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Emphasis mine: Even our own solar system is, in the long haul, a chaotic system. Mercury might well collide with Venus in the far future, for example. You are essentially asking for a predictable outcome for what is inherently a chaotic system. Such a beast does not exist.

Ahh. Misuse of terminology. You mean bounded, not closed. A closed orbit is one that (eventually) repeats state. A bounded orbit is one that (somehow or another) stays within some finite bounds. In other words, no escape. There is no true way to know whether an orbit is bounded in a multi-body gravity field. Escape velocity definitely doesn't cut it. A couple of good boundaries are Hill's sphere and Lagrange's gravitational sphere of influence: [math] \aligned r_{\text{Hill}} \approx a\left(\frac m{3M}\right)^{1/3} &&&\text{Hill's sphere} \\ r_{\text{SOI}} \approx a\left(\frac m{2M}\right)^{2/5} &&&\text{Sphere of influence} \endaligned [/math] Here r is the radius of the orbit of some very small object (e.g. a captured asteroid) about an object of mass m (e.g., a planet), which is in turn is in orbit of radius a about an object of mass M (e.g., the Sun).

Nothing truly follows an elliptical path. The planets perturb one another's orbits. Further afield, the nearby stars perturb the planets' orbits slightly. Even further afield, the Sun is orbiting the galaxy. There is a gravity gradient (very slight, but there) that keeps the planets' orbits from being true ellipses. Then there is the slight issue that Newtonian gravity is but an approximation of reality.

Logistics pipelines cannot be reestablished. That cow got out of the barn long ago. Restarting it would require that new contracts be let and that the designs and processes be re-certified per flight critical hardware evaluation rules. The cost would differ little from the cost of building and designing a new vehicle. Even worse, how the heck are you going to rehire the critically skilled or find their equivalents? Those people are *gone*. Some were laid off, some retired, others went on to other jobs, other employers. Why would they go back to a job that is going to go away again in a few years? Several have already gone through a six month or longer unemployment; moving back would require them to go through the same thing again. Regarding replacing them -- why would a new hire take a job that will end with a layoff in just a few years (and good luck finding those new hires in the first place; young Americans are not pursuing aerospace engineering). Even worse, the Shuttle had a lot of silly requirements levied on it during its initial design. For example, the Shuttle has to be able to launch from Vandenberg, snatch a Russian satellite, and return to Vandenberg -- and do all of that in 90 minutes (one orbit). In that 90 minute interval, Vandenberg has rotated a 1200 miles eastward. This makes landing a bit of a problem. The Shuttle has a 1000 mile+ cross-range capability, never used, to support this requirement. This cross-range capability was a *big* design driver; it will not be a requirement on a new sensibly-designed commercial launch vehicle. The Shuttle launches with a non-reusable external tank. The external tank contract has been canceled. The number of tanks left on hand dictates the number of flights that can be made. Period. Wishing it were otherwise, or saying "make it so", won't make it so. NASA is getting a budget increase, and a good sized one. http://www.nasa.gov/news/budget/index.html Start with the overview. I favor human space flight. Then again, that is why I switched from working on unmanned vehicles to manned vehicles 24 years ago. That's a different topic, however.

That was a decision made quite a few years ago as a result of the Columbia disaster and to make room for the (now to be canceled) Constellation project. Before NASA went too far down the road, it checked with the President and Congress multiple times, essentially telling them that "At some point soon the decision to cancel the Shuttle will be irrevocable. Are you sure you want us to proceed?" Logistics pipelines were shut down, contracts were canceled, and people with critical skills retired or moved elsewhere. By the time Obama became President there essentially was no going back. Reversing that decision would have required a *huge* increase in NASA's budget. NASA's Earth science is increasing by a total of $1.8 billion for the next four years compared to the plans in the FY2010 budget. Not all of that is for studying global warming, and that 1.8 billion is a smallish part of NASA's total budget for those four years. Most of the money will go to NASA's exploration budget -- human spaceflight and robotic precursors. Another big chunk ($6.1 billion over five years) will go to supporting private development. You are talking about the $50 million in Space Act agreements granted immediately upon the announcement of the FY2011 budget. That is but a small part of this change in direction. The budget for FY2011-15 includes $6.1 billion for Commercial Crew & Cargo development. That is far from a token amount of money. NASA is not abandoning human spaceflight, much to the chagrin of those (mostly silly scientists) who wish it would do so.

Moontanman, you are not helping here. In the second quoted post you are clearly talking about the planets moving. There is *no* centrifugal force from the perspective of an inertial reference frame. The gravitational force is not cancelled. Think of it this way. If the force truly was cancelled, the net force on a planet would be zero. Think of what Newton's first law has to say about that situation. A planet follows a curved path. From the perspective of Newtonian mechanics, a force is need to make this happen. This force is gravity, of course, not the goofy "griff energy".

This is the problem of induction as illustrated by Hempel's raven paradox. The problem is not one of opposites. Seeing a green apple or a purple cow does paradoxically (paradox: A seemingly contradictory statement that may nonetheless be true) lend credence to the statement "all crows are black" because that statement is logically equivalent to "all non-black objects are not ravens". Green apples and purple cows are not black and are not ravens. The extent to which the observation of a green apple or purple cow does lend credence to the thesis "all ravens are black" is very, very small, however.

Do you? In some cases it is just a matter of semantics. For example, Newton's law of gravity versus Einstein's theory of general relativity. Scientific laws are specific and simple. Theories are broader and more complex. For example, Newton's Principia represents a scientific theory that embodies several laws. Scientific laws can be, and often are, purely empirical explanations of a specific phenomenon. A good example is Planck's law, the development of which preceded quantum mechanics and statistical physics. (In fact, Planck's law is often seen as the start of quantum mechanics and statistical physics.) After the fact, Planck's law can be derived from the deeper knowledge embodied by quantum mechanics and statistical physics. Scientific laws are simple and are embodied in a small number (preferrably one) equation. Scientific theories typically represent larger bodies of knowledge and typically cannot be written in the form of a single equation. Scientific theories explains scientific laws. The theory of evolution encompasses multiple concepts. So do quantum mechanics and statistical physics. The difference between scientific law and theory remains to some extent a matter of semantics. For example, general relativity is described by Einstein's field equations, which can be written in a single line. The reason general relativity is called a theory rather than a law is that Einstein derived his field equations. The field equations followed the development of general relativity rather than preceded it.

Sign error. The above should be [math]f(x) = e - \frac{e}{2}x + \cdots[/math] which is consistent with [math]\lim_{x\to 0}\frac d{dx}\frac{\ln(1+x)}x = -\,\frac 1 2[/math]

Whoa! certainly you mean [math] f(x) =\Biggl{\lbrace}\aligned &(1+x)^{1/x} && x\ne 0 \\ &e && x=0 \endaligned [/math] Sure they are. Use L'Hopital's rule. The problematic term is [math] \left.\frac d {dx} \frac{\ln(1+x)}x\right|_{x=0} [/math] This derivative is defined for all real [math]x>-1[/math] except for [math]x=0[/math]: [math] \frac d {dx} \frac{\ln(1+x)}x = \frac{x-(1+x)\ln(1+x)}{x^2(1+x)} [/math] The numerator and denominator are both zero at x=0. You will need to apply L'Hopital's rule twice. The oscillation is merely a computational effect. It isn't real.

Emphasis mine: That will is the key. Huge chunks of scramjet technology are at TRL (technology readiness level) 3-4. TRL 6 (working prototype in a relevant environment) is deemed the starting point for what might be real as opposed to just another pipe dream technology. Scramjets are still at the just beyond pipe dream level -- and that is using scramjets for missile delivery. Using the technology for human flight represents another huge leap. This is a case of a technology that cannot even start working without the first stage vehicle. KISS. Think like an engineer.

What about them? The Falcon project was cancelled, and the X-51 has yet to fly (first flight later this month). Moreover, the X-51 will be dropped from an airplane. It is not the technology needed for a first stage. It might be able to get up to Mach 20. It will not attain orbital altitude or orbital speed. Finally, don't forget that X designation. The "X" in X-51 means "experimental." That is exactly what I meant when I said that "Scram jets are still in the experimental stage and are nowhere near being reliable and controllable (yet)." Sometimes the X magic works, sometimes it doesn't.

SS2 will be a suborbital vehicle and will require a bizarre-looking aircraft as a first stage. Apparently, Virgin Galactic and Scaled Composites have scaled back their concepts for SS3. It will still be a suborbital vehicle. Expanding the aircraft as a first stage concept to orbital vehicles would require significant advances in aviation technology and would require a severe violation of the KISS (keep it simple, stupid!) rule. The aircraft first stage would need to get to a significant fraction of orbital speed to make this approach feasible, and that in turn would require reliable scram jet technology. Scram jets are still in the experimental stage and are nowhere near being reliable and controllable (yet). India has plans for a single stage to orbit vehicle that will switch from turbo jets to ram jets to scram jets to rockets. While in the scram jet mode it will collect oxygen from the atmosphere for subsequent use by the rocket. This is all in the drawing board stage for now. All this to avoid having a first stage!

Not at all. First off, most of the velocity increase occurs while the vehicle is still in the atmosphere. Second, the problem of slowing down (safely) is in a very real sense much more difficult than is the initial problem of getting up to orbital speed. SpaceShipOne didn't really address either problem. The ideal rocket equation is a starting point for describing how to achieving some desired change in velocity. A puny little engine is all that is needed to get to Mach 3. A much larger vehicle with larger engines and a lot more fuel is needed to get to Mach 25. A simple way to look at the problem is that a vehicle going Mach 25 has 70 times as much kinetic energy as a vehicle going Mach 3. However, the launch problem is much harder than that. That larger vehicle needs to get itself and all that extra fuel up to speed as well. Launching a vehicle into orbit is more than a couple orders of magnitude harder than the leisurely Mach 3 flights taken by SpaceShipOne. Now comes the even harder part: Getting back down to ground (safely). The atmospheric heating that occurs during launch is much smaller than occurs during entry. SpaceShipOne did not even begin to address the re-entry problem. SpaceX and the to-be-cancelled Orion vehicle use non-lifting bodies to address the problem. SpaceShipThree and SpaceDev's Dream Chaser are lifting bodies. Lifting bodies that go from Mach 25 to subsonic before stalling are a tough problem. That is a *huge* dynamic range.

SpaceShipOne was a suborbital vehicle. It could not orbit, period. It spent a few minutes "in space" (above 100 km altitude). SpaceShipTwo will similarly be a sub-orbital vehicle. It will take very brief ventures into space. If it succeeds, Virgin Galactic and Scaled Composites plan to build SpaceShipThree, which will be an orbital vehicle -- and it will go at Mach 25. If you want to enter LEO you need to be going Mach 25, period. That is orbital speed.

That is Teresa Ghilarducci you are talking about, not the Obama administration. While she did testify in front of Congress at the invite of some dumber-than-cows democratic congresscritters, her ultra-radical ideas are going nowhere (yet). While congresscritters of all ilk are in general dumber than cows, the Obama administration is not that dumb (yet). THe DJIA recently fell to under 10,000 in part due to worries about the collapse of the Euro. At the moment of my writing this post, the DJIA has once again risen above 10,000, partly due to reassurances from the European Union that they will not let Greece, Spain, Italy, and Ireland go bankrupt. Look at it this way: Even though the funk-o-nomics that precipitated the 2008 economic collapse were largely a US phenomenon, the collapse spread world-wide. What happened in the US in 2008 was not restricted to the US. Similarly, if the European Union collapses, the ramifications will be world-wide.

My nominal retirement date is less than a decade away. My real retirement date, thanks to my 401k 301k plan is a lot further off. This is helping turn my 301k turn back into the 201k plan that I had a year ago: ================================================================== Back to the original topic: Social Security has been a fraud from day one. When it was originally proposed, most people died by age 65. There was no lockbox then, and there is no lockbox now. If there were, what would it mean? In the long run, 401k plans and their kin have helped people retire because the stock market has done amazingly well. That option is not available to Social Security. Putting the money in a lockbox at zero percent interest would be incredibly stupid. The only option available to the government is to loan the money to the government itself -- and that is essentially what has been done. The problem is not that a lockbox doesn't exist. The problem is lack of proper accounting. Social Security has been collecting more than it pays out, and this surplus artificially makes the national debt appear smaller than it is.

With regard to the above, and with regard to one of my predictions for the NASA budget, kFPNcWN7QnM

The numbers came out. See http://www.nasa.gov/pdf/420990main_FY_201_%20Budget_Overview_1_Feb_2010.pdf (pdf). So how did I do? That was a no-brainer. What did surprise me a bit is that the proposed budget also eliminates Orion and Altair. Another no-brainer. This budget represents a *huge* move toward commercialization, starting with spending $50 million today. A sizable increase in the Earth science budget, 26.8% ($380 million) 11% increase in the planetary budget, 2.5% decrease in astrophysics (although it rebounds in out-years). Most of the increase in the planetary budget will go toward cost overruns in the Mars Science Lab and to restart the DOE plutonium program. (Without plutonium there are no missions to the outer planets.) Not enough detail yet to say whether this item becomes real. (Google "Project M" for more on this project.)

Agreed, particularly with respect to FY 2009. Bush gave NASA an underfunded mandate. NASA did what they could to follow the mandate, and that included cutting the planetary budget for FY 2009. The FY 2010 planetary budget was restored to its prior level, plus some. That is naive. A change in that policy frees up monies for general use. It might stay within NASA, it might not. It might not even stay within budget function 250 (science and technology). Wrong, particularly NSF. NASA and NSF are the purview of the same committees in both branches of Congress and both fall within the same budget function. The budgeting process nominally starts with giving various government agencies the same budget they had the previous fiscal year, plus inflation. Major changes in the policy throw those nominal starting points for a loop. The monies might stay within the same budget function for smallish changes (small in terms of the overall federal budget). Big enough changes entails modifications to the entire federal budget. Suppose for the sake of argument that the President and Congress decided to cancel human space flight altogether. There is no guarantee that those funds would transfer from NASA's human space flight program to its other budgets. I would argue that the opposite would occur: NASA's planetary budget in particular would shrink rather than expand. I disagree that that is the relevant paradigm. I switched my career from working on unmanned space flight to human space flight precisely because I saw more value in our human space flight endeavors. I have given multiple examples of indicating that politicians do not follow your paradigm. You have yet to discuss those.

It is not "as simple as that." The scientists assumption is that if funding were cut from human space flight (not manned flight, BTW; stop being sexist ), those funds would transfer to NASA's science budget. That assumption does not follow. Politicians in particular think otherwise. Some examples: When the US ended the Apollo program, the monies spent on sending men to the Moon were not transferred to NASA's science budget. NASA's budget just shrank all around, including its science budget. When Great Britain banned government funding of human space flight activities, the monies spent on those efforts were not transferred to the BNSC's science budget. Those monies were used on other non-related efforts. The BNSC's science budget shrank. When the US cancelled the Superconducting Super Collider project, the monies allocated to that project were not transferred to collider projects. Politics ain't rocket science. Politics isn't science, period. That's why scientists make lousy politicians. Politicians think differently. In a politician's eye, the cancellation of a big project means more money becomes available for their pet projects, even if their pet project has nothing to do with the cancelled project. That is assuming NASA is judged on its scientific output. If that were truly the case, NASA would be a tiny little program that occasionally launches Earth observing satellites (only). Those robotic interplanetary missions are cheap only in comparison to human missions. They are ridiculously expensive when compared to other science programs. How much research could the NIH or NSF do with $400 million (the cost of delaying the launch of the Mars Science Laboratory by two years)? With $2.3 billion (the total cost of the Mars Science Laboratory)? Besides, this is a bit moot. Obama will not cancel NASA's human space flight program. My predictions for the proposed FY2011 NASA budget: A proposed cancellation of Ares I and Ares V. This project is floundering from lack of funding (it was never adequately funded by the Bush administration) and from internal turmoil (too many rocket scientists do not know how to think like a politician). Congress critters will fight the above. Increased spending for the Commercial Crew Development project. Whether this gambit will work is a big question. If it does work, it will mean cheaper access to space. Failure means anything from a huge waste of money to lost lives. A slight increase in NASA's Earth observation budget. Not much of a change in NASA's planetary science budget. JPL is rather poor at managing money. MSL is grotesquely over-budget, for example, and that supposed 90-day rover mission has made it rather clear how JPL operates (i.e., intentionally underestimate mission duration to make it appear cheaper). Infighting between JPL, Goddard, and Ames does not help. Possibly, a humaniform robot on the Moon in 1000 days.

Yep. I suspect that JSC's CCDEV project, Commercial Crew Development, is going to see a lot more development in the future. http://procurement.jsc.nasa.gov/ccdev/

Those two sentences are contradictory. Without CO2 there would be no plants, and without plants there would be no animals (including us).

What blueprints? Those plans don't exist, at least not in enough detail to replicate them. A lot of the studies don't exist. NASA was under the gun to get a *huge* job done in less than a decade. Do a rush job on anything and something will suffer. In the case of Apollo, what suffered was adequate documentation to replicate what they did. A lot of what they did was very empirical. For example, the pogo problem (see http://en.wikipedia.org/wiki/Pogo_oscillation and http://yarchive.net/space/rocket/pogo.html) was solved by trial-and-error. The rocket scientists of the 1960s did not have computational fluid dynamics techniques to analytically determine how their propulsion systems worked. They "solved" the pogo problem by experimentally adding baffles, dampers, etc. to change the characteristic frequency. They never really did solve the problem; they just mitigated it. Pogo remained a problem on all Apollo launches. Apollo 13 in particular was very lucky: Had the second stage not cut off early, the pogo oscillations they were experiencing would have torn the vehicle apart. Apollo 13 was seconds away from blowing up before it even got on-orbit.