There a lot of talk about the idea of an Earth mass Primordial Black Hole punching through Earth and the effects of such an event. However, Planet nine is predicted to be about five Earth masses, not one.
I don't have a physics degree, but how close would Earth have to get to such an object before the Earth is within that object's Roche limit?
The Roche limit depends on the density difference between the two bodies in question. For a black hole (of any size), the density is basically infinite compared to regular planets, so the Roche limit is basically zero. As in, less than one meter.
The radius of the event horizon for a black hole even the size of Jupiter is only 2.5 meters.
The gravity field of a spherical object only depends on its mass and not its density/radius. So for the Roche limit only the density/radius of the object at risk of breaking apart (called minor object on wikipedia) (earth) should matter, not the one of the major object (black hole).
Wikipedia gives the formula d=R_m*(2m_M/m_m)^{1/3} which matches that intuition.
Yes, but you don't have to be within the Roche limit to have substantial tidal effects, which could destroy habitability at a much greater distance. Just look at Io.
Very close, in astronomical terms. At a guess, no further than the distance from Earth to the Moon, and probably much less. I'd love to see real numbers though. :)
Edit: According to https://en.wikipedia.org/wiki/Roche_limit the Roche limit d = Rm * (2 * MM/Mm)^(1/3) for Rm = radius of the satellite, MM = mass of the primary, and Mm = mass of the secondary. So in this case d = 6380 * (2 * 5/1)^(1/3) = 13,745km. In astronomical terms, very nearly a bulls-eye.
At a brewery, or a restaurant for that matter, aren't you there to basically recreate a product based on a recipe someone else formulated? The person tasked with creating the recipe has the opportunity to practice artistry in this scenario, but they, too, may be under business related pressure.
You're right, even the recipe makers can't escape business pressure to make undesirable products. With the hard seltzer craze going on (in the US at least), a lot of brewers are starting to make it. They didn't get into brewing to make hard seltzer, but they can't ignore the fact that they will sell well and are cheap to produce.
I'm currently listening to the Great Courses course called "Machiavelli in Context" on Audible, and his take was more that Machiavelli viewed monarchical rule as a stepping stone to a republic. In the Discourses on Livy, he gives the example of the people of the Roman Kingdom rising up to dethrone itheir king to establish the Roman Republic.
He goes on to say that, depending on the circumstances, a republic could backslide into monarchical or despotic rule, as the Roman Republic did when it transitioned into the Roman Empire.
The idea of a monarchy or a dictatorship being a stepping stone to a republic isn't something I see expressed online as much.
I'm taking this with a grain of salt. It's popular for fringe scientists to assert that gravity can be controlled via electromagnetism. I've seen a couple UFO schematics online over the years that use electromagnetism to play with gravity and produce thrust.
Also, my understanding of gravity is that it really isn't a force at all, but rather a warping of spacetime by an object with mass, which makes the concepts of a field a bit strange to me...
The author gives a good overview of the psychology of an anti-vaxxer:
1) Anti-vaxxers aren't paranoid misfits
TL;DR: Anti-vaxxers are normally rational people, but with an incorrect view on a topic.
2) It's all about fear
TL;DR: Anti-vaxxers hold their view out of an irrational fear, similar to arachnophobia, and simply using reason and facts won't work, as they're not in a frame of mind to accept them.
3) If you think something is dangerous, it's logical to avoid it
TL;DR: Though their starting premise is misguided, an anti-vaxxer's reaction to vaccines is logical. Thus, there is an emotional component in the initial premise that, when confronted with facts and reason, lead them to dig their heels into the sand and hold the line instead of thinking logically.
4) There's an industry supporting anti-vaxxers — and we're driving them into its arms
TL;DR: There are people positioned to exploit fear, and it is these people who are validating the anti-vaccination movement, despite various ethical concerns, and allowing it to thrive. Without these people, the movement would have died out shortly after it had started. Also, anti-vaxxers seeks support from loved ones and people who have experience with the subject matter to validate their worldview.
5) Changing someone's mind doesn't just take love. It takes empathy.
TL;DR: Anti-vaxxers come to their erroneous conclusion about vaccinations after bad experiences, not logic. The road to change minds is through empathy, not attack.
He makes an interesting quote in his article: "The anti-vax position was not a deal breaker for me, but suggesting that we should expose her daughter to grave dangers for no good reason was a deal breaker for my wife." This reasoning could (and arguably should) be applied in reverse: suggesting that we should expose children to easily preventable dangers (various potentially lethal childhood illnesses) for no good reason should be a deal breaker in any kind of relationship. While empathy could change an anti-vaxxer's mind, the dangers of having children unvaccinated while this strategy is employed is too risky, so a more direct approach, in my mind, must be taken. It's like trusting someone to drive you to the store while they're very drunk when it's better to never get into the car and to stop them from driving, if possible.
Likewise, he compares the anti-vaxxer movement to arachnophobia. His conclusion to drop his stance on vaccination doesn't logically follow from this comparison, however, as arachnophobia is a mental illness, treated by certified therapists when the phobia starts preventing people from living their lives or driving people to impact other people's lives. The logical conclusion to this comparison is to treat the anti-vaccination movement as a mental illness, encourage anti-vaxxers to seek out certified therapists, and enact laws to prevent people who don't vaccinate their children or themselves from spreading easily preventable but potentially life and quality of life threatening diseases.
I don't have a physics degree, but how close would Earth have to get to such an object before the Earth is within that object's Roche limit?