HINT:#
The question asks us to determine the distance that the blob of material appeared to move in three years.
HINT:#
The prompt for the problem tells us the observed change in the angular position that the blob over a period of three years. The previous activity gave us the distance from the earth to the blob.
HINT:#
L/3 years = Δθ/3 years * d

NOTE: This formula uses the approximation that when angle θ is small, sin(θ) ≈ θ.
HINT:#
Δθ/3 years = 0.002 arc-seconds/3 years
d = 800 Mpc
HINT:#
Let's use unit analysis:
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 arc-seconds/3 yr * 1 radian/206,265 arc-seconds = 9.696 x 10-9 radian/3 yr
d = 800 Mpc = 8 x 108 pc * 1 ly/0.30659 pc = 2.61 x 10-9 ly
HINT:#
L/3 years = Δθ/3 years * d
= 9.696 x 10-9 radian/3 yr * 2.61 x 10-9 ly = 25.3 ly/3 years

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