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I'm gonna write some things based on high school physics. Suppose we need to send a person to the moon. Then, we need to calculate two things, the speed v and the angle $\theta$ with which the spacecraft should be launched.

Suppose we have considered all the factors like gravitational forces of Earth and moon and sun and of other planets also and taken into consideration Earth's rotation and all other factors and have calculated accurate values of these two quantities. I don't know what the accurate value of v will be but since escape velocity is 11.6Kmps and moon is much closer than infinity, so let's take v=5Kmps.

Now, for the spacecraft, all we need is a strong box, maybe of iron, having necessary oxygen and food for the astronauts. We just have to launch this box with the astronatus inside at 5Kmps. If the combined mass of astronauts with the box is 1000 Kg. Then, the kinetic energy of the spacecraft will be 1.25*$10^{10}$J. So, we have to do this much work on the box.

But now we have nuclear energy, so we don't really need to burn diesel or natural gas. 1/5g of uranium-235 can produce more than that. And then we just need to supply that heat to a high specific heat capacity to raise its temperature, transfer that heat to a very cool temperature body like very cool ice, so that the efficiency of the engine is maximum and we'll obtain the work required from that heat engine. Maybe such engine will hit the box of astronauts with tremendous force.

But we can minimize the force by a hydraulic lift. The engine will push a piston of larger area with great force through smaller distance and hence the piston of smaller area will hit the box with less force through a larger distance. So, the box will get the required energy.

If this is not a feasible idea, then what are some corrections that you would apply to this? I think that the apparent weight of astronauts when the box is accelerating is not a problem, because we can use magnetic suits and magnets to balance the pseudo force and keep their weight normal. I'm only minimizing the force to the extent the material of the box can endure and not according to the weight experienced by the astronauts.

The wikipedia article says that the working stress for AISI 1018 Steel with a 4 factor of safety is 110MPa. So, if our box is a cube made of this material of surface area, say, 5m$^2$, then it can endure a force of 550MPa, which means an acceleraton of 550 Kms$^{-2}$ for our 1000 Kg box. But our magnetic forces are limited, so we'll somewhat minimize this force by some orders of magnitude, so that 11Kmps is reached over a convenient distance on the second piston and such that our magnetic forces can somewhat cancel the pseudo force. Does anyone have an idea for landing?

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  • $\begingroup$ Vote to move to Space Exploration. $\endgroup$ – StephenG Jan 2 '17 at 14:59
  • $\begingroup$ @Kyle Kanos: Please don't ban this post or something. Please edit yourself whatever you feel is unnecessary. $\endgroup$ – Dove Jan 3 '17 at 1:49
  • $\begingroup$ @Kyle Kanos: I've already removed all the things about cost analysis from the post. If there's still something wrong, please edit it. $\endgroup$ – Dove Jan 3 '17 at 2:03
  • $\begingroup$ Jules Verne has a quite a discussion of this problem in "A Trip to the Moon". His launch method is nearly identical to your long piston. $\endgroup$ – C. Towne Springer Jan 3 '17 at 2:06
  • $\begingroup$ @Kyle Kanos: I don't think talking about applications of sciences should be against the rules. So, if there's some way to have this post on-topic, then please edit whatever is against the rules, otherwise leave it. $\endgroup$ – Dove Jan 3 '17 at 2:13
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I don't know what the accurate value of v will be but since escape velocity is 11.6Kmps and moon is much closer than infinity, so let's take v=5Kmps.

Mistake number one. The delta V cost to launch traditionally into low Earth orbit is about 10 km/s. The delta V cost to get near the Moon is almost Earth escape velocity. The delta V needed to land on the Moon is more than Earth escape velocity.

Now, for the spacecraft, all we need is a strong box, maybe of iron, having necessary oxygen and food for the astronauts. We just have to launch this box with the astronatus inside at 5Kmps. If the combined mass of astronauts with the box is 1000 Kg.

Mistake number two. "Just" is one of the most dangerous words in engineering (and software development, for that matter). Unless that box carries a rocket and propellant, you "just" smacked that box into the Moon at at least 2.4 km/s. Your box needs to be a lot bigger in order to softly land the box and its content on the Moon. It needs to be considerably bigger yet if the people in the box are to come back to Earth.

Maybe such engine will hit the box of astronauts with tremendous force.

Maybe? That's mistake number three. Suppose we want to accelerate an object to 11 km/s via a rail launcher / big gun / piston / whatever, while keeping the acceleration to 30 m/s2 (a bit over 3*g*). The rail launcher / big gun / piston / whatever would have to be over 2000 km long.

Now we have yet another problem, which is atmospheric drag. Objects going at Mach 5 a dozen kilometers or so above the surface of the Earth have a nasty tendency to melt. Orbital velocity (low Earth orbit) is Mach 25 or higher. Your 11 km/s is Mach 32 at standard temperature and pressure. The heating rate due to atmospheric drag is roughly proportional to the cube of velocity. An object going at Mach 32 at STP accumulates heat at 260 times the rate needed to start melting things.

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  • $\begingroup$ Do you have some remedy for this atmospheric drag problem and for the landing? I've solved the 'long piston' problem in the edit of my question. $\endgroup$ – Dove Jan 3 '17 at 1:29
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    $\begingroup$ @Dove -- You most certainly have not. 550 km/s^2 is 56000 gees. Electronics can withstand perhaps 20 gees, maybe 100. The healthiest of humans can withstand 10 gees, but only for a very, very short period of time. Healthy humans have problems with 3 gees for any extended period of time. (Several minutes is an extended period of time.) Your 56000 gees has turned the humans aboard into a puddle of protoplasm and has shorted out every bit of electronics on the spacecraft. $\endgroup$ – David Hammen Jan 3 '17 at 1:37
  • $\begingroup$ @Davod Hammen- There are close to no electronics on my spacecraft. It's just a steel box which can endure 110 MPa. I don't know what gees is but if it has to do with the tremendous accleration flet by astronauts, then I've written in thw edit that magnetic suits acted upon by electromagnets can minimize that. And, we don't actually need 550Km/s^2 acceleration. We just need to get to 11Kmps over a convenient distance maybe over an accleration of 200m/s^2. I think electromagnets can safely counter that force on the astronauts. $\endgroup$ – Dove Jan 3 '17 at 1:46
  • $\begingroup$ @Dove - One gee is 9.80665 m/s^2. There is no shielding from acceleration. Humans cannot tolerate anything more that 100 m/s^2, or 0.1 km/s^2, and only for a second or so. A bit longer than that and they black out. A bit longer yet and they die. Crewed spacecraft are g-limited to 3 gees, for good reason. $\endgroup$ – David Hammen Jan 3 '17 at 2:03
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    $\begingroup$ @Dove -- No. You don't feel fictitious forces, and there is no electromagnetic force on the astronauts (your iron box shields them from that; google Faraday cage). There is an electromagnetic force on the box, which results in a normal force (a very, very large one in your case) on the astronauts. It is this normal force that kills them. Switching to a non-inertial frame to obfuscate things doesn't make that force go away. $\endgroup$ – David Hammen Jan 4 '17 at 2:57
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First, the Moon is actually quite "close to infinity".

The minimum velocity can be calculated from energy conservation. I.e. you start with some velocity $v_0$ at Earth radius $R$ and end up with Moon's orbital velocity $v_m$ (so that you were in rest in Moon frame of reference) at its orbit $r$, then energy conservation reads, \begin{equation} -G\frac{Mm}{r}+\frac{mv_m^2}{2}=-G\frac{Mm}{R}+\frac{mv_0^2}{2} \end{equation} However $R/r\sim 60$ and because of that the potential energy at Earth radius $G\frac{Mm}{R}$ happens to be much higher than potential energy at Moon's orbit and corresponding kinetic energy. If you calculate it, you'll get $v_0$ about $50$ m/s less than Earth escape velocity which is about $0.5\%$ difference.

Then when you approach Moon it's gravity starts playing and in practice considering ship approaching Moon from infinity is good approximation too. So no matter what you do at Earth, the ship will approach Moon surface with approximately its escape velocity about $2.4$ km/s.

Now what you should remember when you talk about launch and landing is that humans are quite squishy. You can have very hard ship but it's acceleration felt by humans that's important in the end. Let's take $10g$ as maximum "safe" acceleration.

Now your ship may have bumper. When ship lands bumper's front hits surface first and as it deforms slowers the crew cabin. Let's assume that all this time crew cabin has $10g$ acceleration. The problem is that to slower from $2.4$ km/s with this acceleration one needs about $t=\frac{v}{10g}\simeq24.5$ s. In that time the ship will travel $10g t^2/2\simeq 29$ km. So to slower the ship with bumper it has to be at least $29$ km thick... Even worse with your piston dampering the hit at the launchpad idea because now you have to take $v\simeq 11$ km/s.

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  • $\begingroup$ The large pseudo force can be somewhat balanced by electromagnetic force on the magnetic suits of astronauts, so apparent weight isn't much problem. I'm minimizing force only to the extent the material of the box can endure which is very high for some materials like AISI Steel. So, we can have quite large acclerations as soon as we have electromagnets to counter them. $\endgroup$ – Dove Jan 3 '17 at 1:36
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    $\begingroup$ @Dove Suit accelerating at 10g feels as unpleasant to your body as a seat accelerating at 10g. $\endgroup$ – kubanczyk Jan 5 '17 at 16:50
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    $\begingroup$ @Dove your electromagnetic idea cannot work. Even if you could provide some magic force to counteract the acceleration of the astronauts, you might want to keep in mind that a non-accelerated astronaut is not going anywhere, and an astronaut who accelerates at a different rate than his vehicle is going to have a very close encounter with one of its inner surfaces. $\endgroup$ – Organic Marble Jan 5 '17 at 23:15
  • $\begingroup$ The 'vaporization against air' problem can be overcome by going BIG. Make the vessel a really heavy, sturdy, long slug of metallic ablative composite, with the empty space (cabin) occupying a relatively small volume inside. Ablation prevents heat from penetrating too deep too fast. Huge mass vs small crossection efficiently combats air drag. Of course problems of contents not turning to liquid at impact of the shockwave remain, never mind any cost efficiency goes out the window. $\endgroup$ – SF. Jan 6 '17 at 14:01
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You need to leave atmosphere with 12.52 km/sec to reach the moon. You need to leave the atmosphere with 12.61 km/sec to reach infinity.

In addition you have to shed 2.55 km/sec of velocity that you will get from the moon as you fall towards it. You actually need more than this as once you light your rocket you start taking gravity losses. With a sufficiently developed infrastructure on the moon there could be some capture system but that's for well down the road as it's a huge piece of machinery that must operate on tight tolerances between extremely rapidly moving parts. You'll still need maneuvering rockets even then because your launch accuracy won't be perfect and drag in space isn't perfectly predictable.

Trying to anything like a piston arrangement simply isn't feasible. Instead, look at magnetic levitation trains. Since there are no wheels involved there is no actual speed limit, boosting a train car to interplanetary velocities is simply major engineering.

Barring a revolution in physics I expect to see such a system built--on the moon. If we can tack a few nines onto the reliability we might even build such a system above Earth. (This would require a support structure based on tossing projectiles back and forth at hypersonic velocities. While the numbers work it's dynamic--stop throwing the projectiles and it comes crashing to Earth and the anchor stations do crude approximations of atomic bombs.)

We will never build one on Earth, though.

Heating has been mentioned in other posts but that's not even the biggest deal at all.

First there's the shockwave as your capsule goes down the track. That shockwave carries a lot of energy and we don't just have a track underneath. The usual designs involve a string of hoops--but they won't survive the shockwaves. Nobody has come up with a means of making the track survive.

The closest to an answer to this anyone has proposed so far is that the track be evacuated. At that point boosting it to the 12.52 km/sec is simply major engineering. It can't stay in the track forever, though--you need to somehow build an airlock that allows it out while keeping the air away. (Probably something that snaps open at the last instant) but this simply reduces the shockwave problem--you still have incredibly destructive shockwaves as the capsule exits the tube.

Next comes a problem for which I have never seen anything resembling an answer: drag. Your astronauts die when the capsule hits the air. I don't have the physics knowledge to compute the best answer here but from what I have been able to find I have gotten some crude answers that are more than an order of magnitude over what the human body can take.

Finally, for a manned launch you have another problem--your capsule has to be gargantuan if it so reach space at all. The problem is that to make the boost survivable it must be almost perfectly horizontal because there's a limit to how deep underground you can go. While a horizontal launch is no problem from an airless body it's a very big problem if there's an atmosphere in the way. A very high speed projectile will expend it's energy once it has displaced a mass equal to it's own mass. Your capsule needs to be very long and thin and very heavy in order to punch through all the air that it will encounter this way.

We just might see something along these lines for some cargo launches. Bore your launch tube straight down into a mountain and boost at gun type accelerations. Even then it's extremely tricky.

Mankind has launched one projectile from the Earth's surface at something above escape velocity. Perhaps even at solar system escape velocity. (The photographs can assign a minimum velocity but they can't measure the velocity.) It didn't head for the stars, though--it was no doubt vaporized by it's passage through the air. (And don't look to reproduce it, either--the boosting force was a hydrogen bomb.)

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