Once our Sun began to produce energy in its core by fusing hydrogen into helium, it embarked on a long 'middle age.' As the nuclear fires became more efficient, the infant Sun began to expand very slowly. At first the Sun only shone with 70% of its modern brightness. But as it continued to evolve over eons of time, its brightness grew by 7% every billion years. When trilobites first crawled on shallow ocean bottoms 500 million years ago, the Sun was much fainter in the sky than it is today. Earth would have been in a deep-freeze had it not been for the warming actions of an atmosphere laced with trace gases like water and carbon dioxide.
In the eons to come, the Sun will continue to expand and shine more brightly for the next 6 billion years. Then a major physical change will start to happen with unprecedented speed. The inner core has become heavily laden with the helium ‘ash’ of over 11 billion years of fusion. Collapsing steadily under its own weight, it has increased the temperature of the Sun’s core making the fusion reactions burn more fiercely, and making the Sun expand to find a new equilibrium. But suddenly a tipping point is reached and the inert helium ash begins to fuse to form carbon. This unleashes a massive increase in energy and pressure and the Sun’s outer layers are propelled outwards, first beyond the orbit of Mercury, then Venus, and then Earth. The Sun has ended its middle age as a red giant star.
Over the course of a few 100 million years, the Sun continues to shed much of its mass into space as a red giant, and later forms a spectacular ‘planetary nebula’ as its last gesture. There are numerous examples known to astronomers, of what happens to stars like our Sun when they reach their last few millennia of life. Spanning nearly a light year or more, the illuminated veil of gases from the dying sun expand out into space until they invisibly mix with the other gases in interstellar space. Deep within the nebula, a brilliant white dwarf remains; the last vestige of the Sun seen as a hydrogen, oxygen and carbon-rich ember. At first it glows brilliant white at a temperature of 100,000 degrees, but with no nuclear fusion to sustain it, it is destined to cool to a blackened hulk after another trillion years. As the universe grows older in the vastness of time, eventually all galaxies will be dimmed, and the brilliant starlight replaced by dark stellar relics moving silently in the infinite night. 
Here is a future timeline for the Sun based on computer models. Note 'Lsun' = solar luminosity today and 'Rsun' = solar radius today.
1.1 billion years from today
Sun will be 10% brighter than today. Extra solar energy causes a Moist Greenhouse Effect. The Earth's atmosphere will dry out as water vapor is lost to space. Such a situation will probably spell the end of large surface life on Earth. Some types of marine life and simpler life forms will likely survive in the oceans and localized pools. The luminosity of the Sun is 10% greater than it is today (1.1 Lsun), and calculations [Kasting,1988] predict that earth would start to lose its water via a "moist greenhouse."
3 billion years from today
The Sun reaches its hottest effective temperature of 5843 while still on the Main Sequence. It has a radius of 1.275 Rsun and a luminosity of 1.33 Lsun. The base of the convective zone is at a mass of 0.986 compared to 0.975 when it was younger 3 billion years ago.
3.5 billion years from today
Sun will be 40% brighter than today. Extra solar energy results in a Runaway Greenhouse Effect The oceans will evaporate into space, and conditions on the Earth will be like those on Venus today. Such conditions will probably mean the end of all forms of terrestrial life. The luminosity of the Sun is 1.4 Lsun, and calculations predict that a true greenhouse will prevail on Earth and Earth will lose its oceans via evaporation. Clouds reduce the energy absorbed by earth so this event may be delayed, perhaps by several billion years.
4.8 billion years from today
Hydrogen is finally exhausted at the very center of the Sun, but there is still hydrogen left just outsice this depleted region, the Sun will continue to evolve slowly for another 1.6 billion years. Currently its luminosity is 1.67 Lsun, its temperature is 5819 K and its radius is 1.275 Rsun.
6 billion years from today
Studies of old G-type stars such as HD103095 [Baliunus and Vaughn, 1985] still has an average level of chromospheric activity that matches the sun's, and an amplitude that is similar to the suns. The sun's current level of activity appears to be maintained over the entire main sequence phase of the star. The sun has now reached the end of its main sequence phase. A thick hydrogen burning shell is developing and the suns center begins to contract more rapidly. Its luminosity is 2.21 Lsun, its temperature is 6517 K its radius is 1.575 Rsun.
7.4 billion years from today
After having evolved at nearly constant luminosity for the last 700 million years, it takes a big jump to a luminosity of 17.3 Lsun and a radius of 6.38 Rsun with a surface temperature of 4664K. The convective envelope has reached its greatest depth by this time.
7.55 billion years from today
The sun is now at the top of the red giant branch with a radius of 165.8 Rsun, a temperature of 3107 K and a luminosity of 2349 Lsun. Its mass has been reduced to 0.87249 through a solar wind with a rate of 0.00000013 solar masses per year similar to other giant stars. Helium ignition takes place in the core at a temperature of 100 million degrees in a violent core 'flash' which produces a luminosity of 10 billion Lsun. It then settles back to a lower luminosity of 44 Lsun for the next 100 million years. Because the sun has lost 28% of its mass by the peak of the red giant phase, the inner planets have moved out in their orbits significantly. Venus arrives at 1 AU and Earth moves to 1.38 AU. Mercury has been engulfed, but Venus just escapes being engulfed by the Sun.
7.68 billion years from today
The Sun has left the giant branch and is now going through a series of helium shell flashes for the next 100,000 years. Each shell flash in the core causes pulses of enhanced mass loss so that by this time the mass of the Sun is only 0.54 Msun. Its temperature is 3660K and its radius has undergone several short-term changes to 213 Rsun ( 0.99AU) but by this time Venus is at 1.22 AU and Earth is at 1.69 AU escaping being engulfed. If the mass loss has been less extreme than the predictions, the radius could grow to 347AU and engulf Venus and Earth. Mars would be spared at a distance of 2.25 AU.
-  "The Sun: From Craddle to Grave" - Technology Through Time, Issue #48, NASA.
- Baliunus and Vaughn (1985)
- Kasting, 1988 Icarus vol 74 p.472
- "Our sun: Present and Future," Sackman, Boothroyd and Kraemer, 1993 Astrophysical Journal, vol. 418, p. 457.
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"The Colorful Demise of a Sun-like Star" - This image, taken by NASA's Hubble Space Telescope, shows the colorful "last hurrah" of a star like our Sun. The star is ending its life by casting off its outer layers of gas, which formed a cocoon around the star's remaining core. Ultraviolet light from the dying star makes the material glow. The burned-out star, called a white dwarf, is the white dot in the center. Our Sun will eventually burn out and shroud itself with stellar debris, but not for approximately another 5 billion years.
Our Milky Way Galaxy is littered with these stellar relics, called planetary nebulae. The objects have nothing to do with planets. Eighteenth- and nineteenth-century astronomers named them planetary nebulae because through small telescopes they resembled the disks of the distant planets Uranus and Neptune. The planetary nebula in this image is called NGC 2440. The white dwarf at the center of NGC 2440 is one of the hottest known, with a surface temperature of nearly 400,000 degrees Fahrenheit (200,000 degrees Celsius). The nebula's chaotic structure suggests that the star shed its mass episodically. During each outburst, the star expelled material in a different direction. This can be seen in the two bow tie-shaped lobes. The nebula also is rich in clouds of dust, some of which form long, dark streaks pointing away from the star. NGC 2440 lies about 4,000 light-years from Earth in the direction of the constellation Puppis. The image was taken Feb. 6, 2007 with Hubble's Wide Field Planetary Camera 2. The colors correspond to material expelled by the star. Blue corresponds to helium; blue-green to oxygen; and red to nitrogen and hydrogen. View full-size image. (Source: NASA/JPL/STScI/AURA.)