Napkin math: Earth orbits at ~30 km/s, escape velocity is ~42 km/s. So to get Earth to leave the solar system (the inverse of capturing a planet under the most optimal circumstance), you would need to give it 12 km/s. Earth is ~6 * 10^24 kg, so that represents ~4.3 * 10^32 joules. The sun gives out around 3.8 * 10^26 joules per second (i.e. watts).
So with perfect efficiency, working just from conservation of energy, this would require around 13 days of the entire energy output of the sun. Or around a trillion years at Earth's current energy consumption.
So with perfect efficiency, working just from conservation of energy, this would require around 13 days of the entire energy output of the sun. Or around a trillion years at Earth's current energy consumption.