# planning for the past

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#### spacester

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"Escape Velocity" is the most misused term in space science IME<br /><br />It's the initial velocity a thing needs to leave a planet's gravitational field - from wherever it happens to be in that field - starting from rest, ignoring all other gravitational influences, such that it ends up at zero velocity at an infinite distance.<br /><br />It ignores the atmosphere and the Sun and describes a ridiculous mission, among other practical absurdities. It just has nothing to do with real-world space flight except as a theoretical value used for comparison purposes. <br /><br />There is no term I'm aware of for the velocity needed to achieve orbit other than 'Orbital Velocity', which of course varies with the orbit's geometry. <br /><br />One can say that a satellite is "gravitionally bound" to a massive body. This refers to the mathematical concept of 'bound energy' which is the same thing as 'orbital energy'.<br /><br />If you put enough kinetic energy, in the right direction, into a satellite, you 'bind' that energy to the gravitational field of the massive body. The resulting orbit is always an ellipse.<br /><br />If you put enough additional kinetic energy into the satellite, it will break the 'binding' and leave the planet's gravitational field. This is no longer an elliptical orbit. While it's still in the planet's gravitational sphere of influence, its path is that of a hyperbola, not an ellipse.<br /><br />When people refer to 'escape velocity' in terms of leaving Earth, often what they're actually talking about is 'excess hyperbolic velocity'. This is a function of the energy in excess of the energy corresponding to 'escape velocity'.<br /><br />To do the actual math, you need to use the term 'C3'. When you see a paper proposing an interplanetary probe, they will specify the C3 parameter so folks know how much energy the upper stage needs to impart to the probe.<br /> <div class="Discussion_UserSignature"> </div>

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#### teije

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As good a moment to ask a question as any.<br />Spacester: I've seen this 'C3' term a few times in charts and tables usually with a 'payload mass to C3' term or something like that to go with it. Usually refering to a launch vehicle. I've never known what it was until now. All I knew was that it was always a lower figure then 'payload to leo' or 'payload to geo' <img src="/images/icons/smile.gif" /><br /><br />Can you elaborate a bit more on this? <br />Thanks in advance!<br />Teije

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#### spacester

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C3 was quite a mystery for me for a while. Please understand that I am not an actual expert, I just play one on the internet. This whole spacester gig has been an exercise in seeing how much I can learn and do about space using only the internet.<br /><br />When you talk about orbits, you need to be careful whether you use 'energy' or 'velocity'. Fortunately, the relationship is simple: it's the definition of Kinetic Energy.<br /><br />KE = 1/2 m * v^2<br /><br />from which you can see that<br /><br />v = sqrt (2*KE / m)<br /><br />Applied to orbital energy, the total bound energy which is the potential energy plus the KE, this equation becomes<br /><br />v = sqrt (2*E / m)<br /><br />This shows why you talk about 'energy' in terms of 'velocity': Velocity is independent of mass. <br /><br />If you want to talk about 'energy', you have to account for the mass, so if you define<br /><br />specific energy = E / m<br /><br />You can now talk about velocity being a simple function of specific energy and it's easier to put sentences together (as long as the audience understands what specific energy is).<br /><br />In particular you can say that<br />v^2 = 2 * specific energy<br /><br />Anyhoo, that had something to do with C3. Oh yeah, orbital energy.<br /><br />Accounting for potential energy as well as kinetic energy is done with the vis-viva equation, which can be combined with the formula for escape velocity to get a simple, understandable formula for C3:<br /><br />C3 = v^2 - Vesc^2<br /><br />which says<br /><br />"The specific energy to be added by the upper stage is 1/2 of the difference between the squares of the excess hyperbolic velocity and the escape velocity"<br /><br />What you prolly saw was a spec for "payload mass to C3=0", which is saying "We can get this much payload to a velocity equivalent to escape velocity for the distance from Earth where we rele <div class="Discussion_UserSignature"> </div>

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#### teije

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Wow, thanks.<br />My (admittedly limited) math skills tell me I understand this. Getting the complete picture and actually seeing what it implies is something else of course. <img src="/images/icons/smile.gif" /><br />But your last sentence helps a lot there thankfully. <br /><br />Learned something today. <br />Thanks again!<br />Teije

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#### spacefire

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<font color="yellow">You didnt answer any relevant part of the question How excatly, with what revenue stream are you going to pay back the investment ? </font><br />why, that's obvious: we have a reusable spaceship that can take people and/or payload to Mars, maybe it will even be the only one, in any case, it will only cost 1 billion to build.<br />With around 1.2 billion price tag(to make some profit)-including launches and delivery of people and payload to LEO, a lot of agencies(companies too) are gonna be able to afford to buy one. We'll sell the &%\$#@!ers like beads and plastic boobs at Mardi Gras.<br />Think Virgin/Scaled but for the big boys. <div class="Discussion_UserSignature"> <p>http://asteroid-invasion.blogspot.com</p><p>http://www.solvengineer.com/asteroid-invasion.html </p><p> </p> </div>

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#### no_way

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<blockquote><font class="small">In reply to:</font><hr /><p> a lot of agencies(companies too) are gonna be able to afford to buy one<p><hr /></p></p></blockquote><br />Huh, igonring your optimism for final price tag of such a system, why would a lot of agencies and companies, heck, even one, want to pay a billion dollars for a craft that can take people to mars and back ?<br />Where is the payback for them ?<br />

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#### jtkirk1701

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i believe the ship for the most part must be payed for by the government. companies would pay for the transporation. It will be for science and exploration, but its main roll could almost be like that of the coast gaurd. in the begainning it will do everything but as private industry from all around the world move into space. the mission will change.

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#### craig42

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Dr Wayne<br /><br /><blockquote><font class="small">In reply to:</font><hr /><p>The amounts of hydrogen and oxygen in space are negligible. <p><hr /></p></p></blockquote><br /><br />I meant NEO and/or Lunar derrived Hydrogen and Oxygen.

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