Question

If the mass of the sun reduced by was one-half, approximately how much longer would the sun live than it would with its current mass?

Answer 1

5.95+ billion years, nearly, against the current 10+ billion years.

Explanation:

Units:

1 unit mass = mass of Sun = `1.989 X 10 ^ 30 kg`

1 unit luminosity = Luminosity of Sun = `38.5 X 10^26` watts

With current mass, Sun's lifetime is nearly 10+ billion years.

The formula that approximates the life of a star s is

(Mass of of s `(M_s)` )/(Luminosity of s `(L_s)`) X `10^10` years,

where.

`L s = M_s ^ 0.25`, for `M_s in [0.43, 2]`

Here, `M_s=1/2 and L_s=(1/2)^(0.25)=0.8409 = 1.673 X 10^26` watts, nearly.

So, half-mass Sun's life

=`( (1/2)/0.8409) X 10^10 years`

=`5.946 X 10^9 years`

= 5.95+ billion years, nearly.