It doesn't, of course. I don't think anyone said it did? Then we're done. [post=1006349]Like I said early in the thread[/post], Billy's original post assumes that all fuel expended from the launching rocket returns to Earth.
Yes I did. Thank you CANGAS. Are you upset you were wrong about Newton? I was just joking...when I said that you shouldn't hold back and just quote cave paintings - and that was if you were even right about the experiment you were talking about which you know now you weren't. Don't take it so personally it's just friendly humor.
You all keep discussing 'the expended rocket fuel adds angular momentum to the Earth'. Here is what I don't understand. The total momentum of the rocket/fuel system is zero, due to conservation of momentum. The expended fuel has an equal and opposite reaction to the rocket, giving motion to the rocket of course. If the exaust gasses also give momentum to the Earth's rotation, wouldn't that upset the conservation of momentum in the rocket/exhaust gas system, effectly using the exhaust gas to give momentum to both the rocket and the Earth?
Tortise: Whether I was exactly correct in quoting Newton or not, I am too lazy and too disinterested in engaging in an argument which I could only consider pointless to worry about it any further. The origin of the flap was someone's comment or question regarding the theorized nature of inertia, and if anyone has ever proposed a better concept than that of the majority ( or totallity ) of mass in the universe being the agent, I genuinely would appreciate being able to study it. Perhaps Tortise knows how inertia REALLY works?
If it was postulated ( where was that, anyway? ) that all the exhaust remained in planetary confine, then action and reaction, and conservation of momentum have to sum to zero. The only question remaining is the matter of whether the relocation of the satelite from stationary surface location to stable orbit has regaged Earth rotational velocity. The problem is, did the rapture ( snatching up ) of the satelite alter the rotation of the planet?
You're right that the sum would be zero, and that's actually a very good way of looking at the problem. That's actually how scientists look at the problem - if the satellite has more angular momentum in the orbit, then that momentum must have mostly come from somewhere in order for the system to remain the same.
Hi 2inquisitive, Don't forget that momentum is a vector... so if some system starts has zero momentum, it can split in two with each part having momentum in opposite directions. The total momentum of the system is still zero, because the opposite momentums add to zero.
You are correct here. The conservation of momentum applies for isolated systems. By having the rocket exhaust impact the earth the rocket/exhaust system is no longer isolated and must be extended to rocket/exhaust/earth. Momentum is then no longer conserved between rocket and exhaust, but is conserved among all three. This is exactly what D_H was talking about with "drawing the boundaries" being critical in applying conservation techniques and what his argument here has been. The problem has been set up so that all exhaust returns to earth, therefore you can consider the system to just be rocket/earth. D_H (correctly) points out that this is not entirely accurate and some exhaust will escape earth. This then would require knowledge of the momentum of escaping exhaust in order to correctly apply the conservation laws. -Dale
2inq said: In a sense you are right: You could think of it as accelerating the earth but in the oppisite direction that it is rotating. But the end result is still that the period of rotation has slowed.
Answer to first paragraph question is because the thread is ignoring the realities that there are torques on the Earth from moon and other planets, sun, etc. Several times this has been explictitely stated, even to the extreme of suggesting that the Earth as only object in universe was the case considered by thread. Unfortunately, you have not been willing to conform to the threads problem, but want to include many real effects, exo-atmospheric thrusting, moon etc. torques, etc. Several of these real effects are much larger and I believe make the actual observation of the thread's tiny effect impossible. - The unknown variations in some of these other effects, such as the seasonal change in Earth's I, is even "much larger" and thus you can not actually measure a tiny effect, if you can not correctly subtract out a bigger effects because knowledge of exactly how much bigger the larger effect is, is not acailable. I also note that you still have not given even the slightest hint as to a possible mechanism by which the rest of the universe plays a role in torquing the Earth, or making the conservation of angular momentum associated with a man made change, (Place B into orbit in less thn a day), can even be known by objects that are light years away. Again can you please describe how the rest of the universe enters into the change made by man in a day? You still have not attempted an answer to this question - obviously I think there is none, but I will hear you out if you have one.
Don't forget, the rocket is not 'turned' towards East until it is nearly free of the atmosphere. A rocket sent into orbit travels straight up until it reaches the thin upper atmosphere. The less time spent powering through the dense atmosphere, the better. In that situation, most of the exaust gas's effect is directed perpendicular to the Earth, not 'pushing it opposite the direction of rotation'. The rocket gas may push against the atmosphere, but the rocket body pushes against the atmosphere in the opposite direction. Aren't these two 'pushes' supposed to be equal in magnitude due to conservation of momentum in the rocket/exaust gas system?
Another point brought up by D H before is that the supposed slowing of the Earth's rotation through satellite launches is not borne out by evidence. The 24 hours of a solar day equals 86,400 seconds. The Earth rotates once every 86,400.002 seconds today. By the way, the 'true' rotation of the Earth, the sidereal day, is almost 4 MINUTES less than 24 hours. The Earth is actually rotating faster than once every 24 hours. Back to the 86,400.002 second figure. In 1820, the solar day was exactly 86,400 seconds long. The Earth has slowed .002 seconds per rotation since then, about 186 years. By checking ancient observations of eclipses, the Earth is estimated to slow about 2 milliseconds each century for the last few thousand years. The actual slowing of the Earth's rotation seems to be at a slightly lower rate now than in the past, not more due to recient satellite launches. I stand by my statement that satellite launches have zero measurable effect on Earth's rotation.
Weeeelll, Since the poll is closed and the original idea that I had was bogus anyway due to my naievete regarding conservation of angular momentum (thinking that tossing a satellite out from the earth was the same as a skater stretching his/her arms out - no torques though - duh) I will give you my answer assuming that the satellite is raised to geosynchronous orbit by a massless, infinetly rigid telescoping pole. Take that! I find under these very realistic conditions that the angular speed of the earth decreases at a magnitude of 10<sup>-20</sup>. Since the geostationary altitude is related by the cube root of the square of the orbital period, it changes by something on the order of 10<sup>-20</sup> to 10<sup>-21</sup> also. This is somewhere between an angstrom (10<sup>-10</sup>meters) and the Planck length (1.6x10<sup>-35</sup>meters).
It is true that if the centroid of the rocket thrust were directed towards the center of the Earth, until the rocket was far above 99+% of the atmosphere and only then rolled over to the East, there would be even less effect upon the spin rate of the Earth. However this is not the assumption of the thread. Several times I have stated, and DaleSpan at leasst twice also, that NO EXHAUST GAS escapes from the Earth. In actual practice, this restriction is nearly true. For safety reasons a US launch from the begins a roll over to the East so if the rocket explodes, the pieces will fall in the Atlantic ocean. Compared to the thrust of the rocket, the frictional drag of the air is negligible, so getting out of the air quickly s possible is not very important. I would not be surprised to learn that having he exhaust "press against the atmosphere" increases the force on the rear of the rocket more that the friction of air flowing by its side subtracts form the rocket thrust, but do not know if this is true. Likewise, there must be a very small effect fo the atmospheric presure difference between the "top side" of a rocket rolled over to 45 degrees compared to the "bottom side." (Air planes are held up by a reated pressure difference, but of course their wings are designed for this - a fast moving ponted cylinder (the rocket) will "surf" on this pressure difference very little, I think.) Also it cost very little to make part of the the kinetic energy being given to the rocket be associated with Eastward motion, instead only climbing against gravity. For all of these resaons, even in practice, rockets usually roll over to the East, if they are intended to go into orbit. If it is a much less capable rocket, used only to get a few minutes above most of the atmosphere, then a nearly straight up trajectory is desirable, if safety permits. In any case, you like DH, are not accepting the thread's assumptions, but discussing some other case.
Here it is you, me, and SL (and probably several others) against DH. I.e. We all agree the effect is entirely impossible to MEASURE,but if you are still claiming that this is because it is exactly zero, I think you are standing alone.
Poll is closed, but I wonder if anyone want to answer the following closely related question (by math demonstration, preferred or guess/opinion if that temps you still): Assume universe consists of two objects only, one of mass M and the other of mass m. They are rotating about their common center of mass with period P (although without at least a grain of sand on the other side of the universe as a "fixed star" to anchor the reference frame, we will need a bucket of water to see this rotation.) So that all will use the same symbols, the distance between them is D. I think most will now grant that the angular momentum about the center of mass is unchanging constant, L. Guess yes or no to the following four questions: Q1: Is the angular momentum about the center of mass of M also L? Q2: Is it also L about any point on their trajectory where they are not? Q3: Is it also L about any point in the plane of their trajectory? Q4: is it also L about any point off the plane of the trajectory? Note Q4 is asking if it is the same for ALL points in space, even that grain of sand on "other side of the universe." If you answer "no" to any of the above, and can tell / know correct answer, wait until 1 April to do so. If you are just guessing and say "no" to any of the four, guess if angular momentum is greater or smaller, or could be either, depending upon where the point is in case of Q2, q3, & Q4. Lets see how many "April fools" we have. (Remember "fool," at least originally, referred to one who amuses us, sort of an honor, or at least a service.)
by Billy T: "It is true that if the centroid of the rocket thrust were directed towards the center of the Earth, until the rocket was far above 99+% of the atmosphere and only then rolled over to the East, there would be even less effect upon the spin rate of the Earth. However this is not the assumption of the thread. Several times I have stated, and DaleSpan at leasst twice also, that NO EXHAUST GAS escapes from the Earth." ================================================================ Billy T, no exhaust gas will escape the Earth unless that gas is moving away from the Earth at above escape velocity. Since that exhaust gas is directed toward the Earth even when the rocket trajectory is tilted in the upper atmosphere, it does not escape Earth's gravitational field until the rocket is in the vacuum and only then if the gas were directed away from the Earth at escape velocity relative to the Earth. A rocket does not reach escape velocity itself, if the objective is to place a satellite in ORBIT. This has nothing to do with conservation of angular momentum in Earth's rotation, however. The exhaust gasses are still a part of Earth's mass. The only loss of mass concerning the Earth's angular momentum would be if the mass of the rocket itself escaped Earth's gravitational field (escape velocity, not orbital velocity) and entered orbit around the sun. Your gedankin specifically states ORBITAL insertion of a rocket/satellite.
The way I see it, if the effect is impossible to measure, even after the accumilated effects of thousands of launches, the effect is zero. You do know the Earth is getting more spherical due to the loss of angular momentum, don't you? Angular momentum is a centrifugal force, causing the Earth to be a larger diameter around the equator than around the poles. As the Earth slows in its rotation, this relationship is changing. The crust of the Earth is literally tearing apart around the equator, the Pacific and Atlantic ridges. The crust of the Earth is falling and drifting north/south around the equator, causing moltent rock to ooze through the cracks. This has been confirmed by the LAGEOS satellite. It has been measured.
