Chapter 5.3, Problem 18E

Reminder Round all answers to two decimal places unless otherwise indicated.

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 5.47.) For stars that are 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 small ${}^{43}$ and is normally measured in seconds of arc. The distance to a star can be determined from the parallax angle. The table on next page gives the parallax angle $p$ measured in seconds of arc and the distance $d$ from the sun in light years.

Star	Parallax angle	Distance
Markab	$0.030$	$109$
Al Na’ir	$0.051$	$64$
Alderamin	$0.063$	$52$
Altair	$0.198$	$16.5$
Vega	$0.123$	$26.5$
Rasalhague	$0.056$	$58$

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

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

c. The star Mergez has a parallax angle of $0.052\text{second}$ of arc. Use functional notation to express how far way Mergez is, and then calculate that value.

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