I read about an equation; [tex]E = mc^2[/tex] and concluded that [tex]m=\frac{E}{c^2}[/tex]. Therefore, I assume that one can create earth gravity by emitting energy equivalent to mass of earth. I also read that, simply put, that a stars gravity can be amplified when it's core collapses, or compresses creating intense gravity field. I put everything together and assume that you can create earth gravity by compressing a fractional amount of E equivalent to mass of earth. You can compress it using magnetic fields similar to what they use in experimental fusion generators. And one would already have such a thing because I would assume it would require lots of energy to compress E of size [tex]n \% M[/tex] to size some size [tex]m[/tex]. Why would this not work, I assume it would not since NASA is not researching any thing like because they are proposing spinning people like a spinning top to get earth gravity.
I really would know nothing about this, but my first guess would be E=mc^2 is saying that a certain amount of mass is equivalent to a certain about of energy proportionate to 1/c^2, and that they can be transferred back and forth between the two. Not that they act in the same way (energy can't act as mass, and vice versa, until they are transformed into the other one). But like I said, I don't really know anything about it. I would be curious to see what someone who really knows their stuff would say.
In general relativity, "mass" is not the (only) source of gravity. In fact, there is something called the stress-energy tensor (for some basic information about it, you can consult the wiki entry on it http://en.wikipedia.org/wiki/Stress-energy_tensor). That tensor contains energy (including the mass-equivalent) but also motion, pressure and things like that. All that generates "gravity".
I'm not quite sure what you mean by compressing energy, but the most "compressed" form of energy we have is mass. To get the mass of the earth requires a body about the size of the earth. The worldwide total energy production corresponds to about 100 pounds, which has virtually no perceptible gravitational force.
That is incorrect. The mass is an intrinsic quality of matter independent of size. This might also be the basis of Earamsey's error regarding the amplification of a gravitational field. If a supermassive star spews its guts and becomes a black hole, its gravitational field is actually less than that of the original, since there is less mass remaining. The critical factor is that the gravitational attraction is based upon the distance between the centres of the involved masses, not the diameters. If our sun were to somehow be compressed into a neutron star or a black hole (not possible by natural methods), the orbits of the planets would not be altered.
True...but. Bodies that weigh as much as planets are the size of planets. (I'm ignoring exotic things like neutron stars and black holes, which are even less realistic) Sure, we could make something that weighs as much of the earth but out of tungsten instead - it's radius would be 2/3 the radius of the earth.