Hannu2

If you assume that target and projectile moves at constant velocities problem is relatively simple. You can make calculations in robot's frame of reference and take current time as t=0 moment. At first you can formulate a pair of equations for target. For example if target's position at t=0 is (ax,ay) and velocity (ux,uy) it is simple tx(t) = ax + ux*t and ty(t) = ay+uy*t. For projectile you get px(t) = vx*t and py(t) = vy*t. Now we have 2 equations for 3 variables, vx, vy and t at hit. Fortunately we know the speed of the projectile v and can write vx^2 + vy^2 = v^2. Now we have 3 equations. ax + ux*t = vx*t ay + uy*t = vy*t vx^2+vy^2 = v^2 Non linear equation systems are generally very nasty to solve but this is not. We can square 2 first equations and add them together. After little algebraic manipulation we get nice second degree equation for time. Generally you have 2 solutions and you can take one which is smaller positive (it means trajectories meet at future) and calculate vx and vy and aiming direction. If you do not have any positive t it means that projectile can not hit target (it happens if target's speed is larger than projectile's and geometry do not allow hit from front). Generalization to 3 dimensions is very straightforward. If yoy want to take target's acceleration or projectile's drag into account, things go very complicated very soon. If velocities are constant it is. With more realistic model it depends on many things. Usually one bullet is easy to avoid but that's why they use machine guns for aerial defense. Shoot few tens of bullets per second and give small deviation for individual bullets and target's day will be long and hard. I made decades ago a small game in which I flew simple craft in 2D world and tired to avoid and shoot enemy's machine gun turrets. They assumed that I have constant velocity and even I could dodge bullets I had to nerf their guns many times before it was playable.

Those lines and ideal lenses are oversimplifications (called geometrical optics). They can be used to understand very basic operation of single lense but real life is much more complicated and generally you have to solve Maxwell's equations with suitable boundary conditions, which are defined by lenses' geometry and material properties. Most lenses are for dispersion correction. Refractive indices of all real materials are dependent on wavelength which leads to chromatic aberration. It is managed to acceptable levels by using suitable set of different lenses made from different materials which dispersions cancel each other. Then there are lenses for correcting geometric errors (often aspherical shapes). And all corrections should happen at all focal distances (and lengths in zoom lenses). There are usually 10-20 lenses in several groups in modern camera lens which acts as single "ideal lens".

If density of atmosphere is 65 kg/m^3 it would not be a bad idea. Mass of 1 m^3 sphede made from 0.5 mm titanium sheet is about 11 kg. If it was filled with hydrogen at ambient pressure hydrogen would take about 3-4 kg and submarine or balloon or whatever would lift about 50 kg control systems and scientific payload. Or maybe also machine gun but it may take couple of decades before anyone on Earth think Venus is worth conquering.

Interesting articles, thank you for searching them. List of suitable metals seems to be very short and impractical. Titanium seems to be only option for large structures.

As far as I know that rain may happen high in atmosphere. But temperatures near surface are well beyond water's and sulfuric acid's boiling point and liquid rain can never reach the surface. It is difficult to say how dry acid vapor affects to metals based on corrosion in normal conditions on Earth. Usually dry acid vapors are far less corrosive than in humid environment. I planned once a reactor for semiconductor epitaxy. It used HCl gas in 316 stainless steel tubes at several hundreds of C and over 1000 C in quartz tubes. Trick was that it was extremely dry gas (2 % HCl in H2 if I remember correctly). A little bit water vapor in mixture and life of tubing had been minutes. I think sulfuric acid is also much less reactive on Venus's surface than water solutions commonly used in laboratory or industry. But I do not have an idea how just titanium can handle it.

I think he can but you have to pay the fuel. It would probably not achieve full thrust with fuel I need to keep my house warm a year (comparable to about 1.5 tons of methane).

Industrial standards will change when completely new products are developed. Single raptors have been tested but whole booster is too powerful to full duration full power static tests. Materials able to handle that stress probably do not exist. It is faster and cheaper to build flying expendable test objects than to development technomagical test stand for static test.

Probably. But if some capital investor bought Falcon 9 business, the price of launch would triple immediately and most of benefits of reasonable prices to industry would be lost for several years or even decades. Blue Origin seems to be maximizing profits instead of developing space tech and they would be happy if they could keep prices higher than SpaceX. Other companies need many years to develop large rockets.

I hope FAA officer who handle application of licensing external seat has enough KSP experience to understand that it is very natural and practical way to pilot space ships.

Money is very small compared to budgets of USA or European states. And public money is used very inefficiently to support high tech companies near top politicians. USA has SLS, ridiculous pork project, and ESA has even worse bureaucracy to force ESA order components from certain countries based on their payments - and not even working satellite launcher currently. Space race rhetorics is from space organization's leaders and officials who wants to lobby more money for their departments. Not from ministers or members of parliaments who has actual power to decide funding and is it used for results in space or political support for certain companies. I was impressed how Indian prime minister used his time to celebrate achievement. There has not been anything like that after Kennedy's speeches in 60's in western countries. Space is not an argument which gives votes in elections or funding from economic supporters.

Commercial operations can work on very limited applications in mature areas of technology. Now satellite launching and services are practically only enough mature space tech companies (and their investors) believe profitable in reasonable timescale and predictability. It seems that basic crew transportations and station services on LEO may be next but most customers will be public roganizations, like NASA or ESA. There is not much profitable business humans can do in space. If there will be "commercial lunar lander" it will be tailored project for NASA payed by state and it will never have any private customers. I can not imagine that there will be any commercial motivation to manned Moon research or asteroid mining in foreseeable future. Especially mining will probably be profitable at some day in very distant future, but it takes clearly many decades, if not centuries, and unpredictable amount of money to develop any profitable production infrastructure. No investor dare to put significant money on such things.

I fear that this is common problem for all western countries. Our politicians see space tech as futile money sink or excuse for subsidizing their hometown's high tech companies and do not take especially India's and China's space programs as serious competition. I do not know what prime minister of India said in his speech after successful landing, but if their highest politicians think that space tech and utilization of extraterrestrial resources is important for their countries development in foreseeable future there may be nasty surprises for western countries in next decades.

Or maybe target was 40 m at early planning but they had to make some trade off to get some scientifically more important. I think that number psychology works better for average consumers than astronomers or professional funders. This is true. They have probably ordered important parts from companies and made contracts. Modifications would cost billions now.

I have understood that worst problem is heat loss from plasma. If you put plasma in container with permanently cool walls it cools down and you have to input more energy than you get out. Energy output goes also through walls. Material which has constant temperature independent on energy flow could not conduct heat. Such material violates known conservation laws and energy produced in fusion would be lost. But as you said, such material would be excellent heat sink for all imaginable purposes.

So, that odd material converts all energy to hydrogen gas at some temperature (less than 1500 C) which metal has when it is activated. I do not see how that would lead fusion any easier than hydrogen gas taken from regular gas cylinder. You should still give hydrogen atoms huge energy somehow, which is the main problem. However, your material would be very nice for perpetuum mobile industry. You can cool it to 4 K and activate. After that it would be practically infinite cold sink. Any industrial power would produce just trace amounts on hydrogen which would be easy to ventilate safely away.