Calculate iron container acceleration in railgun system on the Moon

[PlanetGazer8350]

Having a cylindrical iron container with wall thickness of 20 cm, and a total weight of 500 tons when filled with its cargo, how would you be able to calculate its required voltage and current input in a vertical railgun system (relative to the Moon's surface), with an exit acceleration of 2km/s², for example? The gravitational acceleration would be 1.65km/s², pulling the cylinder due to its gravity. It should then, at an specific height, for example, 300km, meet with another spacecraft (in an elliptical orbit), just before its aphelion, with the cylinder and spacecraft having a very near velocity. Exactly what exit acceleration should be required for the cylinder to be able to reach the 300kms of height, when it is already starting to decelerate, for it to be captured by that spacecraft (the previous 2km/s² being just an example for that situation)?

 

[Dr.D]

The current required will be out of this world in the strictest sense. Some years ago (like 15) when I was involved with rail guns, the objects being accelerated were a few pounds at most, and the currents were around 5 megaamperes to obtain about 6 km/s. Your 500 ton mass is going to require an exorbitant amount of current to reach the speeds you want.

 

[PlanetGazer8350]

I already knew that the required current would be astronomical, but is there exactly any way of calculating the current with a formula? Or, in the other hand, calculate the acceleration with an specific current and voltage input (not in the previous case, but in a different, for example, 5 kilograms)?

 

[Dr.D]

The attached PDF describes a good bit about the modeling and simulation of a rail gun. While it is dated, the basics have to remain unchanged.