In a research paper published in the November 20, 1993 Astrophysical Journal, astronomers I.-Juliana Sackmann, Arnold Boothrayd and Kathleen Kraemer from Caltech, University of Toronto and Boston University, used the best stellar evolution models now available to do just that. They 'watched' as the Sun started-out 4.6 Billion years ago (Byrs) with a luminosity of 0.70 of today's value, and brighten to 2.2 times its current value by 6.5 Byrs hence. A luminosity of 1.1 times the present value was reached in 1.1 Byrs, and 1.4 times its present value some 3.5 Byrs from now. This means that in 1.1 Byrs, the Earth will experience a permanent "moist greenhouse effect" as the oceans begin to evaporate into the atmosphere, and by 3.5 Byrs, a "runaway greenhouse effect" similar to what Venus is enjoying will be in place.
As the Sun evolves into a red giant it grows to a luminosity of 2300 times its present value and a size of 150 times its current extent, shedding about 27 percent of its mass and engulfing/incinerating the planet Mercury. It continues to evolve up the so-called Asymptotic Giant Branch and experiences at least four 'thermal pulses'. After the first one, the Sun's size has swollen to 213 times its present size, but at a mass of only 0.6 of its current mass, the orbits of the planets have crept outwards from their present distances. Venus is now located about 1.22 times farther from the Sun than where the earth is now. Earth has moved to about 1.7 times farther out, so neither if these planets are engulfed by the Sun. The Sun has reached a peak luminosity of 5300 times its current rate after the fourth thermal pulse. The timetable is as follows:
11 Byrs on the Main Sequence 0.7 Byrs cooling towards the Red Giant Branch 0.6 Byrs to ascent up the Red Giant Branch 0.1 Byrs on the Horizontal Branch 0.02 Byrs on the early Asymptotic Giant Branch 0.0004 Byrs on the thermally-pulsing Asympotic Giant Branch 0.0001 Byrs evolving to become a planetary nebula / white dwarf system
The Sun has already spent 4.5 billion years on the Main Sequence , so it has another 6.5 billion years to go before it undegoes major structural changes. These are caused by the Sun reaching a critical point in its conversion of hydrogen into helium in its deep core. So far as life on Earth is concerned, beginning some 1 billion years from now or probably somewhat earlier, the polar icecaps will permanently vanish and the oceans begin to evaporate making the Earth un-livable. I know we have 'more pressing problems' today, like paying the rent and balancing the federal budget, but we better have some plans for getting us off this planet. A billion years is not a very long time!