Why Mars can't be terraformed

Mars is too small.
As we can see from Equation 1, Mars will need additional gravity to hold Hydrogen in it's atmosphere.
Equation 2 can be used to determine how much additional mass is needed.

What about Mars and Mercury combined?
Move Mercury to a martian orbit, use it as a core, shatter Mars into a trillion pieces and spread it across the surface of Mercury. Even with Mercury and Mars combined, it would only raise the H-value from 0.25356 to 0.34551. This is still not high enough.

What about adding asteroids to Mars?
Remember Venus. It has a major CO2 problem, so adding more carbon to Mars would be a mistake. 1 Ceres is the largest asteroid, and 2 Pallas the third largest. Both are high-carbon asteroids. The second largest asteroid: 4 Vesta is coated in igneous rock and would be a good addition to Mars. Metallic asteroids would be better. Metallic asteroids include: 16 Psyche, 21 Lutetia, 22 Calliope, 69 Hesperia, 75 Eurydice, 77 Friga, 97 Clotho, 135 Hertha. With all of the metallic asteroids combined, this would still not be high enough.

Ideal conditions
Under ideal conditions, an unlimited supply of high-density mass can be added to Mars to increase it's gravity. Iron is the most common, high-density material available. The entire surface of Mars would be buried under solid iron 2,400km! deep to hold Hydrogen within it's atmosphere. This is an additional mass of 5.16x1024kg. The additional mass is more than the current mass of Mars. It's clear Mars cannot remain the planet as we know it and be a viable candidate for terraforming. Instead, it should be preserved, or better still, used as a resource to terraform other planets.

Present conditions
The available resources of the solar system limit our ability to terraform Mars. Even if we did try to terraform Mars, Simulations 8 and 9 prove conclusively that an Earth-like planet in a Martian orbit can't support life.