More naive physics applied to the Terra-Uranus project.

I would like physicists to critique this, please.

How much energy, in terms of hours or days of solar output, would it take to strip the atmosphere off of Uranus and get at its valuable rocky core, which I call Terra-Uranus?

Uranus has an escape velocity of 21.3 X 10³ m s^-1. It has a mass of 8.68 X 10²⁵ kg, equivalent to 14.5 Earths. The rocky core has a mass of 0.55 Earth's mass, so the mass of everything else on Uranus you'd want to remove suggests the calculation [(14.5 - 0.55)/14.5] X 8.68 X 10²⁵ kg = 8.35 X 10²⁵ kg.

The kinetic energy E of a mass m moving at a subrelativistic velocity v has the formula E = 1/2 mv².

Therefore I can naively calculate the kinetic energy of moving that much mass away from Uranus at its escape velocity:

E = 1/2 X 8.35 X 10²⁵ kg x (21.3 X 10³ m s^-1)² = 1.89 X 10³⁴ J

The sun has a power output of 4 X 10²⁶ J s^-1, so to calculate how long it would take the sun's power to release that much energy, divide 1.89 X 10³⁴ J/(4 X 10²⁶ J s^-1) = 47.3 X 10⁶ seconds, or about 550 days of solar output, assuming you could capture it at 100 percent efficiency.