Earth's atmospheric CO2 concentration is on the rise, currently exceeding 420ppm. This is far above the 180ppm to 280ppm range of the past one million years and the anticipated safe limit of 350ppm. Consequently, halting fossil carbon emissions is necessary but insufficient to navigate to a safe climate future - massive and permanent removal of CO2 is inevitable. Humanity needs to do both: transit from the current fossil to a solar energy supply system and clean-up excess CO2 emissions from the atmosphere. The required global-scale transformation is ultimately limited by the availability of energy, beyond political ambitions and economic considerations. In this paper, the 3-machines energy transition model, a global system dynamics model based on energy balances, is presented and used to explore the energy frontiers for stabilizing the Earth's climate. The model comprises a hypothetical fossil engine, a solar engine including energy storage, and a carbon scrubber. These machines interact with Earth's carbon cycle and satisfy humanity’s energy demand. In 25 simulation experiments, shaped by a set of parameters regarding e.g. energy demand, energy storage and progression of the machines, the dynamics of the transformation and the effect on cumulative CO2 emissions were analysed. The resulting pathways reveal that, theoretically, atmospheric CO2 concentration can be reduced to 350ppm well before the end of this century while staying below 1.5°C with more than 50% probability. However, this requires the fastest possible energy transition, a massive and lasting carbon removal from atmosphere and hydrosphere, minimization of energy storage and a reduction of energy demand per capita.