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Question : 20 of 33
Marks: +1, -0
The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?
Solution:  
Distance =4.29=4.29 light year \text{ light year }
=4.29×9.46×1015 m=4.29 \times 9.46 \times 10^{15} \ \mathrm{m}
(∵1(\because 1 light year =9.46×1015 m)=9.46 \times 10^{15} \ \mathrm{m})
=4.29×9.46×10153.08×1016 parsec=\frac{4.29 \times 9.46 \times 10^{15}}{3.08 \times 10^{16}} \ \mathrm{parsec}
(∵1(\because 1 Parsec =3.08×1016 m)=3.08 \times 10^{16} \ \mathrm{m} )
=1.318 Parsec=1.32 parsec= 1.318 \ \mathrm{Parsec} = 1.32 \ \mathrm{parsec}
Parallax of the star,
θ= Arc  Radius \theta=\frac{\text{ Arc }}{\text{ Radius }}
=bs=2 AU1.32 parsec=\frac{b}{s}=\frac{2 \ \mathrm{AU}}{1.32 \ \mathrm{parsec}}
=1.515′′=1.515^{\prime\prime}
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