# The Force of an Array of Perm. Magnets on a Large Iron Body

1. Apr 10, 2014

### Bobbo Snap

For my senior physics research project I've developed an orbital analysis program that calculates the minimum $\Delta V$ required (applied in an instantaneous impulse) to deflect an inbound Earth impacting asteroid. I've generated data for several different hypothetical orbits and now my advisor would like me to compare my data with a slow-push deflection method which uses the force of an array of permanent magnets (attached to a spacecraft) to impart the deflection force. I need to generate a rough estimate of the force I would be able to generate from such an array. Then I can integrate this over some time intervals and compare to the deflection data I have. The goal is to see if this configuration has any advantages over the gravity tractor slow-push method.

The problem is calculating the force this magnet array could generate. I realize this is hugely complicated problem to solve but I was hoping I could calculate a rough estimate if I make some assumptions about the asteroids make-up. I'm thinking of using the pull force equation $$F = \frac{B^2 A}{2 \mu_0}$$ of a single permanent magnet and scaling this up to a particular array size. However, this equation obviously has no explicit dependence on the distance from the magnet. Is this included in B? If so, which equation for B would be applicable to the permanent magnet on a ferrous body situation. Any thoughts would be appreciated. And feel free to ask for clarification, I'm writing this in quite a hurry.

2. Apr 10, 2014

### nasu

Why would the magnets exert a pushing force on the asteroid?

3. Apr 10, 2014

### Bobbo Snap

They wouldn't. I suppose slow-pull would be a better name in this case but slow-push is what it's called in the literature. "Slow-push methods" encompass a multitude of techniques that are designed to work over an extended period of time, as opposed to a nuclear blast, kinetic impact, etc.

4. Apr 28, 2014

### 1ledzepplin1

Bad design. What you need to do if you're going to take on something this complicated is get comfortable with electromagnets that can be switched on and off, not permanent magnets as I believe you mentioned wanting to use. With electromagnets you can actually produced pulsed magnetic fields that would be scary powerful. The only way this would be feasible though is to make it an attraction mechanism though because the favorable result is for their to be atteaction. I recommend a phased array with curvature that will anticipate the inertial mass, the growing proximity and consequential gravitational force that'll be growing by the square of the distance/ time and will create a chain-link effect of issuing n+1 pulses I guess

5. Apr 28, 2014

### Bobbo Snap

To 1ledzepplin1:

I originally wanted to use electromagnets as well. My advisor, who worked in aerospace for many years, believes that generating enough power to operate the electromagnet for any significant period of time will be the problem. I'm using the permanent magnet array at his suggestion. How would you propose supplying the power for a "good design"?

6. Apr 28, 2014

### 1ledzepplin1

I apologize for my blunt post at first, I seemed to have let the noisy environment I was sitting in penetrate as far as my very tone of writing, haha, but this isn't surprising. To properly respond though I'll admit that the power needed for a projectile mass of completely unspecified mass of an unspecified speed at an unspecified distance is absolutely incalculable, however, the delta v wouldn't necessarily have to be so great if we thought outside the box and made sure to incorporate the nifty space characteristics that exist like gravity. By this I mean we can utilize a gravity assist to further change the orbit in complement to the phase array if you wanted to get even fancier, as a gravity-assisted trajectory can provide both positive and negative acceleration to achieve a non-collision.
If we want to stick with using magnets though as far as a power supply goes it seems like there are more possibilities than may be apparent. But to be sure, it has to be an electromagnet and it almost surely will have to rely on a process of explosive flux compression. Essentially this process is whenever the electromagnetic flux of an object is changed by vast amounts in a miniscule amount of time and the internal resistance approaches negligibility, producing the outcome of total destruction of the conductor in discussion simply as a function of Maxwell's flux conservation law. Now, here is where the power question comes into play and the functionality of this without destroying the projectile... Whether you've heard of the Marx generator or not makes no difference as I'm sure you'll be interested in researching it shortly, but essentially this device produces profoundly high voltages of direct current from a steady-DC supply. A brilliant design that can be employed to produce electromagnetic pulses in the form of an array. Capacitors are charged in parallel by a solar sail for 5 billion years and then a are connected in series with n+1 voltage gain across the design, leading to 100 terrawats (arbitrary figure) of DC voltage that can be fed into an inductance coil in the orbit of the projectile, whereby the induced current in the projectile will create an electromotive force in the projectile that will at best obliterate the object or at least produce a force great enough to change the projectiles path. hurray we're all saved