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The glaring error is the fantastic value for the tensile strength of steel. The tensile strength of steel is about 2500 MPa tops, OK let's assume super optimistically 5000 MPa. I have no idea from where you can get steel with a tensile strength of 200,000 MPa. Ignoring the payload, your formula reduces to $S = h\rho g$. Plugging in $h =$ 39,970,000 meters, $\...


11

Entering water at high speed is serious business already before reaching terminal velocity. At what height is it dangerous to jump into the water? Although risky, competitive high divers can enter the water from as high as 27 meters without injury, states Swim England. From this height, divers can reach speeds up to 60 miles per hour. However, serious ...


5

Perturbations in a medium resulting in the formation of black holes have been studied extensively in the context of primordial black holes, though to result from density perturbations in the early universe. There are plenty of analytical and numerical studies of the required amplitude of such perturbations $\delta_c=\delta\rho/\rho$ (e.g. Harada et al. 2016)....


3

Your space ship is limited to an inch long, unless you increase the cosmological constant a tad. The critical density of the universe is 9.9E-30 g/mL. The density of your liquid water universe is (before any subsequent cosmology occurs) 1 g/mL. That means that your rho/rhoc is about 1E+29. Put into this StackExchange problem and that means k=1E+58 (H/c)^2,...


3

The main factor in answering this question turned out to be the requirement for having hydrogen and helium being largely absent from the atmosphere. According to the principle of Jeans Escape, at a temperature of 288K/15°C, Hydrogen and Helium are not retained in significant quantities until the planetary escape velocity is in excess of around 15km/s. Since ...


2

This is not an exact answer, but so called "water worlds" may be the best candidates. Gliese 436 b is an exoplanet believed to be composed primarily of water. It's more than 4 times bigger than Earth and more than 21 times heavier, but its surface gravity is only 1.18 g Temperature, though, is too hot - about 439 °C, but this is a question of ...


1

Redoing your last equation, I got a figure of 2745 GPa (wolfram alpha link), which is quite a bit higher than your number. I'm not sure where the 85.8 GPa mentioned came from That said, I believe you also need a counterweight. Right now, the centre of mass of your system is pretty far from geostationary orbit because the mass of the cable is a lot more than ...


1

Exoskeleton Research While current research may not provide humans with super strength, it can augment and reinforce the abilities of the human body. Ironically, some of the most interesting research in the area addresses how people with injuries, not superhuman, can adapt. Unfortunately, because of the specificity of certain tasks, exoskeletons are not ...


1

In the general case, you can't, because there's no closed form of computing the vibration modes, except for the very simple and very uniform geometries. Even then some 'weird' function may need to be invented - for example, the vibration modes for a circular membrane will use the Bessel functions - which are defined as "they are the elementary solutions ...


1

Use a protoplanetary disk According to this paper, the accretion luminosity of YLW 16B is somewhere between 0.31 and 0.64 times the luminosity of the star. (A different protoplanetary disk is shown in the link above, but you get the idea) Your planet orbits in a gap in the disk, seeing only a portion of it, but from very close by, so it seems just as bright ...


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