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Is there some combination of a plane that flies high enough, with a railgun small enough to fit into the fuselage, and a satellite small and durable enough, to make this feasible?

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    $\begingroup$ The NuSTAR spacecraft was launched from a small rocket attached to an airplane. Since the weight was so small, they saved a bunch on the price of the launch vehicle by using the combo of a modified DC-10 and Pegasus rocket. $\endgroup$ – honeste_vivere Dec 17 '15 at 21:24
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That depends upon what would satisfy your needs as an "orbit". I think its unlikely to do what you are hoping.

A good way of thinking about the problem to make it more intuitive is to say that there is a rule that applies to all satellite orbits that, aside from the effects of the atmosphere, from the point that a manoeuvre ends the satellite will conduct a revolution in "some ellipse" and must pass through the same point in space on the second orbit, no matter how high it goes in the mean time. Atmosphere and other perturbations aside it will continue to do that indefinitely.

Even without an atmosphere this idealisation isn't right because the Earth isn't a point mass, but it will do for the thought experiment.

In our case the end of the manoeuvre is the point that the satellite leaves the railgun. This means that however high the aircraft and however big the railgun the satellite will return to the same altitude after one orbit. If we include the atmosphere, as its necessary for the aircraft, then we have to accept that the first orbit will probably be the last for the satellite due to atmospheric drag.

There are two ways of getting past this constraint.

  1. The railgun gives the satellite such an almighty kick that it takes up a parabolic trajectory at escape velocity and will never be seen again.
  2. The satellite has some means of performing a second big manoeuvre, when it has gained a lot more altitude.

In case 2 this has the effect of "raising the perigee", causing the satellite not to dip back into the atmosphere.

Going back to our thought experiment rule about orbits now causes the satellite to return to the engine cut-off point of the second manoeuvre and it is that point that now defines where the satellite must now return on subsequent orbits.

In summary, an orbital delivery system has to impart velocity increments at at least two points in the trajectory to go from rest at the Earth's surface to a stable orbit. Just in case you are wondering, I've described an idealised impulsive system, if you had a very long thrust duration, with an arc extending most of an orbit, then you'd find a way to do it also.

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    $\begingroup$ consider length of the plane vs difference between airplane speed vs orbital speed to come up with the acceleration required (imparted by the railgun). Then consider components/materials/parts that don't liquefy or shatter at these accelerations. Most ceramics (as common in electronics) will shatter. Most plastics (electrical isolation) will liquefy. Capacitors become mush. For liquid propellant the tanks will need to be rated for pressure massively higher than the inert pressure of the propellant. SRBs would stand a chance - if they don't ignite from the rapid energy influx. $\endgroup$ – SF. Dec 17 '15 at 8:30
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    $\begingroup$ In case 1 it would reach a solar orbit, and after one year it would return to the same point in solar orbit, as would the Earth. So if we ignore the moon and other planets and idealise everything, shouldn't we expect the satellite to return after one year? $\endgroup$ – gerrit Dec 17 '15 at 14:44
  • $\begingroup$ @gerrit Perhaps, if we idealise it so much that it stops being a three body problem, but I'm out of my depth there! $\endgroup$ – Puffin Dec 17 '15 at 22:21
  • $\begingroup$ @Benito Ciaro I don't know where you wanted to go with this next but you aren't far from being able to do some simple calculations yourself to explore the proposition in your comment yourself, have a glance at en.wikipedia.org/wiki/Hohmann_transfer_orbit to see what you can make of it. If you set up delta-V 1 as the railgun impulse then delta-V 2 will be your "mini rocket". It mightn't be so mini in the end though. $\endgroup$ – Puffin Dec 17 '15 at 22:26
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Is it possible? Yes, but not with current technology (sorry not sorry for that pun). Right now railguns can't shoot projectiles fast enough to launch picosats from altitude. At least that's what my back of the envelope calculations say, maybe someone will check my math.

Let's use the General Atomics 32 megajoule (MJ) Multimission Medium Range Railgun Weapon System (MMRRWS). It's the bigger one pictured below and one of the more powerful railguns out there.
enter image description here

Escape velocity on the surface of the earth is 11km/s. The 32 MJ can launch a projectile at about 2.5km/s (5500mph). That's not going to do the trick so let's load the whole rig into the back of a Lockheed Martin c130-30J. The pulsed power system that runs it can fit in a 20 foot shipping container. So the gun itself and the power system can fit in the 55 foot compartment.

According to wikipedia the c130j can get up to 12km in the air. The wikipedia article on escape velocity says that at 9km is you need 7.1km/sec to get escape velocity so this won't quite work out. You'll either need to get higher or build a more powerful railgun.

You might be able to do it in a hybrid airship like the one lockheed martin is making. By my calculations you would need to get up to about 22km to be able to use the railgun.

Of interest, NASA researched a program to do this but in reverse. The idea was to use a 2 mile long railgun at Kennedy Space Center that would launch a scramjet that would then deploy a rocket stage with the payload. You can read more about it here https://www.nasa.gov/topics/technology/features/horizontallaunch.html

This is a pretty good infographic with how railguns work. Railgun info

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Another problem that would rear it's ugly head if you were to try this: Wake turbulence.

Your satellite will be leaving the barrel at a stupendous velocity. It's going to slam into the atmosphere in front of the plane as it goes. Your launching aircraft is going to slam into that turbulence. I would be very surprised if that wasn't followed by pieces of the aircraft slamming into the ground.

And that's assuming you've already managed to overcome:

Puffin's point that you need a circularization motor.

ViennaCodex's point that the railguns of today are nowhere near powerful enough.

The fact that drag is going to be brutal. Drag goes at at least the square of velocity and the smaller the craft the higher the drag/mass ratio and thus the faster it's brought to a stop. Realistically, you need something pretty big and heavy to hope to push it through the atmosphere.

There's also a little problem of recoil. Using the same plane as ViennaCodex I find a max weight of 67,000kg. Lets figure your satellite launcher weighs 100kg and you're kicking it out at 7,000m/s. (I'm ignoring drag here, reality is much worse) You just jolted your plane 10 m/s. So what, you say? The cargo compartment is 12.5m long. To boost it you need 200,000g (note that this is beyond even gun-rated stuff!), applied for 3.5ms. While the gun is boosting your plane is being pushed backwards at 290g. The railgun rips the plane apart. You need a humongous recoil buffer to survive this--and where are you going to put it since the railgun is already as long as the plane?

Now, to power this. You need 2.45GJ assuming 100% efficiency. The best capacitors available are somewhat under 10J/cc. I'll assume 10 as I'm having to pull a number off a graph. You need 245 m^3 of capacitor to power this. That's more than 3x the total cargo capacity of our C130j. Those beefy capacitors didn't come with weight information but looking elsewhere I'm getting around 2g/cc. Your capacitors are something like 490,000kg--about 15x the total payload of the plane.

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  • $\begingroup$ Fair points, but this mainly shows you need a bigger plane. A C130 is not particularly big. Of course, even with a bigger plane the problem remains that the force on the plane is the reverse of the force on the plane, and by F=m*a that force is about 200 MN. That will accelerate the plane backwards. Your capacitor figure is a bit weird - you have a energy density of 2J/g, but typical supercaps are 20J/g. 49 tons is a manageable weight. $\endgroup$ – MSalters Dec 18 '17 at 9:30
  • $\begingroup$ @MSalters I was looking at capacitors meant for very fast discharge rather than maximum power density. Since the boost is 3.5ms the capacitor must dump it's power in the same 3.5ms. Note, also, that I was assuming 100% efficiency--you're not getting anywhere near that as the voltage drops in the bank. $\endgroup$ – Loren Pechtel Dec 19 '17 at 2:57
  • $\begingroup$ accounting for all of this, there's one more factor.. Your altitude only matters as far as air-resistance is concerned. No aircraft ever built by man has anywhere remotely near orbital velocities within an atmosphere, which means that the railgun does almost all the work. If atmospheric drag wasn't a concern, you'd have better results firing your railgun from the ground. As-is, anything able to fire a satellite into orbit probably isn't going to be concerned by a brief interlude of atmospheric drag. $\endgroup$ – Ruadhan2300 Feb 5 '18 at 14:28
  • $\begingroup$ @Ruadhan2300 I'm talking about drag on the projectile. You're right about the airplane's speed being useless--it's just a way to get above as much atmosphere as possible. I'm just saying you can neither lift the railgun nor survive it's firing. $\endgroup$ – Loren Pechtel Feb 5 '18 at 21:10
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    $\begingroup$ One could get around the G-Force problem on the plane by releasing the railgun like a bomb in the same moment that it's fired. resulting in the gun being rocketed away behind the plane, recover it with a parachute and re-attach later. assuming a compact enough system was found you could keep the power-supply inside the plane and allow the cables to detach from the recoil using non-locking connectors. $\endgroup$ – Ruadhan2300 Feb 7 '18 at 16:48

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