The nearest star from our solar system is 4.29 light year away. How much is this distance in terms of par sec? 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?

The nearest star from our solar system is 4.29 light year away. How mu

1.	The nearest star from our solar system is 4.29 light year away. How much is this distance in terms of par sec? 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?
Answer» Solution :(i) 1 light year `=9.46xx10^(15)m` 1 par SEC `=3.094xx10^(16)m` 1 light year `=(9.46xx10^(15))/(3.09xx10^(16))=0.306` par sec Distance of Alpha Centauri `=D=4.29` light years `=4.29xx0.396=1.313` par sec `D=4.29` light year `=4.29xx9.46xx10^(15)m` (ii) One astronomical UNIT `=1AU=1.5xx10^(11)m` The distance between the two LOCATIONS of the earth six months apart in its ORBIT around the sun `=d=2AU` `=2xx1.6xx10^(11)m` Parallax `=theta=? , d = D theta` `theta=d/D=(2xx1.6xx10^(11))/(4.29xx9.46xx10^(15))` rad `=0.0739xx10^(-4)` rad `=0.0793xx10^(-4)xx(180xx60xx60)/(PI)` `theta=1.523` seconds of an arc.