Coil parameters for 5 joule coilgun with 45mm steel spheres

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Hey guys! Not sure if this is the correct place to post this, but this seemed the most relevant...

So I'm working on a coilgun to shoot 45mm steel spheres, but I need to figure out how long [diameter, gauge, etc] my coil needs to be.

I want to generate a force of about 5 Joules or more [preferably more].

Using "magnet wire," what gauge, # of turns, do I need?

The distance between the ferromagnetic material and the solenoid will probably be between 0.75mm-1mm, depending on the size pipe I can find [else I might need to make my own].

Thanks in advance for any help!

EDIT: I gave distance from the top of the projectile to the bottom of the solenoid. ;)
 
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First of all you have to calculate the force from energy [5 Joules].
The energy E=mass*speed^2/2
mass=Vol*specgravity
Vol=4/3* PI()*r^3
r=45/2=22.5 mm [2.25 cm]
Vol=47.71 cm^3 mass=7.81*47.71/1000 =0.372 kg.
speed=sqrt(2*E/mass)=5.18 m/sec
For a time of 0.3 sec acceleration will be: speed/time=17.28 m/sec^2
Then the force will be F=acc*mass=17.28*0.372=6.43 N.
Now you can continue following [for instance]:
http://trg.fke.utm.my/members/dahiru/Journals_published/Journal_Elecmag_Gjet.pdf