Answer:
Option B. 1,100 Earth diameters
Solution:
Angular position of steroid, [tex]\theta = 0.05^{\circ} = 8.726\times 10^{-4} radians[/tex] (given)
To calculate the distance of asteroid, we use parallax method given as:
[tex]\theta = \frac{arc length(l)}{radius(R)}[/tex] (1)
where,
From the relation:
l = [tex]\theta \times R[/tex]
we get:
distance(d) or R = [tex]\frac{Earth diameter}{\theta}[/tex]
distance(d) or R = [tex]\frac{2\times radius of earth}{\theta}[/tex]
d = [tex]\frac{2\times 6350000}{8.726\times 10^{-4}}[/tex]
distance, d = [tex]1.455\times 10^{10} m[/tex]
Comparing it with Earth's diameter:
d = [tex]\frac{1.455\times 10^{10}}{2\times 6350000} = 1,146[/tex]
Since, the value is close to 1,100 Earth diameters, therefore, option B is the right answer.
