Parallax angle: If we view a star now, and then view it again 6 months later, our position will have changed by the diameter of the Earth’s orbit around the sun. (See Figure 5.68.) For stars within...

Parallax angle: If we view a star now, and then view it again 6 months later, our position will have changed by the diameter of the Earth’s orbit around the sun. (See Figure 5.68.) For stars within about 100 light-years of Earth, the change in viewing location is sufficient to make the star appear to be in a different location in the sky. Half of the angle from one location to the next is known as the parallax angle. Even for nearby stars, the parallax angle is very small36 and is normally measured in seconds of arc. The distance to a star can be determined from the parallax angle. The table below gives parallax angle p measured in seconds of arc and the distance d from the sun measured in light-years.

a. Make a plot of ln d against ln p, and determine whether it is reasonable to model the data with a power function.

b. Make a power function model of the data for d in terms of p.

c. If one star has a parallax angle twice that of a second, how do their distances compare?

d. The star Mergez has a parallax angle of 0.052 second of arc. Use functional notation to express how far away Mergez is, and then calculate that value.

e. The star Sabik is 69 light-years from the sun. What is its parallax angle?