The nearest star to our solar system is 4.29 light years away. How mcuh is this distance in terms of par sec ? How mcuh parallax would this star show when viewed from two locations of the earth six months apart in its orbit around the sun?

Answer

`1.52`

Explanation

As 1 light year `= 9.46xx10^(15)m` ,
1 parsec `= 3.08 xx 10^(16)` m
`:. ` Distance of alpha centauri from the earth,
S = 4.29 light years `= 4.29xx9.46xx10^(15)` m
`= (4.29xx9.46xx10^(15))/(3.08xx10^(16))` parsec = 1.32 parsec
In an orbit around the sun, the distance between the two locations of the earth six months apart, b = Diameter of the earth.s orbit = 2AU Parallax of the star,
`theta = (" Arc")/("Radius") = b/S = (2AU)/("1.32 parsec")` = 1.515 s of arc.