At 04:29 pm 18/05/2005 -0400, Stephen wrote:
>Grimer wrote: > >>There seems to be a strangely prevalent idea >>that one cannot get continuous work out of a >>gravitational field because the field is >>"conservative" - "whatever that might mean" - >> >> >Sounds like a question. Rhetorical! 8-). It's not the definition of conservative that I am arguing with but its application. > In a nutshell, a "conservative" field is one which can be expressed as > the gradient of a potential. The necessary and sufficient condition for > that is that the field be curl-free. The work you obtain from the field > by traversing a closed path is equal to the integral of the curl over > the enclosed surface, so if the curl is zero, so's the work obtained as > you travel in a loop. Yep. > Less confusingly, the kinetic energy gained by an object in a > conservative field must always be equal to the difference in its > potential energy at the end point and starting point of its travel. If > it returns to its starting point, its potential energy returns to its > original value, and it must have gained no kinetic energy as a result. > >> This can easily be shown to be a wildly inaccurate belief. >> > I'm not so sure of that. > >> If we fire a space ship out >> into space and we wish to change its direction >> then we have to fire a rocket at right angles >> to the direction of travel. In an increment of >> time this will accelerate our rocket in a >> direction perpendicular to the direction of >> travel. Now if a sideways gravitational wind >> is blowing then we will be able to save energy >> and wont need to fire our rocket. The wind >> will provide the sideways force. >> > Please note that a force applied perpendicular to the line of motion of > the ship does no work on it. Work is done at a rate equal to <V,F> = > power = the dot product of the velocity and the force, and if the force > and velocity are perpendicular then no work is done. > > In other words, the kinetic energy of the spaceship isn't increased as a > result of a force applied perpendicular to its motion. > > Of course the kinetic energy as well as the amount of work done are both > dependent on the frame of reference in which they're evaluated. Quite so. Like many things in life, it all depends on your point of view. For, example, some people think that materials are held together by internal tensions. I am trying to get them to see (amongst other things) that in reality they are held together by external compressions of a real substance. ;-) >> This is the >> principle of slingshot that space vehicle use >> >> > The "slingshot" principle, at least as I've heard the term used, is > actually a little different from what you've described. > > "Slingshotting" a space ship is a way of getting a "free lunch" from a > massive body, such as Jupiter. There are actually two forms, and both > of them are pretty amusing, IMHO. > > First form: You find a planet going in the same direction as you want > your spaceship to go. Have your ship approach the planet from the > "front" (in other words, get going the wrong way to start with). Whip > around the planet in a close, hyperbolic or parabolic orbit, with the > ship coming away from the planet going in the "right direction". From > your point of view (sitting on Earth, or hovering in space watching the > wheels go around) you will find that the ship is now going _faster_ than > it was when it approached the planet. You've gained speed, and energy, > for "free" -- no fuel was needed. This technique was used in getting > our deep space probes into the outer solar system. > > The secret is that the planet slowed down, just a little. You stole > energy from the planet. This becomes apparent when you consider > conservation of momentum: The spaceship's momentum vector is now > pointing in the opposite direction, so the planet must have picked up > the difference. > Second (more amusing) form: Find any old planet, going in any old > direction. Send your spacecraft into a hyperbolic orbit around the > planet, approaching it as closely as possible. At the moment of closest > approach, fire the engines! Accelerate! Lo and behold, when the ship > comes up out of the gravity well of the planet, it will be going > _FASTER_ than it would have gone had you just fired the engines in empty > space. The effect of the engines was "amplified" by using them deep in > the planet's gravity well. The somewhat confusing explanation is that, > once again, power = <V,F> = dot product of velocity with force. The > force of the engine is the same deep in the planet's gravity well, but > the velocity of the craft is much higher. Hence, the spacecraft gains > much more energy for the same expenditure of fuel. This technique has > also been used by Nasa in some number of cases. > > I believe this second trick also works by stealing momentum -- and > energy -- from the planet which is being flown by but I've never worked > out exactly how that happens. You would agree then that one can get energy from a gravitational field. OK. The remote source is the KE of the planet but if we start along that line we will finish up with God [or even G-d ;-) ] >>to alter direction by entering and exiting a >>planet's gravitational field. If you think >>about it, if it wasn't for this gravitational >>energy being continuously supplied to us by >>the vertical gravitational wind, we would all >>fly-off at a Wellsian tangent 8-). >> >>It seems to me that the SMOT is effectively >>deflecting this wind in an analogous way that >>the sails of a windmill deflect the Alpha- >>atmosphere wind or the vanes in a Harrier jet >>engine deflects the flow of the gas jet coming >>from the engine in order to achieve lift. Why, >>the path of the SMOT ball even traces the >>outline of a series of turbine fan blades. >> >>Cheers >> >>Frank
