Respuesta :
Parallax of vega is observed to be 0.13 arc seconds when observed from the standard base of 1 AU.
a) 7.713 parsec is the distance to vega in parsecs.
Thus, 25.15 light year is that distance in light years.
What is parallax?
When the distance is large enough that the parallax angle is very small, the parallax angle is proportional to the inverse of the distance (1/d). Conversely, if we can measure the parallax angle, we know that the distance to the object is proportional to the inverse of that angle.
Given that,
the distance between sun and vega = d
distance between sun and earth = L
angle (θ) = 0.13 arc second
θ = 0.13 × 0.000278°
θ = 3.61 × 10⁻⁵
tan θ = 1 AU /d
or, d = 1 AU / tan θ
or, d = 1 AU / tan (3.61 × 10⁻⁵)
or, d = 1.591 × 10⁶ AU
and 1 AU = 4.848 × 10⁻⁶ parsec
Thus, d = 7.713 parsec.
1 AU = 1.581 × 10⁻⁵
d = 25.15 light year.
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