Change the chapter
Question
Distances to the nearest stars (up to 500 ly away) can be measured by a technique called parallax, as shown in Figure 34.26. What are the angles $\theta_1$ and $\theta_2$ relative to the plane of the Earth's orbit for a star 4.0 ly directly above the Sun?
Question Image
<b>Figure 34.26</b> Distances to nearby stars are measured using triangulation, also called the parallax method. The angle of line of sight to the star is measured at intervals six months apart, and the distance is calculated by using the known diameter of the Earth's orbit. This can be done for stars up to about 500 ly away.
Figure 34.26 Distances to nearby stars are measured using triangulation, also called the parallax method. The angle of line of sight to the star is measured at intervals six months apart, and the distance is calculated by using the known diameter of the Earth's orbit. This can be done for stars up to about 500 ly away.
Question by OpenStax is licensed under CC BY 4.0.
$90^\circ$ or $89.99977^\circ$ if one has 7 significant figures in the measurements.
Solution Video

OpenStax College Physics for AP® Courses Solution, Chapter 34, Problem 19 (Problems & Exercises) (0:49)

Sign up to view this solution video!

Rating

No votes have been submitted yet.

Quiz Mode

Why is this button here? Quiz Mode is a chance to try solving the problem first on your own before viewing the solution. One of the following will probably happen:

  1. You get the answer. Congratulations! It feels good! There might still be more to learn, and you might enjoy comparing your problem solving approach to the best practices demonstrated in the solution video.
  2. You don't get the answer. This is OK! In fact it's awesome, despite the difficult feelings you might have about it. When you don't get the answer, your mind is ready for learning. Think about how much you really want the solution! Your mind will gobble it up when it sees it. Attempting the problem is like trying to assemble the pieces of a puzzle. If you don't get the answer, the gaps in the puzzle are questions that are ready and searching to be filled. This is an active process, where your mind is turned on - learning will happen!
If you wish to show the answer immediately without having to click "Reveal Answer", you may . Quiz Mode is disabled by default, but you can check the Enable Quiz Mode checkbox when editing your profile to re-enable it any time you want. College Physics Answers cares a lot about academic integrity. Quiz Mode is encouragement to use the solutions in a way that is most beneficial for your learning.

Calculator Screenshots

OpenStax College Physics, Chapter 34, Problem 19 (PE) calculator screenshot 1
Video Transcript
This is College Physics Answers with Shaun Dychko. We are going to measure this parallax angle between the Earth and this distant star which is 4 light years directly above the Sun and we can draw this triangle here where this leg is 4 light years; this leg is the Earth-Sun distance and this Θ 2 is the angle we want to find. Now the tangent of Θ 2 is going to be the opposite, which is 4 light years, divided by the adjacent which is the Earth-Sun distance and we can find the angle by taking the inverse tangent of both sides. So the angle is the inverse tangent of four light years converted into kilometers divided by the Earth-Sun distance in kilometers giving essentially 90 degrees to two significant figures or 89.99977 degrees.

Solutions for problems in chapter 34