4000: 3997: 3994: 3991: 3988: 3982: 3978: 3973: 3970: 3967: 3959: 3945: 3944: 3933: 3930: 3927: 3924: 3919: 3916: 3890: 3887: 3865: 3861: 3849: 3848: 3837: 3834: 3825: 3820: 3816: 3813: 3807: 3803: 3795: 3791: 3787: 3778: 3775: 3770: 3767: 3763: 3759: 3756: 3753: 3738: 3735: 3734: 3733: 3698: 3695: 3694: 3693: 3692: 3691: 3690: 3689: 3688: 3687: 3686: 3685: 3684: 3683: 3657: 3656: 3655: 3654: 3653: 3652: 3651: 3650: 3649: 3648: 3647: 3646: 3632: 3621: 3613: 3593: 3547: 3518: 3505: 3504: 3503: 3502: 3484: 3421: 3418: 3401: 3398: 3397: 3396: 3353: 3350: 3337: 3328: 3325: 3324: 3323: 3308: 3307: 3277: 3274: 3273: 3272: 3271: 3270: 3269: 3268: 3267: 3266: 3265: 3264: 3263: 3262: 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2397: 2396: 2385: 2384: 2372: 2367: 2366: 2361: 2356: 2355: 2346: 2341: 2340: 2274: 2273: 2218:+++++++++++++ 2215: 2214: 2204: 2160: 2156: 2130: 2129: 2116: 2113: 2110: 2105: 2102: 2099: 2095: 2091: 2086: 2083: 2080: 2076: 2048: 2045: 2042: 2038: 2026: 2025: 2024:m/s = 469 m/s. 2011: 2006: 2003: 1998: 1995: 1992: 1987: 1984: 1980: 1976: 1941: 1938: 1935: 1931: 1917: 1913: 1912: 1903: 1901: 1888: 1881: 1877: 1871: 1867: 1861: 1858: 1855: 1848: 1845: 1842: 1838: 1834: 1830: 1826: 1812: 1794: 1791: 1788: 1784: 1771: 1767: 1766: 1757: 1755: 1739: 1735: 1732: 1722: 1719: 1716: 1712: 1703: 1699: 1691: 1687: 1682: 1678: 1675: 1671: 1667: 1653: 1637: 1615: 1602: 1601: 1592: 1590: 1579: 1576: 1568: 1563: 1560: 1549: 1546: 1543: 1539: 1530: 1526: 1518: 1514: 1509: 1505: 1502: 1498: 1494: 1480: 1462: 1458: 1448:and ending at 1433: 1429: 1414: 1410: 1409: 1400: 1398: 1385: 1382: 1379: 1373: 1370: 1353: 1334: 1321: 1320: 1311: 1309: 1294: 1291: 1282: 1279: 1276: 1272: 1268: 1263: 1260: 1255: 1249: 1246: 1229: 1210: 1207: 1194: 1192: 1191: 1177: 1167: 1151: 1148: 1145: 1141: 1127: 1123: 1122: 1113: 1111: 1098: 1091: 1088: 1085: 1081: 1077: 1074: 1060: 1033: 1002: 999: 998: 997: 945: 920: 916: 891: 887: 861: 857: 832: 828: 814: 813: 802: 799: 790: 787: 782: 778: 770: 766: 762: 757: 753: 738: 737: 726: 723: 716: 711: 707: 703: 692: 688: 680: 676: 671: 667: 664: 649: 630: 627: 613: 612: 601: 598: 591: 586: 583: 572: 568: 560: 556: 551: 547: 541: 537: 534: 515: 512: 502:Delta-v budget 487: 484: 478:Carrionluggage 473: 470: 467: 466: 460: 459: 458: 442:case-sensitive 436: 435: 434: 432: 420: 419: 416: 415: 412: 411: 404:Mid-importance 400: 394: 393: 391: 374:the discussion 361: 360: 344: 332: 331: 329:Mid‑importance 323: 311: 310: 307: 306: 295: 289: 288: 286: 269:the discussion 256: 255: 239: 227: 226: 218: 206: 205: 202: 201: 194:Mid-importance 190: 184: 183: 176: 170: 169: 167: 150:the discussion 137: 136: 133:Physics portal 120: 108: 107: 105:Mid‑importance 96: 84: 83: 77: 66: 52: 51: 24: 13: 10: 9: 6: 4: 3: 2: 4441: 4430: 4427: 4425: 4422: 4420: 4417: 4415: 4412: 4410: 4407: 4405: 4402: 4400: 4397: 4395: 4392: 4390: 4387: 4385: 4382: 4381: 4379: 4372: 4371: 4367: 4363: 4354: 4352: 4351: 4346: 4341: 4340: 4329: 4325: 4322: 4318: 4317: 4316: 4309: 4303: 4299: 4295: 4291: 4285: 4280: 4275: 4271: 4267: 4266: 4265: 4263: 4259: 4255: 4250: 4244: 4242: 4240: 4236: 4232: 4231:86.140.30.245 4228: 4222: 4220: 4216: 4212: 4208: 4201: 4199: 4196:which is the 4173: 4169: 4163: 4159: 4150: 4147: 4140: 4137: 4134: 4130: 4126: 4123: 4113: 4112: 4111: 4092: 4089: 4086: 4082: 4078: 4073: 4070: 4065: 4059: 4052: 4043: 4042: 4041: 4021: 4007: 4003: 3995: 3992: 3989: 3980: 3976: 3968: 3965: 3957: 3950: 3949: 3948: 3931: 3928: 3925: 3922: 3917: 3914: 3907: 3906: 3905: 3902: 3888: 3863: 3859: 3835: 3832: 3823: 3818: 3811: 3805: 3801: 3789: 3776: 3773: 3768: 3765: 3761: 3757: 3754: 3744: 3743: 3742: 3736: 3732: 3728: 3724: 3720: 3716: 3715: 3714: 3713: 3710: 3705: 3696: 3682: 3678: 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3166: 3162: 3159:Fine for me. 3158: 3157: 3156: 3152: 3148: 3144: 3143: 3142: 3141: 3138: 3134: 3130: 3126: 3125: 3124: 3123: 3119: 3115: 3106: 3104: 3103: 3099: 3095: 3087: 3084: 3083: 3082: 3081: 3080: 3078: 3074: 3070: 3060: 3057: 3056: 3055: 3054: 3053: 3039: 3036: 3031: 3026: 3021: 3016: 3011: 2989: 2985: 2976: 2972: 2968: 2963: 2959: 2947: 2921: 2916: 2911: 2906: 2901: 2891: 2888: 2885: 2874: 2861: 2857: 2849: 2845: 2840: 2836: 2829: 2828: 2827: 2820: 2817: 2816: 2815: 2814: 2813: 2811: 2807: 2802: 2797: 2781: 2774: 2772: 2756: 2749: 2748: 2747: 2725: 2722: 2715: 2712: 2703: 2699: 2691: 2687: 2682: 2678: 2674: 2663: 2662: 2660: 2659: 2658: 2657: 2642: 2639: 2632: 2623: 2608: 2604: 2596: 2592: 2587: 2583: 2579: 2568: 2567: 2563: 2557: 2553: 2549: 2546: 2545: 2544: 2543: 2537: 2536: 2535: 2534: 2528: 2524: 2523: 2522: 2521: 2516: 2513: 2512: 2511: 2510: 2503: 2499: 2498: 2497: 2496: 2495: 2494: 2491: 2487: 2483: 2473: 2470: 2466: 2463: 2459: 2456: 2453: 2450: 2449: 2448: 2447: 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1669: 1658: 1657: 1654: 1651: 1635: 1613: 1600: 1593: 1591: 1577: 1574: 1566: 1561: 1558: 1547: 1544: 1541: 1537: 1528: 1524: 1516: 1512: 1507: 1503: 1500: 1496: 1485: 1484: 1481: 1478: 1460: 1456: 1431: 1427: 1418: 1408: 1401: 1399: 1383: 1380: 1377: 1371: 1368: 1358: 1357: 1354: 1351: 1348: 1332: 1319: 1312: 1310: 1292: 1289: 1280: 1277: 1274: 1270: 1266: 1261: 1258: 1253: 1247: 1244: 1234: 1233: 1230: 1227: 1208: 1205: 1175: 1168: 1149: 1146: 1143: 1139: 1131: 1130: 1129: 1121: 1114: 1112: 1096: 1089: 1086: 1083: 1079: 1075: 1072: 1065: 1064: 1061: 1058: 1056: 1051: 1049: 1048:astrodynamics 1045: 1041: 1037: 1031: 1028: 1025: 1022: 1019: 1017: 1012: 1009: 1006: 1000: 996: 993: 989: 985: 980: 979: 978: 977: 973: 969: 965: 962: 959: 943: 935: 918: 914: 889: 885: 876: 859: 855: 830: 826: 817: 800: 797: 788: 785: 780: 776: 768: 764: 760: 755: 751: 743: 742: 741: 724: 721: 714: 705: 690: 686: 678: 674: 669: 665: 662: 655: 654: 653: 652:The integral 650: 647: 625: 599: 596: 589: 581: 570: 566: 558: 554: 549: 545: 535: 521: 520: 519: 513: 511: 510: 507: 503: 498: 497: 494: 486:Delta V chart 485: 483: 482: 479: 471: 464: 456: 452: 451: 450: 443: 439: 433: 426: 425: 409: 405: 399: 396: 395: 392: 375: 371: 367: 366: 358: 347: 345: 342: 338: 337: 333: 327: 324: 321: 317: 304: 300: 294: 291: 290: 287: 270: 266: 262: 261: 253: 242: 240: 237: 233: 232: 228: 222: 219: 216: 212: 199: 195: 189: 186: 185: 181: 175: 172: 171: 168: 151: 147: 143: 142: 134: 128: 123: 121: 118: 114: 113: 109: 100: 97: 94: 90: 85: 81: 75: 67: 63: 58: 57: 49: 48:its talk page 44: 39: 35: 31: 30: 25: 18: 17: 4358: 4336: 4333: 4308:source check 4287: 4281: 4278: 4251: 4248: 4225:— Preceding 4223: 4211:86.171.45.62 4205:— Preceding 4202: 4195: 4109: 4039: 3946: 3903: 3850: 3740: 3703: 3700: 3636:JustinTime55 3628: 3624: 3609: 3604: 3600: 3596: 3585: 3581: 3551:JustinTime55 3544: 3541: 3537: 3533: 3529: 3525: 3521: 3513: 3487: 3459:JustinTime55 3454: 3450: 3445: 3441: 3423: 3407:JustinTime55 3403: 3359:— 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493:Linguofreak 274:Spaceflight 265:spaceflight 221:Spaceflight 102:Start‑class 43:its history 4378:Categories 4345:Report bug 3590:good-faith 3488:components 3069:vacuum Isp 2661:change to 2174:given by ( 32:page were 4328:this tool 4321:this tool 3472:priority. 2289:"Delta-V" 2285:"Delta-V" 1958:hydrazine 1774:Assuming 1650:one gets 1008:But also 4334:Cheers.— 4227:unsigned 4207:unsigned 3373:contribs 3361:unsigned 3094:Stamcose 2548:Stamcose 2431:Stamcose 2306:Stamcose 2276:I think 2258:topic.- 2244:Stamcose 2228:Stamcose 1055:thruster 968:Stamcose 472:Untitled 379:Rocketry 370:rocketry 326:Rocketry 4258:my edit 4254:Delta-v 3709:.45Colt 3707:vulgar. 3601:because 3425:scalar. 3386:Andyops 3334:obvious 3252:Teapeat 3187:Teapeat 3129:Teapeat 2810:g-force 1128:where 1040:Delta-V 457:before. 406:on the 301:on the 196:on the 155:Physics 146:Physics 99:Physics 70:C-class 38:Delta-v 3851:where 3704:entire 3620:of 0.) 3446:vector 3293:Lehasa 2806:forces 2771:thrust 2746:where 2329:thrust 1417:nozzle 1325:where 1044:change 1016:effect 816:where 615:where 76:scale. 34:merged 4362:Rod57 3671:zero. 3582:never 3526:can't 3517:this. 3339:LP-mn 3250:Isp.) 3161:Gusta 3114:Gusta 2331:of a 2296:Money 174:Start 36:into 4366:talk 4235:talk 4215:talk 3727:talk 3677:talk 3640:talk 3610:then 3605:must 3597:call 3570:talk 3555:talk 3538:Then 3534:must 3496:talk 3478:talk 3463:talk 3431:talk 3411:talk 3390:talk 3369:talk 3343:talk 3336:". 3317:talk 3297:talk 3256:talk 3221:talk 3191:talk 3165:talk 3151:talk 3133:talk 3118:talk 3098:talk 2796:mass 2552:talk 2486:talk 2468:way. 2435:talk 2310:talk 2264:talk 2248:talk 2232:talk 1986:2100 1477:as 1050:. 988:talk 972:talk 438:Tip: 293:High 4302:RfC 4272:to 3627:to 3586:not 3530:not 3455:not 3352:KSP 3285:) 3217:agr 3147:agr 2028:If 2005:0.8 1964:is 1038:or 398:Mid 188:Mid 4380:: 4368:) 4315:. 4310:}} 4306:{{ 4237:) 4217:) 4200:. 4121:Δ 4057:Δ 4019:Δ 3990:− 3915:∫ 3886:Δ 3815:Δ 3812:− 3762:∫ 3752:Δ 3729:) 3679:) 3642:) 3580:I 3572:) 3557:) 3498:) 3480:) 3465:) 3433:) 3413:) 3392:) 3375:) 3371:• 3345:) 3319:) 3299:) 3258:) 3223:) 3193:) 3167:) 3153:) 3135:) 3120:) 3100:) 3022:− 2969:− 2912:− 2841:∫ 2812:. 2683:∫ 2671:Δ 2588:∫ 2576:Δ 2554:) 2488:) 2437:) 2312:) 2266:) 2250:) 2234:) 2193:) 2155:Δ 2138:) 1994:⁡ 1991:ln 1975:Δ 1857:⁡ 1854:ln 1825:Δ 1681:∫ 1677:− 1666:Δ 1562:˙ 1508:∫ 1504:− 1493:Δ 1384:ρ 1381:− 1372:˙ 1290:ρ 1248:˙ 1209:˙ 1176:ρ 1097:ρ 990:) 974:) 781:− 670:∫ 629:¯ 585:¯ 550:∫ 540:¯ 533:Δ 4364:( 4347:) 4343:( 4330:. 4323:. 4233:( 4213:( 4181:) 4174:1 4170:m 4164:0 4160:m 4154:( 4151:n 4148:l 4141:h 4138:x 4135:e 4131:V 4127:= 4124:v 4093:h 4090:x 4087:e 4083:V 4079:= 4074:p 4071:F 4066:= 4060:m 4053:J 4022:m 4014:) 4008:1 4004:m 3999:( 3996:n 3993:L 3987:) 3981:0 3977:m 3972:( 3969:n 3966:L 3958:J 3932:J 3929:= 3926:t 3923:d 3918:F 3889:m 3864:0 3860:m 3836:t 3833:d 3824:t 3819:m 3806:0 3802:m 3794:| 3790:T 3786:| 3777:1 3774:t 3769:0 3766:t 3758:= 3755:v 3725:( 3675:( 3638:( 3629:f 3625:T 3568:( 3553:( 3494:( 3476:( 3461:( 3429:( 3409:( 3388:( 3367:( 3341:( 3332:" 3315:( 3295:( 3254:( 3219:( 3189:( 3163:( 3149:( 3131:( 3116:( 3096:( 3040:0 3037:= 3032:0 3027:v 3017:1 3012:v 2990:2 2986:/ 2982:) 2977:0 2973:t 2964:1 2960:t 2956:( 2928:| 2922:0 2917:v 2907:1 2902:v 2896:| 2892:= 2889:t 2886:d 2879:| 2875:a 2871:| 2862:1 2858:t 2850:0 2846:t 2837:= 2782:m 2757:T 2726:t 2723:d 2716:m 2713:T 2704:1 2700:t 2692:0 2688:t 2679:= 2675:v 2643:t 2640:d 2633:m 2628:| 2624:T 2620:| 2609:1 2605:t 2597:0 2593:t 2584:= 2580:v 2550:( 2484:( 2433:( 2423:. 2308:( 2262:( 2246:( 2230:( 2190:4 2177:4 2159:V 2144:2 2135:5 2115:) 2112:m 2109:( 2104:h 2101:x 2098:e 2094:V 2090:= 2085:h 2082:x 2079:e 2075:V 2047:h 2044:x 2041:e 2037:V 2010:) 2002:1 1997:( 1983:= 1979:V 1940:h 1937:x 1934:e 1930:V 1910:) 1908:6 1906:( 1887:) 1880:1 1876:m 1870:0 1866:m 1860:( 1847:h 1844:x 1841:e 1837:V 1833:= 1829:V 1793:h 1790:x 1787:e 1783:V 1764:) 1762:5 1760:( 1738:m 1734:m 1731:d 1721:h 1718:x 1715:e 1711:V 1702:1 1698:m 1690:0 1686:m 1674:= 1670:V 1636:m 1614:t 1599:) 1597:4 1595:( 1578:t 1575:d 1567:m 1559:m 1548:h 1545:x 1542:e 1538:V 1529:1 1525:t 1517:0 1513:t 1501:= 1497:V 1461:1 1457:t 1432:0 1428:t 1407:) 1405:3 1403:( 1378:= 1369:m 1333:m 1318:) 1316:2 1314:( 1293:m 1281:h 1278:x 1275:e 1271:V 1267:= 1262:m 1259:f 1254:= 1245:V 1206:V 1150:h 1147:x 1144:e 1140:V 1120:) 1118:1 1116:( 1090:h 1087:x 1084:e 1080:V 1076:= 1073:f 1036:V 1034:Δ 986:( 970:( 944:V 919:0 915:t 890:0 886:M 860:1 856:t 831:1 827:M 801:t 798:d 789:V 786:A 777:e 769:0 765:M 761:= 756:1 752:M 725:t 722:d 715:m 710:| 706:T 702:| 691:1 687:t 679:0 675:t 666:= 663:A 626:T 600:t 597:d 590:m 582:T 571:1 567:t 559:0 555:t 546:= 536:v 410:. 305:. 200:. 82:: 50:.

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