Respuesta :
Answer:
[tex]\theta = 0.0038\ arc\ sec[/tex]
option c
Explanation:
given data:
Diameter of a star = 1,400,000 km
star distance from sun [tex]= 7.57\times 10^{13} km[/tex]
we know that
Angle is given as
[tex]\theta = \frac{d}{r} = \frac{14\times 10^5}{7.57\times 10^{13}}[/tex]
[tex]\theta = 1.849\times 10^{-8} rad[/tex]
we know that
[tex]1\ arc\ second = 4.84\times 10^{-6} rad[/tex]
[tex]1 rad = \frac{1\ arc\ sec}{4.84\times 10^{-6}}[/tex]
SO, [tex]\theta = \frac{1.849\times10^{-8}}{4.84\times10^{-6}}[/tex]
[tex]\theta = 3.82\time 10^{-3} arc sec[/tex]
[tex]\theta = 0.0038\ arc\ sec[/tex]
option c
Answer:
Option (C)
Explanation:
Here, Diameter= 1,400,000 km = 1.4 x 10^6 km
Distance= 7.57 x 10^13 km
According to the formula, angular diameter= Diameter/Distance
[tex]\alpha = \frac{Diameter}{Distance}[/tex]
[tex]=\frac{1.4\times 10^6}{7.57}\times 10^{-13}[/tex]
[tex]=0.18\times 10^{-7}\text{ radian}[/tex]
Since 1 radian=206265 arc second,
Therefore,
[tex]206265\times 0.18\times 10^{-7}[/tex]
[tex]=\frac{37127.7}{10^7}[/tex]
= .00371 arc second
Hence, the approximate answer is option (C) i.e. 0.0038 arc second.
