Astronomers often measure large distances Using astronomical vosu (AU) vohere i)
AU is the average distance from Earth to the Sun. In the image, drepresemts the distance from a star to the Sun. Using a technique called "stellar parallax"
astronomers determined $θ$ is 0.00001389 degrees.
NOT TO SCALE
a. How far away is the star from the Sun in astronomical units? Round your answer to the nearest thousand.

Answer

Expert–verified

Hide Steps

Answer

Round the distance to the nearest thousand: $4, 125, 000$

Steps

Step 1 ：Convert the angle θ from degrees to radians: $θ_{r a d i a n s} = θ_{d e g r e e s} \times \frac{π}{180}$

Step 2 ：Use the formula for stellar parallax to find the distance in astronomical units: $d i s t a n c e_{A U} = \frac{1}{\sin (θ_{r a d i a n s})}$

Step 3 ：Round the distance to the nearest thousand: $4, 125, 000$