- First, the
hydrogen burning
rate
(i.e., rate of burning to helium-4 (He-4))
is easily found.
- We know the
atomic masses
of hydrogen (H, Z=1)
and helium-4 (He-4, Z=2):
respectively,
1.008 (fiducial value) and
4.002602 in
atomic mass units (AMU).
When 4 hydrogen nuclei are hydrogen burned to 1 helium-4 (He-4), there is a relative atomic mass loss from reactants to product of 0.007291 = 0.7291 % ≅ 0.7 %.

- Recall conservation of energy principle.
So the rest mass is
lost by the reactants is
converted into some other form of energy.
In fact, it is converted heat energy
which can be calculated using
E=mc**2.
Note

E = mc**2, and thus 1 kilogram of rest mass in energy terms is 1 kg * (3*10**8 m/s)**2 = 9*10**16 joules = about 2.5*10**10 KW-hours (Note 1 kW-hr = 3.6*10**6 J ) = the explosion energy yield of about 20 megatons of TNT ( 1 megaton TNT = about 4*10**15 J ) .

- Now let's find the
hydrogen burning
rate
in fiducial values:
R = (rate of rest mass converted to heat energy)*[(H mass burnt)/(H mass converted)] = (L/c**2)*κ , where κ = [(H mass burnt)/(H mass converted)] = (1/0.007291) = (L_☉/c**2)*(L/L_☉)(1 M_☉ / 1.98855*10**30 kg)*(3.1557600*10**16 s / 1 Gyr)*κ = 9.270*10**(-3)*(L/L_☉)*(M_☉/Gyr) .

We now assume the approximate mass-luminosity relation known from a combination of observations and stellar structure modeling: L = L_☉*(M/M_☉)**3.5 which holds approximately for the stellar mass 0.1--50 M_☉ (see Wikipedia: Main sequence: Lifetime, Wikipedia: Mass-luminosity relation). This gives usR = 9.270*10**(-3)*[(M/M_☉)**3.5]*(M_☉/Gyr) .

- Next, assuming luminosity
is constant on the main sequence
(which is approximately true), the
main sequence lifetime formula is
t_lifetime = fM/R = (10 Gyr)*(f/f_☉)*[(M_☉/M)**2.5]

in general where we have rounded the coefficient from 10.78 to 10 since the 0.78 quantity is insignificant to the accuracy we are working at. Note f is the general hydrogen burning efficiency factor and f_☉ = 0.1 is a fiducial value for the Sun**NOT**an exact value. Thus,t_lifetime = fM/R = (10 Gyr)*(f/f_☉)*[(M/M_☉)**(-2.5)] in general , = 10 Gyr for the Sun , ≅ 3000 Gyr for a 0.1 M_☉ star assuming f ≅ 0.1 , ≅ 3*10**(-2) Gyr = 30 Myr for a 10 M_☉ star assuming f ≅ 0.1 .

- Note the
hydrogen burning
rate
is for the hydrogen
mass burnt.
The rate of rest mass
converted to heat energy
is smaller by a factor
of the relative atomic mass
loss 0.007291.
Also note that if an initially pure hydrogen star converted all its hydrogen to helium-4 (He-4), it would decrease in mass by the same factor 0.007291.

- Since the main-sequence lifetime of
a star is overwhelmingly its longest phase
as a nuclear burning object, our
approximate
main sequence lifetime formula
applies to the whole
nuclear burning lifetime of
stars as well
as the main-sequence lifetime.
- Using our
main sequence lifetime formula,
we have calculated the values in
Table: Approximate Main-Sequence Lifetimes.
____________________________________________________________________________ Table: Approximate Main-Sequence Lifetimes ____________________________________________________________________________ M t (M_☉) (Gyr or Myr) ____________________________________________________________________________ 0.1 3,200 Gyr 0.5 57 Gyr 0.88 13.8 Gyr ≅ Gyr the age of the observable universe 0.9 13 Gyr 1.0 10 Gyr ≅ lifetime of a G2 V star (e.g., the Sun) 1.5 3.6 Gyr 3 640 Myr 5 180 Myr 8 55 Myr 10 32 Myr 20 5.6 Myr 30 2.0 Myr 60 0.36 Myr ____________________________________________________________________________

- Our approximate
stellar lifetimes
in the above
Table: Approximate Main-Sequence Lifetimes
are
**NOT**so bad as we can see by comparison to the more accurate results given in the image. However,**NOT**surprisingly our results become poorer as stellar mass increases well above 1 solar mass. They are also expected to be poorer as stellar mass decreases well below 1 solar mass, but the accurate results in the image do**NOT**give values for comparison in this case.