Lifetime of the Sun :

The lifetime of the Sun, T, can be computed from the amount of fuel that the Sun has and the burning rate.

burning rate x T = total fuel

burning rate corresponds to the solar luminosity: L_o

total fuel corresponds to the mass available for nuclear reactions: E = mc²

10% of the solar mass can be converted into He.

The efficiency of H --> He fusion is 0.7%.

total fuel = m c² = M_o x 0.1 x 0.007 c²

Lifetime

T = M_o x 0.1 x 0.007 c² / L_o

M_o = 2 x 10³⁰ kg (mass of the Sun)

c = 3 x 10⁸ m/sec (speed of light)

L_o = 3.9 x 10²⁶ Watts (luminosity of the Sun)

T = 3.2 x 10¹⁷ sec = 10 x 10¹⁰ years = 10 billion years