![]() |
"Donal" wrote in message ... "Jeff Morris" wrote in message Consider an astronaut space walking outside a space station. They both float together, feeling no force, although they are both in freefall in their orbit. If the astronaut moves to a lower orbit, he will feel a stronger pull and be drawn in, unless he speeds up to compensate. If the astronaut moves to a higher orbit, the force is reduced. As I said, the force can be calculated without consideration of momentum. I don't understant this. In orbit, momentum is the force that balances the effect of gravity. Without momentum, your astronaut wouldn't "float" - he would crash straight into the Earth. Momentum is not a force. You're right that the astronaut has momentum, and that the force of gravity alters his momentum. In fact, Force is defined by how much it changes momentum. (Many people learn F=ma; in physics that is normally written as F=dp/dt, or Force equals the rate of change of momentum with respect to time.) My point is that you can determine the force on the astronaut without considering his momentum. To figure out how the force would alter his orbit, you would probably take momentum into account. Remember, I'm not trying to calculate the tides, only to show how gravity can cause two equal size bulges on the Earth. In fact, I think that your use of the word "float" reveals that you don't understand the situation at all. Your astronaut wouldn't feel any difference between a free fall orbit and a headlong race into deepest space, - would he? So tell us, what is the difference? Floating in a space station is call "free fall" because it feels the same as jumping off a cliff. Furthermore, if he slowed down, then he would still feel like he was floating -- apart from the temperature, and perhaps the braking effect of the atmosphere. Yes, but that's not the point. The point is, if he is in a lower orbit, he experiences more gravity; in a higher orbit, less gravity. If his speed is not adjusted to compensate, he will drift further away from the space station. Just like the tides. This makes me think that the orbiting "free-fall" astronaut doesn't feel that he is floating at all. Haven't you ever seen astronauts floating? He must feel a constant force as his direction of travel changes. I wonder if this has been documented on the Internet? http://science.howstuffworks.com/weightlessness1.htm What does your physics friend say about this? He would probably deplore the lack of education in your country. A purist might say momentum is considered because the mass and velocity of the every object in the system is folded together. And, the pure way force is defined is by how it changes momentum. But I don't think this is what you're talking about. I'm not sure. I'm certainly *not* a purist. Regards Donal -- |
Jeff Morris wrote: No, you never said it wasn't needed, but you did minimize its importance, claiming that it can't be used alone to predict the tides. You said: "Even worse, the site then goes on to use the _differential_ expression to calculate the ratio of forces between the moon and sun!" Yes that's right for that site. The differential of the gavity equation does not give a force it gives the rate of chnage of force with distance. That's basic calculus. You even produced a bogus formula to support your claim that centrifugal force varies across the Earth. This would predict a tidal force 65 times stronger than differential gravity. If that isn't minimalizing differential gravity, I don't know what is. Nothing bogus abot F=m r omaga^2. It's high school physics. It is quite easy to explain the tides without Centrifugal force - I mentioned the approach in one of my first posts. There is a gravitational force pulling the Earth and Moon together. This creates an acceleration such that the Earth is in free fall, and no net force is felt at the Earth's center. However, there is a larger force on the Moon side, and a smaller force on the far side. Since the average force has been accounted for it must be subtracted from these two forces, and the smaller force ends up being the same magnitude as the larger, but in the opposite direction. Hence, two tidal bulges, both caused solely by gravity. Jeff, stop a moment and put what you just said into an equation. According to you subtraction of a constant from both sides of an inequality makes an equality? You, however, have claimed that the variation of the centrifugal force from the near side to the far creates a force that dominates the tides. Your formula predicts a force 65 times greater than the differential formula, which would seem to create tides 100 feet or more. That's because you've forgetten that the tiode is due to the difference between forces -how many times do I have to repeat this???? Your explanation that land masses dampen these tides runs counter to common experience. And, your formula predicts the Sun's contribution is only 1% of the Moon's, which is clearly not the case. No it doen't. It's your miscomprehension about the force balance. As to your claim that the rotation around the barycenter "powers" the tides, well, that's not true. Jeff, don't be hysterical. Of course it's true. Furthermore, the barycenter is not the same distance from all points on earth so the centrifugal force varies across the earth. Here is the equation for the force on a mass m of water on the far side for a non-rotating earth (to keep it clear): GmM/(R+r)^2 + GmE/r^2 - m(r+s)omega^2 On the near side: GmM/(R-r)^2 + GmE/r^2 - m(r-s) omega^2 M is the moon mass, E the earth mass, s the distance from the center of the earth to the barycenter, omega the angular velocity of the earth-moon pair G the gravitational constant. Now look very carefully at the three terms in each equation. The first two are gravity, the third centrifugal. Two terms are different in both cases. The gravity term is smaller on the far side and the centrifugal term is bigger. On the near side the gavity is bigger and the cenbtrifugal is smaller. That is the proof of my argument. Cheers |
Jeff Morris wrote: Remember, I'm not trying to calculate the tides, only to show how gravity can cause two equal size bulges on the Earth. Equal? That'll be hard when it's non-linear. Think about it. Take as long as you like. Cheers |
"Nav" wrote in message ... Jeff Morris wrote: No, you never said it wasn't needed, but you did minimize its importance, claiming that it can't be used alone to predict the tides. You said: "Even worse, the site then goes on to use the _differential_ expression to calculate the ratio of forces between the moon and sun!" Yes that's right for that site. The differential of the gavity equation does not give a force it gives the rate of chnage of force with distance. That's basic calculus. Simply differentiating the gravitational force is not enough. But the equation normally given for differential gravity is dimensionally correct. You even produced a bogus formula to support your claim that centrifugal force varies across the Earth. This would predict a tidal force 65 times stronger than differential gravity. If that isn't minimalizing differential gravity, I don't know what is. Nothing bogus abot F=m r omaga^2. It's high school physics. That formula is correct. Applying it with a varying "r" is bogus. That's the issue here, but you haven't noticed it. It is quite easy to explain the tides without Centrifugal force - I mentioned the approach in one of my first posts. There is a gravitational force pulling the Earth and Moon together. This creates an acceleration such that the Earth is in free fall, and no net force is felt at the Earth's center. However, there is a larger force on the Moon side, and a smaller force on the far side. Since the average force has been accounted for it must be subtracted from these two forces, and the smaller force ends up being the same magnitude as the larger, but in the opposite direction. Hence, two tidal bulges, both caused solely by gravity. Jeff, stop a moment and put what you just said into an equation. According to you subtraction of a constant from both sides of an inequality makes an equality? I have no idea what you're saying. If the force at the center is X, and on the near side is X+D, and on the far side is X-D, then if you subtract the central force, the near side is D and the far side is -D. You, however, have claimed that the variation of the centrifugal force from the near side to the far creates a force that dominates the tides. Your formula predicts a force 65 times greater than the differential formula, which would seem to create tides 100 feet or more. That's because you've forgetten that the tiode is due to the difference between forces -how many times do I have to repeat this???? I just tried to follow all your instructions. You challenged me to work the math, I did, it produced bogus answers. The difference in the centrifugal force that your equation predicts is 65 times more that the difference in the gravitational force, so subtracting still won't help much. Why don't you work out the math? And don't forget to do it for the Sun also. Your explanation that land masses dampen these tides runs counter to common experience. And, your formula predicts the Sun's contribution is only 1% of the Moon's, which is clearly not the case. No it doen't. It's your miscomprehension about the force balance. I'm just reporting the numbers your equation predicts. As to your claim that the rotation around the barycenter "powers" the tides, well, that's not true. Jeff, don't be hysterical. Of course it's true. Furthermore, the barycenter is not the same distance from all points on earth so the centrifugal force varies across the earth. This is your basic mistake. Even the web site you pointed to for support explicitly says this is not true. Let me repeat it again http://www.co-ops.nos.noaa.gov/restles3.html "While space does not permit here, it may be graphically demonstrated that, for such a case of revolution without rotation as above enumerated, any point on the earth will describe a circle which will have the same radius as the radius of revolution of the center-of-mass of the earth around the barycenter. Thus, in Fig. 1, the magnitude of the centrifugal force produced by the revolution of the earth and moon around their common center of mass (G) is the same at point A or B or any other point on or beneath the earth's surface. Any of these values is also equal to the centrifugal force produced at the center-of-mass (C) by its revolution around the barycenter. This fact is indicated in Fig. 2 by the equal lengths of the thin arrows (representing the centrifugal force Fc) at points A, C, and B, respectively." it continues with: "While the effect of this centrifugal force is constant for all positions on the earth, the effect of the external gravitational force produced by another astronomical body may be different at different positions on the earth because the magnitude of the gravitational force exerted varies with the distance of the attracting body." Go on. Read it, think about it. You were quick to cite this page when you thought it supported you. Here is the equation for the force on a mass m of water on the far side for a non-rotating earth (to keep it clear): GmM/(R+r)^2 + GmE/r^2 - m(r+s)omega^2 On the near side: GmM/(R-r)^2 + GmE/r^2 - m(r-s) omega^2 M is the moon mass, E the earth mass, s the distance from the center of the earth to the barycenter, omega the angular velocity of the earth-moon pair G the gravitational constant. Nope. This is incorrect. The proper equations a Farside: GmM/(R+r)^2 + GmE/r^2 - m s omega^2 On the near side: GmM/(R-r)^2 + GmE/r^2 - m s omega^2 Further, since GmE/r^2 = m s omega^2, we are left simply with: Farside: GmM/(R+r)^2 On the near side: GmM/(R-r)^2 This leads to the traditional differential equation 2GmMr/R^3 as shown in http://mb-soft.com/public/tides.html Now look very carefully at the three terms in each equation. The first two are gravity, the third centrifugal. Two terms are different in both cases. Nope. Only one term is different. The gravity term is smaller on the far side and the centrifugal term is bigger. On the near side the gavity is bigger and the cenbtrifugal is smaller. That is the proof of my argument. The proof fails because of a faulty assumption. Sorry Nav, Centrifugal Force is constant. You can use it if you chose, but it doesn't really change the math and isn't particularly interesting. The part of the equation that actually produces the two tides is the differential gravity. |
Yes, I should have said "roughly equal." But don't your equations show a huge
difference between the near and far side tides caused by the barycenter being closer to the near side? Shouldn't that be a clue that something is amiss in your theory? "Nav" wrote in message ... Jeff Morris wrote: Remember, I'm not trying to calculate the tides, only to show how gravity can cause two equal size bulges on the Earth. Equal? That'll be hard when it's non-linear. Think about it. Take as long as you like. Cheers |
"Jeff Morris" wrote in message ... "Donal" wrote in message ... "Jeff Morris" wrote in message Consider an astronaut space walking outside a space station. They both float together, feeling no force, although they are both in freefall in their orbit. If the astronaut moves to a lower orbit, he will feel a stronger pull and be drawn in, unless he speeds up to compensate. If the astronaut moves to a higher orbit, the force is reduced. As I said, the force can be calculated without consideration of momentum. I don't understant this. In orbit, momentum is the force that balances the effect of gravity. Without momentum, your astronaut wouldn't "float" - he would crash straight into the Earth. Momentum is not a force. You're right that the astronaut has momentum, and that the force of gravity alters his momentum. In fact, Force is defined by how much it changes momentum. (Many people learn F=ma; in physics that is normally written as F=dp/dt, or Force equals the rate of change of momentum with respect to time.) Ok. What force opposes gravity so that a body may remain in orbit? My point is that you can determine the force on the astronaut without considering his momentum. In which case, there must be a "force" that is counteracting the effect of gravity. After all, gravity is trying to pull the orbiting Astronaut straight towards Earth. There must be another force that is opposing gravity. To figure out how the force would alter his orbit, you would probably take momentum into account. Remember, I'm not trying to calculate the tides, only to show how gravity can cause two equal size bulges on the Earth. Do you think that centrifugal force plays any part? If so, what do you think the ratio is between the centrifugal and differential gravity forces? In fact, I think that your use of the word "float" reveals that you don't understand the situation at all. Your astronaut wouldn't feel any difference between a free fall orbit and a headlong race into deepest space, - would he? So tell us, what is the difference? Acceleration. Floating in a space station is call "free fall" because it feels the same as jumping off a cliff. Furthermore, if he slowed down, then he would still feel like he was floating -- apart from the temperature, and perhaps the braking effect of the atmosphere. Yes, but that's not the point. The point is, if he is in a lower orbit, he experiences more gravity; in a higher orbit, less gravity. If his speed is not adjusted to compensate, he will drift further away from the space station. Just like the tides. This makes me think that the orbiting "free-fall" astronaut doesn't feel that he is floating at all. Haven't you ever seen astronauts floating? Yes.... but they are constantly changing direction.... and therefor they should be aware of the effects of acceleration. He must feel a constant force as his direction of travel changes. I wonder if this has been documented on the Internet? http://science.howstuffworks.com/weightlessness1.htm That is a very simplistic explanation. It refers to the fact that the astronauts will feel the acceleration at take-off, and yet it doesn't seem to understand that a change of direction is also acceleration. We humans can detect acceleration. If you sit in an automobile with your eyes closed, then you can feel an increase or decrease in speed .... or a change of direction!! As the astronauts are subjected to a constant change of direction, I suspect that they might not feel that they are completely free-floating. What does your physics friend say about this? He would probably deplore the lack of education in your country. Ask him anyway! Perhaps, if you allowed him to read the thread, he might be amazed at your lack of reading ability. After all, I've already explained that I gave up Physics at an early stage. Regards Donal -- |
"Donal" wrote in message ... I don't understant this. In orbit, momentum is the force that balances the effect of gravity. Without momentum, your astronaut wouldn't "float" - he would crash straight into the Earth. Momentum is not a force. You're right that the astronaut has momentum, and that the force of gravity alters his momentum. In fact, Force is defined by how much it changes momentum. (Many people learn F=ma; in physics that is normally written as F=dp/dt, or Force equals the rate of change of momentum with respect to time.) Ok. What force opposes gravity so that a body may remain in orbit? Nothing. The body remains in orbit because it has enough forward velocity (momentum also, but its the velocity that counts) so that while it "falls" into the Earth, the forward velocity keeps the body from hitting the Earth. For a low orbit, we normally thing of circular orbits, but for high orbits they can be quite eccentic. If the Earth were a "point source" it would only take a small velocity to stay in orbit. Of course, there are many ways to calculate this - somtimes its done in terms of "energy," other times as "delta V" so if you want to say the momentum of the body keeps it from falling into the Earth, that's OK. My point is that you can determine the force on the astronaut without considering his momentum. In which case, there must be a "force" that is counteracting the effect of gravity. After all, gravity is trying to pull the orbiting Astronaut straight towards Earth. There must be another force that is opposing gravity. See above. If the body were motionless (WRT Earth), it would fall directly in. But if it has any velocity, its has a chance of missing it. The reason why I say velocity is important, and not momentum, is that two bodies of different mass (and hence, different momentum) will float together in orbit. Of course, if you want to calculate the amount of fuel to burn, momentum becomes important. On Earth, we always have air resistance, and other forms of friction, so momentum is more significant. To figure out how the force would alter his orbit, you would probably take momentum into account. Remember, I'm not trying to calculate the tides, only to show how gravity can cause two equal size bulges on the Earth. Do you think that centrifugal force plays any part? If so, what do you think the ratio is between the centrifugal and differential gravity forces? It is possible to look at the problem without considering Centrifugal Force. However, even if you use CF, it is a constant, and equal to the net gravitation force. So if it helps to expain how there can be a force away from the moon, that's OK, but you must remember that it is the gravitation force that varies, so that's where the interesting math comes from. In fact, I think that your use of the word "float" reveals that you don't understand the situation at all. Your astronaut wouldn't feel any difference between a free fall orbit and a headlong race into deepest space, - would he? So tell us, what is the difference? Acceleration. No, the acceleration is the same, more or less. (Not counting the difference in distance from the Earth, or air resistance, etc.) The only real difference is that the astronaut has enough velocity (hopefully) to miss the Earth as he falls. Floating in a space station is call "free fall" because it feels the same as jumping off a cliff. Furthermore, if he slowed down, then he would still feel like he was floating -- apart from the temperature, and perhaps the braking effect of the atmosphere. Yes, but that's not the point. The point is, if he is in a lower orbit, he experiences more gravity; in a higher orbit, less gravity. If his speed is not adjusted to compensate, he will drift further away from the space station. Just like the tides. This makes me think that the orbiting "free-fall" astronaut doesn't feel that he is floating at all. Haven't you ever seen astronauts floating? Yes.... but they are constantly changing direction.... and therefor they should be aware of the effects of acceleration. I must admit this subtlety has perplexed me - clearly the don't feel the G force, since it the same as a car in a tight turn. But I keep thinking it should be detectable, if only because the path is curving. He must feel a constant force as his direction of travel changes. I wonder if this has been documented on the Internet? http://science.howstuffworks.com/weightlessness1.htm That is a very simplistic explanation. It refers to the fact that the astronauts will feel the acceleration at take-off, and yet it doesn't seem to understand that a change of direction is also acceleration. We humans can detect acceleration. If you sit in an automobile with your eyes closed, then you can feel an increase or decrease in speed .... or a change of direction!! As the astronauts are subjected to a constant change of direction, I suspect that they might not feel that they are completely free-floating. Of course, from a General Relativity, Gravity Well point of view, the obital path is a straight line in curved space. I should know the answer here - let me cogitate ... What does your physics friend say about this? He would probably deplore the lack of education in your country. Ask him anyway! Actually, it was Scout's friend. However, you should remember I majored in physics and worked for NASA doing spacecraft navigation. I may be rusty now, but 25 years ago I really knew this stuf! Perhaps, if you allowed him to read the thread, he might be amazed at your lack of reading ability. After all, I've already explained that I gave up Physics at an early stage. I haven't forgotton that. It was just a little dig since usually you Brits complain about our sorry education. |
Jeff Morris wrote: I must admit this subtlety has perplexed me - clearly the don't feel the G force, since it the same as a car in a tight turn. But I keep thinking it should be detectable, if only because the path is curving. (1) How tight is the turn and (2) how big is the imbalance between centrifugal and garvitational forces for such a small body? Of course, from a General Relativity, Gravity Well point of view, the obital path is a straight line in curved space. I should know the answer here - let me cogitate ... Eat some bran? :-P Cheers |
"Jeff Morris" wrote in message ... "Donal" wrote in message ... In fact, I think that your use of the word "float" reveals that you don't understand the situation at all. Your astronaut wouldn't feel any difference between a free fall orbit and a headlong race into deepest space, - would he? So tell us, what is the difference? Acceleration. No, the acceleration is the same, more or less. (Not counting the difference in distance from the Earth, or air resistance, etc.) The only real difference is that the astronaut has enough velocity (hopefully) to miss the Earth as he falls. That was a very revealing answer. Earlier in the thread you were confident enough about your position to question my lack of education. Now you seem to think that an object travelling at "x" miles an hour in a straight line ("headlong into space") has the same acceleration as a body travelling at "x" miles an hour in orbit. It's probably time that you consulted your physics partner. Before you let him read what you have written, you should make sure that there is a cloakroom near the PC. Otherwise, have a potty close at hand - because he is really going to **** himself when he reads your words. Haven't you ever seen astronauts floating? Yes.... but they are constantly changing direction.... and therefor they should be aware of the effects of acceleration. I must admit this subtlety has perplexed me - clearly the don't feel the G force, since it the same as a car in a tight turn. But I keep thinking it should be detectable, if only because the path is curving. Yeah. It's called acceleration - a bit like G-force. Please note that "a bit" = "exactly" in European understatement. He must feel a constant force as his direction of travel changes. I wonder if this has been documented on the Internet? http://science.howstuffworks.com/weightlessness1.htm That is a very simplistic explanation. It refers to the fact that the astronauts will feel the acceleration at take-off, and yet it doesn't seem to understand that a change of direction is also acceleration. We humans can detect acceleration. If you sit in an automobile with your eyes closed, then you can feel an increase or decrease in speed .... or a change of direction!! As the astronauts are subjected to a constant change of direction, I suspect that they might not feel that they are completely free-floating. Of course, from a General Relativity, Gravity Well point of view, the obital path is a straight line in curved space. I should know the answer here - let me cogitate ... No, you don't know the answer. Trust me. Despite my dreadful education, I am confident that someone who doesn't understand the basic principles of acceleration is incapable of getting their head around the TGR. Cogitation would be a complete waste of your time. What does your physics friend say about this? He would probably deplore the lack of education in your country. Ask him anyway! Actually, it was Scout's friend. However, you should remember I majored in physics and worked for NASA doing spacecraft navigation. I may be rusty now, but 25 years ago I really knew this stuf! GULP!!! So why do you not seem to understand the difference between "velocity" and "speed"? Perhaps, if you allowed him to read the thread, he might be amazed at your lack of reading ability. After all, I've already explained that I gave up Physics at an early stage. I haven't forgotton that. It was just a little dig since usually you Brits complain about our sorry education. Little digs are very welcome. I appreciate a good insult - and calling me "you Brits" is definitelay a reasonable insult. You're not lagging too far behind Joe! He called me a Brit about six months ago. Regards Donal -- |
"Donal" wrote in message
... "Jeff Morris" wrote in message ... "Donal" wrote in message ... In fact, I think that your use of the word "float" reveals that you don't understand the situation at all. Your astronaut wouldn't feel any difference between a free fall orbit and a headlong race into deepest space, - would he? So tell us, what is the difference? Acceleration. No, the acceleration is the same, more or less. (Not counting the difference in distance from the Earth, or air resistance, etc.) The only real difference is that the astronaut has enough velocity (hopefully) to miss the Earth as he falls. That was a very revealing answer. Earlier in the thread you were confident enough about your position to question my lack of education. Now you seem to think that an object travelling at "x" miles an hour in a straight line ("headlong into space") has the same acceleration as a body travelling at "x" miles an hour in orbit. Actually, I was saying that any body under the influence of Earth's gravity will "feel" the same force, more or less. It doesn't matter whether its falling off a cliff, in orbit, or leaving orbit into space. The pull of the Earth is the same, adjusting of course, for the distance. It turns out that most non-technically inclined people think that these are three completely different situations (as they are, in some respects) but in all three the body is being accelerated by gravity exactly the same. Sorry Donal, that's physics. If you had taken a physics course, you might understand that. Your continued rant is making you look rather silly. It's probably time that you consulted your physics partner. Before you let him read what you have written, you should make sure that there is a cloakroom near the PC. Otherwise, have a potty close at hand - because he is really going to **** himself when he reads your words. Actually, my partner was given a PhD in Astrophysics only if he promised to continue as a programmer. How about my former boss, he won the Nobel Prize in Physics a few years ago. Haven't you ever seen astronauts floating? Yes.... but they are constantly changing direction.... and therefor they should be aware of the effects of acceleration. I must admit this subtlety has perplexed me - clearly the don't feel the G force, since it the same as a car in a tight turn. But I keep thinking it should be detectable, if only because the path is curving. Yeah. It's called acceleration - a bit like G-force. Please note that "a bit" = "exactly" in European understatement. He must feel a constant force as his direction of travel changes. I wonder if this has been documented on the Internet? http://science.howstuffworks.com/weightlessness1.htm That is a very simplistic explanation. It refers to the fact that the astronauts will feel the acceleration at take-off, and yet it doesn't seem to understand that a change of direction is also acceleration. We humans can detect acceleration. If you sit in an automobile with your eyes closed, then you can feel an increase or decrease in speed .... or a change of direction!! As the astronauts are subjected to a constant change of direction, I suspect that they might not feel that they are completely free-floating. Of course, from a General Relativity, Gravity Well point of view, the obital path is a straight line in curved space. I should know the answer here - let me cogitate ... No, you don't know the answer. Trust me. Despite my dreadful education, I am confident that someone who doesn't understand the basic principles of acceleration is incapable of getting their head around the TGR. Cogitation would be a complete waste of your time. OK, why don't you explain to us? How does someone in orbit determine they are travelling a curved path. No fair using outside references. No fair looking for effects over time. What sort of device will instantaneously tell you the local gravitational field? I'm not saying its impossible, but its not obvious. What does your physics friend say about this? He would probably deplore the lack of education in your country. Ask him anyway! Actually, it was Scout's friend. However, you should remember I majored in physics and worked for NASA doing spacecraft navigation. I may be rusty now, but 25 years ago I really knew this stuf! GULP!!! So why do you not seem to understand the difference between "velocity" and "speed"? Where did I talk about that??? You're losing it Donal. So, please explain to all of us: what is the difference between velocity and speed, and how was that relevent to anything I said? Perhaps, if you allowed him to read the thread, he might be amazed at your lack of reading ability. After all, I've already explained that I gave up Physics at an early stage. I haven't forgotton that. It was just a little dig since usually you Brits complain about our sorry education. Little digs are very welcome. I appreciate a good insult - and calling me "you Brits" is definitelay a reasonable insult. You're not lagging too far behind Joe! He called me a Brit about six months ago. Oh, sorry, I forgot. That explains your lack of education. |
All times are GMT +1. The time now is 03:36 PM. |
Powered by vBulletin® Copyright ©2000 - 2025, Jelsoft Enterprises Ltd.
Copyright ©2004 - 2014 BoatBanter.com