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?

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

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.

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