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Question

# 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 ?

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Solution

## Given: The distance of the nearest star from the solar system is 4.29 light years. Light year is abbreviated as ly. We know that, 1 parsec = 3.08× 10 16  m. The distance travelled by light in one year is given as, 1 ly=3× 10 8  m/s ×1 year× 365 day 1 year × 24 hour 1 day × 3600 s 1 hour =9.46× 10 15  m 4.29 ly in terms of metre is given as, 4.29 ly=4.29×9.46× 10 15  m =4.06× 10 16  m× 1 parsec 3.08× 10 16  m =1.32 parsec Thus, the distance of 4.29 ly in terms of parsec is 1.32 parsec. After six months, the distance between the two positions of the Earth in its orbit is equal to two times the radius of the Earth’s orbit. The diameter of the earth's orbit is 3× 10 11  m. The parallax shown by the star is given as, θ= d D Where, d is the diameter of earth's orbit and D is the distance of the star from solar system(earth). By substituting the values in the above equation, we get θ= 3× 10 11 4.06× 10 16 =7.39× 10 −6  rad =7.39× 10 −6  rad× 1 sec 4.86× 10 −6  rad =1.5 2 ″ Thus, the parallax shown by the star is 1.5 2 ″ .

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