The question wasn't "why do protons have +1 charge", it was "why do protons have +1 charge, *considering electrons have -1 charge". The fact that possible charges are restricted to a few values is a much more satisfying answer to the latter than the former
Not so much for takeoff! Most rocket designs better than chemical rockets trade off thrust for specific impulse. That's an improvement in orbit, since delta-v is delta-v. But imagine a 10kg rocket- it's receiving ~100N of gravity. If your engine doesn't put out 100N of thrust you'll just sit there on the launch pad. As you pick up speed you no longer have to deal with that (after all, LEO has basically the same gravity and doesn't have to burn against gravity at all) but when you're launching off something other than a point mass, some of your thrust has to go towards ensuring you don't hit the planet, or you will not into space today.
The practical designs we have for NTRs are solid core, which after long effort got up to a thrust to weight ratio of 7:1, meaning they could in principle carry up to 6 times their weight and accelerate up in Earth's gravity rather than down. Chemical rockets can get 70:1. No one ever had plans to use NTRs in lift platforms- instead they could serve as more efficient upper stage engines, for orbit-orbit transfer burns and the like. In principle there are engines which are technically NTR and offer much better performance, but no one's ever gotten a working prototype. Also you probably wouldn't want to launch with an open cycle rocket, since the open part describes how the radioactive fuel is ejected out the rear. Unfortunately, with the technology we have, we have to make tradeoffs between efficiency and thrust. For the lift stages chemical rockets are, for now, unrivaled.
(Unless of course your nuclear propulsion is of the more, shall we say, entertaining variety. Project Orion has its proponents...)
When discussing potential alien civilizations, one can’t discount the existence of civilizations which exist on substantially more radioactive planets.
If the background radiation of earth was 100x higher, would we care about an Orion launch? Or a small nuclear exchange…
The more fuel you have to pile onto the rocket, the less the weight of the engine matters.
Using the chart in the accepted answer, launching with chemical engines takes 50 thousand tons at 3x gravity and 3 million tons at 4x gravity.
Now consider a theoretical engine that has a 7:1 thrust to weight ratio at 1G but sips fuel. Take a 25 ton engine, strap 10 tons of fuel to it and 1 ton of payload. Watch it go to orbit on a single stage.
A real NTR doesn't save nearly as much fuel, but it can still be useful in certain ranges.
I can't help but think that any species insane enough to use Orion drives in the first stage probably already found a way to blow itself up before it gets to that point.
And maybe I'm taking Terra Invicta too seriously but maybe they would wait until they figure out nuclear fusion and have more options.
It actually bottoms out pretty low though. The apparent fractal dimension changes over scales, but is sufficient that ruler length really does make a huge distance in coastline length
I think what you're referring to is the false proof suggesting that pi=4. That is not what squaring the circle is, and does not in fact become smoother and smoother but rougher and rougher
Sure, but you should only be using space heaters and not heat pumps (or non-electric sources of heat) if you're using them infrequently, at which point the cost of silicon over resistive wire is not worth it.
Large carnivores are kind of the pricey boondoggles of evolution. They work, they are successful, but they're balanced on a knifes edge. Every step a large carnivore takes consumes vastly more energy than it would cost a smaller animal. It is all too possible for such a creature to expend more energy pursuing small prey than it would get back. That is why lions don't hunt small game- they'll scavenge small game by driving off smaller carnivores from their kills, and they certainly won't turn down eggs if they find any, but they will not pursue prey beneath a certain size. Imagine trying to catch a rat with your hands- exhausting work, and the rat isn't much food
I was watching "Our Planet 2" on Netflix last night and they showed a pack of lions taking down a huge male cape buffalo. 3 min from start to meal time. Very efficient!
In analytic number theory we usually only care about growth rates in a very coarse sense- up to scaling by some constant, and asymptotically. Because the log of any base is precisely the same up to constants, it doesn't actually matter. If you look at the expression, to the right of the equals sign is a big O- that's the same big O as the one you might be familiar with in complexity.
That being said, in math more generally when we need a concrete log the natural log is pretty much always the way to go- I haven't seen ln in a little while.
