Caption: In the adjacent image, we calculate the Sun's main sequence lifetime to be ∼ 10 Gyr making use of the fact that the Sun only burns about 10 % of its hydrogen. This means it has a hydrogen burning efficiency factor f_☉ = 0.1 which is a fiducial value, NOT an exact value.

Both the fiducial and more exact efficiency factors f_☉ can, in fact, only be known by stellar structure modeling.

Note in the image that the second "H" in the 3rd sentence should be "He" for helium.

For stellar lifetimes and main-sequence lifetimes in general, see star_lifetimes.html.

Features:

1. The essential reason why the Sun can only nuclearly burn about 10 % of its hydrogen is that only in its core (here meaning the innermost ∼ 20 % by radius) is it hot and dense enough for hydrogen burning. Thus only a fraction of its H can be burnt to helium-4 (He-4). So the Sun CANNOT burn H for 100 Gyr.

2. The Sun's current age ≅ 4.6 Gyr, and so it has ∼ 5.4 Gyr left on the main sequence (see Wikipedia: Sun: After core hydrogen exhaustion). It will live as a nuclear burning star (i.e., a post-main-sequence star) for ∼ 1.5 Gyr thereafter (see Wikipedia: Sun: After core hydrogen exhaustion).

3. Actually, at ∼ 1.5 Gyr the post-main-sequence will have rather complicated rapid evolution first as a horizontal branch star when it will burn its helium-4 (He-4) core to carbon (C) and oxygen (O) via helium burning. But only a fraction of its helium-4 (He-4) will burnt. The Sun's core NEVER gets hot and dense enough to burn carbon and oxygen.

   Then it will become an asymptotic giant branch (AGB) star and lose much of its outer layers in thermal pulses (AKA helium shell flashes). Then it will settle down as a white dwarf and cool off forever (see Wikipedia: Sun: After core hydrogen exhaustion).

4. Note we know the solar mass M_☉ = 1.98855*10**30 kg from knowing the Sun's gravitational force in the celestial mechanics of the Solar System. The rate of hydrogen burning in kilograms per second is just calculated from the solar luminosity L_☉ = 3.828*10**26 W and knowing the heat energy released in nuclearly burning a kilogram of hydrogen (H).