Final answer:
Doubling the size of the Sun would most likely cause Earth's temperature to significantly increase, leading to conditions that could make the planet uninhabitable. This massive change could potentially lead to changes in Earth's orbit, but the more immediate effect would be the intense heat. The actual future of Earth due to Sun's expansion into a red giant is complex, involving changes in both orbit and temperature.
Step-by-step explanation:
If the size of the Sun were to double, it would have catastrophic effects on the Earth. One major effect would be on Earth's orbit, which would likely become unstable due to changes in gravitational forces; however, this is a simplified view because the actual dynamics depend on whether the Sun's mass changes along with its size. If the mass remains constant while the size doubles, the orbit would not change, but this is an unlikely scenario because size and mass are related for celestial bodies like the Sun. Nevertheless, the immediate and significant impact would be an increase in Earth's temperature, which could render the planet uninhabitable due to the increased radiation. Changes in temperature could lead to expanded orbits, but the main concern would be the immediate increase in heat.
When considering the actual long-term evolutionary path of the Sun, as it turns into a red giant, it is expected to lose some mass, which would lead to an increased diameter of Earth's orbit according to Kepler's third law. However, countervailing tidal forces could cause the orbit to shrink. In any case, life on Earth would likely be incinerated long before these changes fully take effect.