Question

the nearest star named alpha centuari of the solar system is 4.29 light years away. Express this distance in terms of parcecs?

Answer 1

Answer:

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 × 1011 m

∴ 4.29 ly = 405868.32 × 1011 m

∵ 1 parsec = 3.08 × 1016 m

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

Using the relation,

θ = d / D

where,

Diameter of Earth's orbit, d = 3 × 1011 m

Distance of the star from the earth, D = 405868.32 × 1011 m

∴ θ = 3 × 1011 / 405868.32 × 1011 = 7.39 × 10-6 rad

But, 1 sec = 4.85 × 10–6 rad

∴ 7.39 × 10-6 rad = 7.39 × 10-6 / 4.85 × 10-6 = 1.52"

Answer 2

Answer:

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 × 1011 m

∴ 4.29 ly = 405868.32 × 1011 m

∵ 1 parsec = 3.08 × 1016 m

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

Using the relation,

θ = d / D

where,

Diameter of Earth’s orbit, d = 3 × 1011 m

Distance of the star from the earth, D = 405868.32 × 1011 m

∴ θ = 3 × 1011 / 405868.32 × 1011 = 7.39 × 10-6 rad

But, 1 sec = 4.85 × 10–6 rad

∴ 7.39 × 10-6 rad = 7.39 × 10-6 / 4.85 × 10-6 = 1.52“