Statistics homework help. 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.
