Solve the Problem $0.314$ Arc Seconds (Parallax Is the Change in Position of the Friedrich

question 41

Multiple Choice

Solve the problem.
-In 1838, the German mathematician and astronomer Friedrich Wilhelm Bessel was the first person to calculate the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61 Cygni, at $0.314$ arc seconds (Parallax is the change in position of the star measured against background stars as Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about $150,000,000 \mathrm {~km}$ and $\theta = 0.314$ seconds $= \frac { 0.314 } { 60 }$ minutes $= \frac { 0.314 } { 60 \cdot 60 }$ degrees, determine the distance d from Earth to 61 Cygni using Bessel's figures. Express the answer in scientific notation.

• A) \(1.97 \times 10 ^ { 14 } \mathrm {~km}\)
• B) \(1.05 \times 10 ^ { 14 } \mathrm {~km}\)
• C) \(2.28 \times 10 ^ { 13 } \mathrm {~km}\)
• D) \(9.85 \times 10 ^ { 13 } \mathrm {~km}\)

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