Jamie123

I think you're right - it's a sloppy formulated question, but that can have its advantages. It helps examiners separate the duller candidates - the sort of people who give lazy answers like "how long is a piece of string?" - from those with a spark of inquisitiveness and speculation. A better candidate will think "OK I don't have all the information I would like, but maybe if I make some assumptions I can still go somewhere with this!"

I think Jamie, Mores, and Scott have covered it pretty well.
From a modern perspective, the question is poorly worded, starting with the laughable (from a modern perspective) idea of a comet knocking half of the earth's mass away. Then there is the confusion as to whether the earth's loss in mass is effectively instantaneous, and if not, whether the mass left the earth along the axis of the moon's orbital plane or whether it was more along the plane. And, of course, the whole thing is silly, because any impact with enough energy to literally strip away half of the earth's mass would undoubtedly create a condition where the remaining earth was reduced to a rubble cloud, one that would then eventually recoalesce, almost certainly including the moon in its body. The moon would likely become the new center of accretion; it could hardly avoid being pelted by very large pieces of the earth's rubble cloud.
Jamie's proposed amendment is much better from a modern perspective: What if Harry Potter magically vanished away half of the earth's mass? As has already been discussed. it looks like the result would be indeterminate, with a good probability that the moon would escape the remnant earth's gravitation. Except, again, that's not a good answer if you take it further. Because the moon will still remain in the same basic orbit as it was with the earth, and the remnant earth will likewise remain in that same orbit. Both orbits will probably become somewhat elliptical, but they'll stay in the same general area, with their orbits intersecting at one or two points. So it's only a matter of time until the moon collides with the remnant earth or rubble cloud, and eventually you'll get a new, much smaller planet where the earth once orbited.
The first rule of solving any physics problem is to know what is being asked for. A probem like this is hard exactly because it's not clear what's being asked for. In this case, the difficulty is more precisely that you're not sure what the assumptions are supposed to be, and until those assumptions are clarified, you're not likely to arrive at a good solution.

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.

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".

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.

That's a very interesting thought, but also very odd in other ways.  Most of that territory you are discussing was obtained by treaty.  Thus, legally, one could argue that the territory thus was granted or given by treaty and legal treatise.
However, the ethics of it could also be called into question, that when a treaty is signed under duress or under lack of ability and knowledge, is the treaty legal?
The US would say that it IS legal in that they can obtain that which is legally given.
However, the next thought is whether the inhabitants even had the ability to give land that they themselves claimed was not theirs to give...OR, in other instances had been claimed by them without giving the other parties or inhabitants the process to object or deny such claim?
The Utah territory could be seen as both claimed by parties by force or by withholding the ability of objection to the parties that controlled that land, OR, later, by treaty to those that were under ignorance or force, OR, later...by treaty between those that claimed these lands in giving it to the US (by force one could claim).
On the otherhand, when ever land is ceded by treaty ending a conflict or war, that treaty is in most instances seen as binding.  A question not asked by you, but could be raised, is if the original parties ceding the land never truly legally obtained it by treaty but instead by claim and force...could they legally cede that land away again to another party that forced them to do so by treaty?
I would not say it is so much as class that gave them the ideas that they legally had hold of the land, but more of force and the ability to enforce treaties of claim.

Wish me luck! I'm off to inform the missus that I've formally adopted this title for domestic use.

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!)

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? 😁
 

😄
My attempt was not not one-up the US over the UK. My point was to describe why America matters, at least in my mind. Is it because we're insanely rich? No, that's not America's value to the world, and it's not really the promise that America gives, no more than Hollywood films are. Americans are not better, more valuable human beings than anyone else, and nor is America as a place more holy than other places. I believe America has been uniquely blessed, and I want to believe that Americans have given some great gifts to the world that makes the population of the whole planet better off than they would be without an America. That's what I'm trying to express.
Americans speak English, a language we inherited from, well, England. Our law (indeed, the law of the western world) is based on English common law. Our very Constitution is inspired by and, really, based on English documents such as the Magna Carta. Our Founding Fathers were a bunch of Englishmen that wanted to put into practice some English (and French) ideals in their own country, a place where the government would not tax everyone and give part of the proceeds to the Church of Whatever Nation We're In. America took in English and other important European political and societal ideals and used them to form a new government, built on what came before but much different. And if the experiment was far from uniformly successful, I believe it was nevertheless enormously successful, standing then and now as a beacon to the world.
I am not saying the UK is evil, and heaven knows I'm not saying the US is perfectly good. Far, far from it. But the specific point I was making there was that class distinction has been a huge thing for literally centuries, probably millennia, in Great Britain, and continues to be so, if not as visibly. The US was founded on the principle rejecting that sort of formal political class distinction. We aren't entirely free of it, but I do think that overall, we show great improvement from our English ancestors.
Again, my point is not to compare the US with the UK, but to argue that the US stands for something noble, or at least is supposed to. And despite the remnants of an ancient political system that I consider corrupt, I see your Queen as attempting to do something that may be personally uncomfortable or even excruciatingly painful for her, but for what she sees as a higher purpose. Such an action strikes me as admirable, indeed as—dare I say it?—noble.

I knew it.

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? 😁
 

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

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.

On 23 Nov 1963 President Kennedy was assassinated. 5 days later on Thanksgiving morning my little sister Karen Louise  [Sept 8 1953 - Nov 28 1963]passed away from a brain tumor.
It has been 56 Thanksgivings ago. It took nearly a decade of thanksgivings for me to see them in gratitude and true thanksgiving, rather than as a holiday that my little sister no longer would be with us.
Christmas' were really hard too. As were her birthdays. Easters, Halloween, our siblings birthdays, Mom & Dad's birthdays and wedding anniversaries.
Karen brought a lot to the table in our home. She and I fought like most siblings do. She was a *dirty* fighter too ~ she would get me pinned down and then tickle me until I wet my pants. 😷
I once heard Mom telling the neighbor that Iggy and Karen were like two peas in the same pod. We would finish each others sentences, we were always together -arm in arm. She loved pedal pushers and I loathed them. Karen would initiate playing with others and if the little kid next door wanted our toys, she would just give it to them! I would run to Mom so she could get it back, and Mom would say - Give it time, they will put the toy down and then you can get it back. Karen instinctively knew this - how? She was 15 months younger than me, so how did she gain this knowledge?
Karen also knew that she would die. After her brain surgery, she talked about Jesus and the Angels that were always surrounding Him and us. I was too young to understand that she was trying to ease the road for me, us. She was saying goodbye and doing her level best as a loving10 year old to let me, us, know that she was going to be okay. That she was going to be living with Jesus and Heavenly Father and all the Greats and Grands.
The hole in my universe that ripped open the day she passed away is still there. For years and years I never thought the rawness would ease up. It has. Don't know exactly when the jaggedness smoothed out but it has. 56 years later it is a hole, a smoothed edged hole.
In those 56 years there have been so many more of my family members who have passed away. They are there with Karen and the Greats, Grands, family members, Jesus and Heavenly Father.
Karen was 10 when she passed. The proxy ordinances of baptism, confirmation, and sealing to our parents have been done. In June of 2001 I was sealed to our parents. The eternal link to my little sister and all my kindred dead is solid and it is now my responsibility to live my life in accordance to the gospel and obey the covenants I made with Heavenly Father and I will be joined with my eternal family.
On all of these holidays the knowledge of the Plan of Salvation brings me peace.

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.

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!

I'm not going to say anything about Epstein, or if Randy Andy (as they used to call him) did anything naughty in his house, or on his island, or anywhere else. I don't know whether he did or not, and I've no way of finding out, so I'm not going to talk about it.
What does bother me though is the way everyone on TV keeps banging on about how he's the Queen's "favourite son". How anyone knows that either I don't know, but ideally, a good mother doesn't have a favourite son/daughter. She loves all her sons and daughters exactly the same.
Of course, we're all only human and some of us are bound to love some of our kids more than others - but that's a fault us. It's something we should strive to avoid.
All this "Queen's favourite son" stuff is basically saying: "Yah! Boo! The nasty old Queen's a horrible favouritist!"
Which isn't very nice!

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!

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!

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!

I've been a subscriber to Physics World for many years now, and these days it always comes with an extra "Focus" magazine. This month's is all about computing - with the Internet of Things, Raspberry Pi and (naturally) quantum computing. It starts with this very interesting graph:

When a new technology is proposed, expectations are high, but as it is developed problems emerge and the hype falls off. Quantum computing is just one example. When I was an undergraduate everyone was talking about "optical computers" - then it was "molecular electronics" and goodness-knows what else. Do you ever hear of these things now?
However, if enough researchers continue to pursue an idea, the problems are gradually overcome and the technology does achieve usefulness.
I felt sure I'd seen this before, and sure enough it's the well-known Dunning-Kruger graph:
 
In case you don't know, the Dunning-Kruger effect is the idea that a people who have a little knowledge of something have an inflated confidence in that knowledge, and that confidence wanes as they learn more. Dunning and Kruger were inspired by the peculiar story of McArthur Wheeler (which you'll easily find on YouTube or Google) but Alexander Pope was also familiar with the phenomenon:
When I post things here, I'm usually at the peak of Mount Stupid. That's because I've been here long enough not to be worried about looking stupid, and I know full well that someone like Vort or Anatess (particularly Anatess) will at least try to help me down the other side. Some people (I think Mores is in this category) take me a bit more seriously than I would wish, but everyone here always helps me get a wider perspective on things. (Even of I don't always change my views!)
I really appreciate everyone on this forum - thanks!

I've been a subscriber to Physics World for many years now, and these days it always comes with an extra "Focus" magazine. This month's is all about computing - with the Internet of Things, Raspberry Pi and (naturally) quantum computing. It starts with this very interesting graph:

When a new technology is proposed, expectations are high, but as it is developed problems emerge and the hype falls off. Quantum computing is just one example. When I was an undergraduate everyone was talking about "optical computers" - then it was "molecular electronics" and goodness-knows what else. Do you ever hear of these things now?
However, if enough researchers continue to pursue an idea, the problems are gradually overcome and the technology does achieve usefulness.
I felt sure I'd seen this before, and sure enough it's the well-known Dunning-Kruger graph:
 
In case you don't know, the Dunning-Kruger effect is the idea that a people who have a little knowledge of something have an inflated confidence in that knowledge, and that confidence wanes as they learn more. Dunning and Kruger were inspired by the peculiar story of McArthur Wheeler (which you'll easily find on YouTube or Google) but Alexander Pope was also familiar with the phenomenon:
When I post things here, I'm usually at the peak of Mount Stupid. That's because I've been here long enough not to be worried about looking stupid, and I know full well that someone like Vort or Anatess (particularly Anatess) will at least try to help me down the other side. Some people (I think Mores is in this category) take me a bit more seriously than I would wish, but everyone here always helps me get a wider perspective on things. (Even of I don't always change my views!)
I really appreciate everyone on this forum - thanks!

Did you know she's afraid of sea urchins too? 
 

Who?