/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 The nearest star to our solar sy... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 20

The nearest star to our solar system is \(4.29\) light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun ?

Short Answer

Expert verified
Alpha Centauri is 1.316 parsecs away with a parallax angle of about 0.76 arcseconds.

Step by step solution

01

Understanding Light Years and Parsecs

A light year is the distance light travels in one year. A parsec is a unit measuring large astronomical distances. One parsec is equivalent to approximately 3.26 light years. Therefore, to convert light years to parsecs, divide the light years by 3.26.
02

Converting Light Years to Parsecs

Given that Alpha Centauri is 4.29 light years away, we convert this to parsecs using the formula: \[ \text{Distance in parsecs} = \frac{4.29}{3.26} \approx 1.316 \, \text{parsecs} \]
03

Understanding Stellar Parallax

Stellar parallax is the apparent shift in position of a nearby star against the distant background when observed from two different positions in Earth's orbit. The parallax angle is inversely proportional to the distance in parsecs: \[ \text{Parallax angle (arcseconds)} = \frac{1}{\text{distance in parsecs}} \]
04

Calculating the Parallax Angle

Using the distance of 1.316 parsecs: \[ \text{Parallax angle} = \frac{1}{1.316} \approx 0.76 \, \text{arcseconds} \] This means that Alpha Centauri would have a parallax angle of approximately 0.76 arcseconds.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Light Year
A light year is a unit of distance that describes how far light travels in one year through a vacuum. To put it into perspective, light can travel about 299,792,458 meters per second. Over the course of a year, this translates to roughly 9.46 trillion kilometers, or about 5.88 trillion miles. This incredible distance makes light years a very convenient unit when discussing the vast expanses between stars and galaxies.
  • One light year equals the distance light covers in a year.
  • Equivalent to approximately 9.46 trillion kilometers or 5.88 trillion miles.
  • Helps express large astronomical distances in comprehensible terms.
Using light years allows astronomers to communicate and record the distances even in our cosmic backyard, such as Alpha Centauri, which is 4.29 light years away.
Parsec
A parsec is another unit for measuring astronomical distances. It stands for "parallax of one arcsecond". A parsec bridges our understanding of stellar distances using the angle of apparent motion (parallax) of objects. This becomes especially relevant when observing nearby stars as the Earth moves around the Sun.
  • 1 parsec equals approximately 3.26 light years.
  • It links directly to the observable parallax angle of a star.
  • A practical measure when calculating vast interstellar distances.
Calculating parsecs simplifies understanding distances by linking them to parallax angles, which is critical in astronomy. For example, converting 4.29 light years from Alpha Centauri to parsecs shows about 1.316 parsecs.
Parallax Angle
The parallax angle is a fascinating concept that reveals the distance of stars by measuring their apparent shift in position as Earth orbits the Sun. This apparent movement is called stellar parallax, and it's vital for measuring distances to stars within a couple of hundred light years.
  • The parallax angle is usually measured in arcseconds.
  • Smaller angles indicate greater distances.
  • It is inversely proportional to the distance in parsecs.
To observe this phenomenon, astronomers look at nearby stars like Alpha Centauri from different points in Earth's orbit, six months apart. The calculation for the parallax angle uses the formula: \[ \text{Parallax angle (arcseconds)} = \frac{1}{\text{distance in parsecs}} \]With Alpha Centauri at approximately 1.316 parsecs away, its parallax angle would be roughly 0.76 arcseconds, illustrating its relative proximity in space terms.

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

Precise measurements of physical quantities are a need of science. For example, to ascertain the speed of an aircraft, one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War II. Think of different examples in modern science where precise measurements of length, time, mass etc. are needed. Also, wherever you can, give a quantitative idea of the precision needed.

State the number of significant figures in the following: (a) \(0.007 \mathrm{~m}^{2}\) (b) \(2.64 \times 10^{24} \mathrm{~kg}\) (c) \(0.2370 \mathrm{~g} \mathrm{~cm}^{-3}\) (d) \(6.320 \mathrm{~J}\) (e) \(6.032 \mathrm{~N} \mathrm{~m}^{-2}\) (f) \(0.0006032 \mathrm{~m}^{2}\)

Explain this statement clearly : "To call a dimensional quantity 'large' or 'small' is meaningless without specifying a standard for comparison". In view of this, reframe the following statements wherever necessary : (a) atoms are very small objects (b) a jet plane moves with great speed (c) the mass of Jupiter is very large (d) the air inside this room contains a large number of molecules (e) a proton is much more massive than an electron (f) the speed of sound is much smaller than the speed of light.

A famous relation in physics relates 'moving mass' \(m\) to the 'rest mass' \(m_{0}\) of a particle in terms of its speed \(v\) and the speed of light, \(c\). (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes: \(m=\frac{m_{0}}{\left(1-v^{2}\right)^{1 / 2}}\) Guess where to put the missing \(c\).

The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding \(10^{7} \mathrm{~K}\), and its outer surface at a temperature of about \(6000 \mathrm{~K}\). At these high temperatures, no substance remains in a solid or liquid phase. In what range do you expect the mass density of the Sun to be, in the range of densities of solids and liquids or gases? Check if your guess is correct from the following data : mass of the Sun \(=2.0 \times 10^{30} \mathrm{~kg}\), radius of the \(\operatorname{Sun}=7.0 \times 10^{8} \mathrm{~m}\).
See all solutions

Recommended explanations on Physics Textbooks

Work Energy and Power

Read Explanation

Waves Physics

Read Explanation

Wave Optics

Read Explanation

Force

Read Explanation

Nuclear Physics

Read Explanation

Magnetism

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.