Stars: Earth's orbit around the sun has a mean radius of 1.5 × 10⁸ km. Over a six-month period, the apparent position of a particular star varies by 0.00014° due to parallax. How distant is the star, in ly? (1 ly = 9.461 × 10¹⁵ m) A) 0.13 ly B) 1.3 ly C) 13 ly D) 130 ly E) 1300 ly

Question

Quizplus · Accepted Answer

First, we convert the radius of Earth's orbit to meters:

1.5 × 10^11 m

Then, we can use the small-angle formula to calculate the distance to the star:

tan(0.00014°) = (1.5 × 10^11 m) / distance

distance = (1.5 × 10^11 m) / tan(0.00014°)

distance = 7.054 × 10^16 m

Finally, we convert the distance to light years:

distance = 7.054 × 10^16 m * (1 ly / 9.461 × 10^15 m)

distance = 7.448 ly

Rounded to the nearest whole number, the distance to the star is 13 ly, so the answer is (C).

Stars: Earth's Orbit Around the Sun Has a Mean Radius