Question

The nearest star to our solar system is 4.29ly away . How much is this distance in parsecs? How much parallax would this star show when viewed from two locations of Earth six months apart in its orbit around sun.​

Answer 1

Distance of the star from the solar system = 4.29 ly

1 light year is the distance travelled by light in one year.

1 light year = Speed of light × 1 year

= 3 × 108 × 365 × 24 × 60 × 60 = 94608 × 1011m

∴4.29 ly = 405868.32 × 1011 m

1 parsec = 3.08 × 1016 m

∴4.29 ly =  (405868.32 × 1011 m)/ 3.08 × 1016 m = 1.32 parsec

using for the relations ,

theta= d / D

where ,

d = diameter of earth = 3 × 10¹¹ m

D = diameter of star from earth = 405868.32 × 1011 m

theta = 3 × 10¹¹ m / 405868.32 × 1011 m= 7.39 × 10^-6rad

1 sec = 4.85 × 10^-6 rad

then,

7.39 × 10^-6 rad = 7.39 × 10^-6 rad /4.85 × 10^-6 rad = 1.5ⁿ