Thanks. Your knowing this and yet thinking the distant stars are significant and prevent conservation of angular momentum in the Earth + rocket + satellite system plus your knowledge about Kepler, orbits, etc. makes me willing to guess about you also: Your role is in the math of trajectories, planet swing by effects etc. not in the physics of building satellites and testing them - right? or wrong? I.e what do or did you do wrt satellites?
I see what you're saying, but the point is not how accurate we are - even if we were off by 5 minutes - I think that is besides the point - a satellite off by 5 minutes still expended enormous amounts of fuel to get there and any small corrections it makes while in orbit is 1/10,000 at most the fuel it took to get into orbit. So while I can understand what you're saying, do you really think it is relevant to this discussion? The question was meant to be a thinking exercise I thought, not a litteral one.
Was just about to trun off computer for day and have not read rest of this, but know you are repeating Mach's position do you not? will read tomorrow more.
Yes, I know I am repeating Mach's principle, and I also know it doesn't fully agree with General Relativity. So I live in a world of conflicting models. They are the best ones available. I too must turn off the computer and go study a different kind of rotational inertia. Thursday night is when my wife and I go out dancing.
An interesting question it is... perhaps another thread? Would you mind if we assume Newtonian mechanics and gravity in this thread? The exhaust of the rocket applies a torque to the Earth. Yes (undetectably, of course), if the rocket's exhaust reaches Earth. Same answer. The exhaust from the rocket around Jupiter isn't likely to reach Earth. What does Newton's laws predict? If a satellite was launched from a planet in an otherwise empty universe, do Newton's laws predict that the angular momentum of the planet+satellite would be conserved?
I think for most quantities defined by a cross product you wind up with a Pseudovector. If you invert the coordinates so that R' = -R and V' = -V then L' = L instead of -L. -Dale
Pete: I have bad news for you. It was Newton who first proposed that inertia is the result of the gravitational activity of all of the mass in the universe. It was the result of his famous water bucket experiment. Not to be confused with Faraday's famous ice pail experiment. It has also been expressed as the result of the majority of mass of the universe. Mach belived this also, according to his public statements. Einstein believed this also, according to his public statements. He also said that he regretted that he had failed to be able to incorporate Mach's principle ( actually Newton's principle ) into the relativities. The concept that inertia is the result of all the mass in the universe IS NEWTONIAN PHYSICS.
Yes indeed. And was it not Newton that said: " All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction - except when a rocket is delivering a satellite in to an earth orbit". That's my favorite quote of Newton's (wipeing eyes - blowing nose) - I just get so emotional when I read Newton. Angular momentum can also be calculated by multiplying the square of the distance to the point of rotation (look familiar), the mass of the particle and the angular velocity.
I agree. I only want all to assume for this thread, but not in actual launches, that the rocket burn within the atmosphere placed the satellite into perfect geostationary orbit without any exhaust being releast into space. At times, some here have stated that angular momentum is not conserved. DH has requently spoken of exo-atmospheric burns and interactions with the distant stars, etc. I have been trying to keep thread question focused onthe problem I intended, and most have understood, which can assume only the Earth and the two satellites, A & B, exist. Specifically there are no distant stars or exhaust gasses releasted into space in the thread's problem, however I do understand that given the view of Mach & DH about the origins of inertia etc, it makes no make no sense to pose the problem as I have. That is offset inmy view at least that the nearest star (Baryards?) can not even know about the launch of B until years after B is in orbit so to further define the problem I might say that both A & B were perfect launches (no positioning exo-atmospheric burns, the sun and all else of our solar system, save Earth does not exist and if distant stars must exist to make inertia, etc. then the "SLIGHTLY" of the thread is the radial difference shortly (well be the closest star "knows" about the launch of B) after B is in perfect geo-stationary orbit about the Earth which all but 2inqusitive believe to be spinning "SLIGHTLY" more slowly BECAUSE B has been placed into orbit than it was prior to launch of B.
Hi CANGAS, Not all of Newton's ideas are included in what we refer to as "Newtonian Physics" (even if it's in capitals). Assuming Newtonian mechanics and Newtonian gravity means assuming the truth of the three laws of motion and the universal law of gravitation.
CANGAS said: "For around 200 years Newton's arguments in favour of absolute space were hardly challenged. One person to question Newton was George Berkeley. He claimed that the water became concave not because it was rotating with respect to absolute space but rather because it was rotating with respect to the fixed stars" http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Newton_bucket.html even if you were right (which you were not).... what the crap does that have to do with anything? Stay on subject. We need a moderator in this thread. So don't quote quantum physics or anything...quote some 300 year old experiment. Way to stay ahead of the curve. Next time don't hold back, quote something even older like cave paintings or something - but make sure you get it right. (And yes I appologise for being a smart ass)
To DH: You have asked, more than once: "[1]What mechanism causes the Earth's spin rate to change?" AND more recently: "Turning the table, how exactly does a thrusting rocket change the Earth's rotation rate?" And have been answered more than once. Pete's reply is much shorter than mine. (I am always too long winded, but the details I gave earlier expand Pete's correct response to the finer details of how Earth is torqued.) I asked you for the mechanism by which you imagine that the distant stars / "universe" are used to conserve the angular momentum. You said that it was not conserved locally in the Earth+satellite system, etc. so how do the distant stars /universe assist in the conservation? Mechanistic details, like I gave you yesterday at 47 minutes past the hour, would be a nice reply. I said: NOW YOU HAVE TWO ANSWERS - HOW ABOUT GIVING US ONE?
Hard to believe, but 18 pages and a day to go before this two-week only poll closes. Least people think my last post is attacking DH, let me again note I have learned from him more about the utility of the Taylor series than I did in college, where it was usually just a math exercise to be done on an exam etc., with little, (for me) real meaning or practical use (except to get good grade on the test). Thanks to DH, I now see /understand it is powerful, easy to us, tool for problems like this thread's. Thanks again DH.
I agree with Billy T. For me, the object of writing in these threads is to learn. That we get into arguments is besides the point and hopefully we don't take it personally. I'm really laughing half the time over these arguments and I think they should inspire learning and not be taken too seriously. And let's be honest - when we are in an argument - isn't that when we do some of our best thinking and research?
I have always been a bit leery regarding arguments by way of the conservation laws. They are a bit more handwaving than I like. They sweep all the details under the rug; they pay little attention to cause and effect. Most importantly, the results will be incorrect if the boundaries are drawn incorrectly. Because the details have been swept under the rug, there is no sanity check to ensure that the results are true. It is imperative that the boundaries be drawn correctly when applying the conservation laws. Why did you choose the Earth+satellite for the boundaries? Why not the Earth, Moon, and satellite, the solar system+satellite, or the Milky Way + satellite? That is not to say that I don't resort to the conservation laws myself in my work. They are very powerful because they sweep all the details under the rug. For example, I don't care about the details of contact dynamics. I definitely do care how a spacecraft behaves after docking or undocking is complete. I just sweep the details of docking by means of the conservation laws. The reason I specifically asked about exo-atmospheric burns is because the exhaust from such burns is, for the most part, swept away from the Earth by solar radiation pressure. How does that exhaust exert a torque on the Earth? It never contacts the Earth. To argue that it must because of the conservation laws begs the question. I want forces and torques; I want equations of motion. I do agree that, up to the point that the satellite leaves the atmosphere, the exhaust from the spacecraft does indeed change the angular momentum of the Earth by an immeasurable amount. Conservation of angular momentum can be applied to assess this change. All bets are off once Elvis has left the building.
DH said: The percentage of the total burn of putting the satellite into orbit excapes the earth's gravity I think it is less then .1 % Why even argue about this? But you may be right - for that very small amount - it is conserved in the universe and not the immediate system.
Because it is easier. That's also why we required that all of the exhaust return to the earth. We are all aware that real rockets spew exhaust to the far reaches of the universe and said exhaust must be included in a realistic analysis, but we did not want to complicate the problem. It is just an estimation game. -Dale
Because the original question was about GEO, not LEO. Getting out of the atmosphere is but a fraction of the total problem of getting to geosynchronous orbit.
Ya in as much as 9/10 is a fraction. But that's besides the point - we are talking about where the fuel winds up, we are not talking about logistics - or what a pain in the but it is. I submit that 999 parts of gas out of 1000 of the origional feul that the rocket started out with, remains in, or winds up in the earth's atmosphere, (subsequently causing friction) and you of all people should know that.
