Jamie123

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Everything posted by Jamie123

  1. Jamie123

    If the Earth were hit by a comet...

    Not at all. You can prove it from first principles without memorizing any data whatsoever. I'll attempt the proof textually: Before impact the moon is in a circular orbit so the centripetal force mv^2/r=GMm/r^2 where v is the moon's velocity, r is orbital radius, m is the Moon's mass and M the Earth's mass and G the gravitational constant. This gives us v^2=GM/r so the Moon's kinetic energy mv^2/2=GMm/2r. Now the energy needed to escape the Earth is the integral between r and infinity of GMm/r^2 which is GMm/r, so we halve this (since only half the Earth is left) to get GMm/2r - which by a startling coincidence is exactly how much kinetic energy the moon has.
  2. Jamie123

    If the Earth were hit by a comet...

    You got it! Theoretically - and with the assumptions made - the moon would only just escape. To prove this you only need the inverse square law and the formulas for kinetic energy and centripetal force and the fact that gravity is proportional to mass. Oh - and you need basic integration too. I'm not sure that counts as "astronomical trivia". Next time I have access to a scanner (probably Monday) I'll scan and post my own solution. If it were "moved away" very rapidly - in a time too short for the moon to significantly respond before the missing portion were too far away to have any gravitational effect, and if none of the momentum were transferred to the remaining portion then it would in effect have "vanished". Its not very likely - for one thing i suspect the "comet" would need to be terrifyingly large and travelling close to the speed of light - but it's the only way (I think) you can get a precise answer out of this - but like you rightly point out that answer has to be qualified. I think it's quite a good question - though not as far as eliciting a cut-and dried answer - but it does force you to make the best of incomplete information - something a scientist very often needs to do.
  3. Jamie123

    If the Earth were hit by a comet...

    This is assuming that the path of the moon remains circular, with a larger radius. The sudden reduction in centripetal force would cause the moon to recede, but its path would no longer be circular. It's exactly the same situation as when a satellite breaks out of low earth orbit when it fires its second stage booster - and enters an elliptical transfer orbit to its higher (permanent) orbit - but it still remains gravitational bound to the Earth. The only difference here is that instead of gaining kinetic energy, the moon suddenly needs less kinetic energy than it already has to maintain its circular path - so it continues in a non - circular path just as the satellite does. The moon's trajectory still bends towards the earth slowing as it converts its excess kinetic energy to potential energy. But given that exactly half the gravitational force has gone, will it eventually curve around and come back?
  4. Jamie123

    If the Earth were hit by a comet...

    I quoted "impulse" directly from the original and (if you'll excuse me contradicting you) I think it makes sense. Impulse means force acting over time and is equal to change of momentum. The force of a comet's impact acting over the duration of that impact would equal the change of momentum of the fragment knocked off the Earth. It's already been pointed out there's no comet big enough to do that but I agree it's not really a very realistic scenario being proposed anyway.
  5. Jamie123

    If the Earth were hit by a comet...

    If you make the simplifying assumptions that (i) the Earth does not accelerate around the Sun, (ii) the Moon's original orbit is exactly circular, (iii) the mass of the Moon is negligible relative to that of the Earth so the Earth does not "wobble" due to the Moon's gravity - then the answer I got is so elegant I think it must be what the examiner was looking for. (Though who knows - maybe there were extra marks for pulling the assumptions apart!) P.S. Having thought about it a bit assumption (ii) may not be necessary to get the same result - but the maths for an elliptical orbit would be a lot more complicated I suspect.
  6. Jamie123

    If the Earth were hit by a comet...

    I agree - it's a badly worded question. It would make more sense to say "if a wizard waved a magic wand that made half the mass of the Earth suddenly disappear". To make the situation sound a bit more feasible, the examiner has suggested a situation which creates a lot of ambiguity. It reminds me a bit of this Kenny Everett sketch: https://www.youtube.com/watch?v=DCNJNAJtpCk
  7. Jamie123

    If the Earth were hit by a comet...

    I think I get part of what you're saying - at some points on the Moon's orbit it would receive a "slingshot" effect of the Moon's velocity plus the Earth's, while at other's it would be the Moon's velocity minus the Earth's. This is quite true and it is why rockets are generally launched from near the equator in the direction of the Earth's rotation - to get an "assist" from that rotation. However, if we are concerned with moon's orbit relative to the Earth (rather than to the Sun) I don't think this is relevant. For practical purposes we can assume the Earth-Moon system to be in an inertial frame of reference
  8. Jamie123

    If the Earth were hit by a comet...

    I think that the change is instantaneous. (We are not told this explicitly, but if the change were gradual we would need more information to do any calculation.) Also I think we can reasonably model the Moon's regular orbit as circular (which it very nearly is) - in which case its velocity is always at a right angle the line between Earth and Moon.
  9. Jamie123

    Prince Andrew

    If you had been brought up in England and your family was not particularly anti-monarchy then you would get it. To "Middle England" (by which I mean the conservative middle and upper-working classes) the royals are seen as a kind of extended family. People gossip/winge about them in the same sort of way they do about Uncle Jim or Aunt Jenny. (Right now Prince Andrew is the "disgraceful uncle" who's brought embarrassment on the rest of the family.) As a kid, listening to the way grown-ups talked about the royals, I sometimes vaguely felt they really were our relatives.
  10. Jamie123

    If the Earth were hit by a comet...

    That's what I thought too - but the big question is would it drift away permanently, or would it stay in a captive orbit around the remaining fragment of Earth?
  11. Jamie123

    Prince Andrew

    Actually that set me thinking. The origin of the Crown Estates is not something I ever really thought about before, and it's an interesting question. It seems that in the general "tidying up" that followed the Norman Conquest, all land which was not otherwise spoken for was assumed to belong to the king. (What they did in Anglo-Saxon times I don't know; perhaps all unclaimed land was "up for grabs" - though I daresay it took a brave man to set up on his own with marauding vikings rampaging everywhere. Better to stay on your local theign's land where you had some safety in numbers.) I suppose this could be seen as a "spoil of war" since William had to fight Harold for the throne - though that's hardly the way he would have seen it himself. (He was claiming a throne he considered rightfully his anyway, regardless of whether his invasion had been successful.) But let me ask you this: when the pioneers moved west across America, claiming lands which had previously belonged to the Native Americans, were they not claiming it on the basis of "class" membership? (White Europeans as opposed to red-skinned "Injuns".) And when Andrew Jackson forced the Cherokee's off their land and onto the "Trail of Tears" was he not stealing land from one "class" of humans in order to give it to another? Are the people who now "own" that land now having that ownership questioned because it was originally seized from a different class of people in order that they could have it?
  12. Public Christmas decorations are a pale shadow of what they used to be, because everyone is terrified of "offending" people who are not Christians. (Not that most actual Jews, Muslims, Hindus, Buddists and Sikhs ever are offended by them - they know that although they do live here, this is still a Christian country. It's a bunch of virtue-signalling tub-thumpers who want to make a name for themselves by demanding "inclusivity" and the kind of "tolerance" that never tolerates anything but itself.) (Yes I know that's nothing to do with employers refusing to employ Christians. I was just doing a bit of tangentially-relevant tub-thumping of my own.) But having said that, what about your man Ken Ham and his replica "Noah's Ark" in Kentucky? He refuses to employ anyone but Christians. (And when Ken Ham uses the word "Christian" he's not referring to you or me!)
  13. Jamie123

    "Well Behaved Women . . . "

    It reminds me of this quote from C.S. Lewis' The Great Divorce.. The protagonist (a fictionalized Lewis) has a dream of arriving in Heaven, where he meets his literary hero George Macdonald. While they are talking, a lady approaches them: We learn as the story goes on that Sarah Smith was a very ordinary housewife who was kind to everyone. Every boy felt like a son to her, and every girl a daughter. In our world she was a nobody, but in Heaven she is one of the "great ones".
  14. Jamie123

    Prince Andrew

    Absolutely! What I don't agree with is that this is more true for Americans than it is for the British. OK you can point at people like Boris dePffeff[whatever] Johnson and say that his current position as PM had something to do with his privileged upbringing...Eton...Oxford etc. But I could just as easily point at George W. Bush and say the same thing. And sorry to keep banging on about Lord Sugar, but he started his career selling car radio antennas out of the back of a van which he bought for 50 quid.
  15. Jamie123

    Prince Andrew

    I don't know any nobles, but if I did I would call them "lord" or "lady" because that's what their title is. I wouldn't tug my forelock or grovel on the ground. As for the royals you're talking about the civil list. Yes that money does come from taxes. What *you* don't seem to realize is that in return for that, the government gets all the revenues from the crown estates. The only way you're going to get around that is saying that "all property is theft" and those estates belong to the country anyway because the royals (ore more precisely the Queen) didn't work for them but inherited them. But Americans have no problem with inherited wealth so....yah boo right back at you, sister!! 😛
  16. Jamie123

    Prince Andrew

    Really? Are you telling me that anyone with "Lord" or "Lady" in front of their name is siphoning money out of my pay packet? That's news to me!
  17. Jamie123

    Prince Andrew

    As a matter of fact they do...somewhat. The hereditary peers are allowed to elect 93 of their number to sit and vote in the Upper House. But compare that with the 600+ life peers who were NOT born noble. Tony Blair tried to get rid of the hereditaries altogether, and the residual 92 were a temporary compromise he had to agree to. Their days are numbered - I reckon in another generation they'll be gone and irrelevant. Even now we don't think about them anything like as much as you seem to think we do. Oh yes...absolutely. Every morning I put on my peasant's smock and go down to Lord Muck's pig farm, tug my forelock and say "OO arrr m'lord do you want me to shovel away all last night's pig muck, and then polish all the piglets shiny with patent piglet polish?" Actually he was a prince, not a noble. (He only got a noble title after the marriage.) But your point is...? You can lose a peerage. It's uncommon, but it does happen. You can do it voluntarily: Alec Douglas Home gave up his title Earl of Home in 1963 so he could stand for election to parliament. Tony Benn (Lord Stansgate) did the same thing the same year. Admittedly it is very uncommon for a peer to be stripped of their title involuntarily, but I think sooner or later there will be laws to allow this to happen more often. (A lot of people thought it should have happened to Jeffrey Archer after he got convicted of telling porkies in court!) Also marrying into the peerage doesn't make you a substantive peer. If you were for example to marry Lord Muck you could style yourself Lady Muck - but it would be a title and nothing else. Most peers of any importance these days are life peers - they were appointed by the government and they vote in the Upper House. The closest equivalent to them are the US Senate. To some very limited extent yes - but it's rapidly becoming a permanent nothing. If you don't have money and lands, what does it actually mean to be an Earl or a Marquis? Most of the great country estates collapsed during the 20th Century, and the few who are left are strapped for cash. Many had to marry into rich Anglophile American families to stay afloat. *BUUURRPP* It's a fing that's used to create objects, innit? 😁
  18. Jamie123

    Prince Andrew

    I'm curious - how much experience do you really have of English society?
  19. Jamie123

    Prince Andrew

    I don't disagree, but the same thing is true in the uk. Look at Thatcher - ok she didn't come from the "dregs" of society, but she wasn't born with a silver spoon either. Her father was a simple shopkeeper. And look at Lord Sugar - do you think the way he speaks mark's him as an aristocrat? True you cannot be a king or queen without being born to it, but just about everything else is as accessible to the "low born" as it is in the us.
  20. Jamie123

    Prince Andrew

    In theory for sure, but do think George W Bush would ever have become president if his father hadn't been before him?
  21. Jamie123

    Prince Andrew

    Well the official spin is that he "asked the queen" if he could take a break from his royal duties and she agreed. But...who knows?
  22. Jamie123

    Prince Andrew

    Curiously enough, "back in the day" kings (and probably queens too, though I don't suppose they advertised it quite as widely) had personal butt-wipers. The king's butt-wiper was called the Groom of the Stool, and despite what you might expect it was the job everybody in the palace wanted. The advantage was that you got to be alone with the king, and you could tell him who you thought ought to get "the chop" without having them interrupt you!
  23. Jamie123

    Masculine hair question

    Samson didn't cut his hair, and he brought the house down!
  24. Jamie123

    Hook, line and sinker

    Solar furnaces have certainly been around for a few years. I remember seeing something about them on TV back in the 1970s. Also "back in the day" Archimedes invented a weapon to defend Syracuse from the Romans, by concentrating the rays of the sun onto attacking Roman ships, causing them to burst into flame. He also invented a giant mechanical hand which reached out to sea, grabbed enemy ships and tipped them upside down: Amazing!
  25. Jamie123

    Anne Sacoolas

    https://www.independent.co.uk/news/uk/home-news/jeffrey-epstein-prince-andrew-bbc-interview-extradition-investigation-latest-a9208171.html What Anatess proposed as a thought-experiment could be coming true!