Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 2

Why does it take at least six months to make a measurement of a star's parallax?

Short Answer

Expert verified
Answer: It takes at least six months to make a measurement of a star's parallax because we need Earth to be in two different positions in its orbit around the Sun to create the largest possible baseline and get the most accurate measure of the parallax angle. Observations taken at shorter intervals would result in a smaller baseline, leading to a smaller parallax angle and making it more difficult to accurately estimate the distance to the star due to observational errors and limitations.

Step by step solution

01

Understanding parallax

Parallax is the apparent shift in the position of an object (like a star) when viewed from different viewpoints. In the case of a star's parallax, the two different viewpoints are the Earth's position at two different times in its orbit around the Sun.
02

Visualizing Earth's orbit and stellar parallax

To measure a star's parallax, we compare the position of the star against the background of more distant stars at two different times when Earth is in different positions in its orbit. The parallax angle is formed by the apparent change in position of the nearby star from these two observations.
03

Earth's movement in six months

When measuring a star's parallax, it helps to have the greatest possible distance between the two observation points. The Earth takes one year (approximately 365.25 days) to orbit the Sun. In six months, Earth will have moved to the opposite side of the Sun, creating a baseline equal to twice the Earth's distance from the Sun (the diameter of Earth's orbit). This provides the largest possible angle for parallax measurement and helps to reduce errors.
04

Calculating the parallax angle

From the two observation points (six months apart), the parallax angle can be calculated using trigonometry. The parallax angle (p) is typically measured in arcseconds. The distance (d) to the star in parsecs can be found using the formula: d = \frac{1}{p} where d is in parsecs and p is the parallax angle in arcseconds. A parsec is a unit of distance equal to about 3.26 light-years or 3.086 x 10^{16} meters.
05

Importance of the six-month interval

The reason it takes at least six months to make a measurement of a star's parallax is that we need Earth to be in two different positions in its orbit around the Sun to create the largest possible baseline and get the most accurate measure of the parallax angle. Observations taken at shorter intervals would result in a smaller baseline, leading to a smaller parallax angle and making it more difficult to accurately estimate the distance to the star due to observational errors and limitations.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Sketch a Hertzsprung-Russell diagram. Indicate the regions on your diagram occupied by (a) main-sequence stars, (b) red giants, (c) supergiants, (d) white dwarfs, and (e) the Sun.

If a red star and a blue star both appear equally bright and both are the same distance from Earth, which one has the larger radius? Explain why.

Why is the magnitude scale called a "backward" scale? What is the difference between apparent magnitude and absolute magnitude?

What information about stars do astronomers learn from binary systems that cannot be learned in any other way? What measurements do they make of binary systems to garner this information?

What is the inverse-square law? Use it to explain why an ordinary lightbulb can appear brighter than a star, even though the lightbulb emits far less light energy per second.
See all solutions

Recommended explanations on Physics Textbooks

Electromagnetism

Read Explanation

Modern Physics

Read Explanation

Electricity and Magnetism

Read Explanation

Particle Model of Matter

Read Explanation

Force

Read Explanation

Engineering Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free