
The question asks us to determine the distance that the blob of material appeared to move in three years.




NOTE: This formula uses the approximation that when angle θ is small, sin(θ) ≈ θ. 

d = 800 Mpc 

L/3 years (lightyears) = Δθ(arcseconds)/3 years * d(Mpc) For our relationship to hold up, we must express Δθ in radians. After that conversion, using the approximate equality of small angles and the sin of that angle, the first term in our equation will be effectively dimensionless. In order to get the light year unit in our final answer, we will have to convert the distance from Mpc to ly. Δθ = 0.002 arcseconds/3 yr * 1 radian/206,265 arcseconds = 9.696 x 10^{9} radian/3 yr d = 800 Mpc = 8 x 10^{8} pc * 1 ly/0.30659 pc = 2.61 x 10^{9} ly 

= 9.696 x 10^{9} radian/3 yr * 2.61 x 10^{9} ly = 25.3 ly/3 years 
close window 