Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 25

A space traveler takes off from Earth and moves at speed \(0.988 c\) toward the star Vega, which is \(26.0\) light-years distant. How much time will have elapsed by Earth clocks \((a)\) when the traveler reaches Vega and \((b)\) when the Earth observers receive word from him that he has arrived? ( \(c\) ) How much older will the Earth observers calculate the traveler to be when he reaches Vega than he was when he started the trip?

Short Answer

Expert verified
(a) As observed on Earth, the time it will take for the traveler to reach Vega is 26.3 years. (b) The Earth observers will receive word from him 52.3 years after his departure. (c) The Earth observers will calculate the traveler to be 19.32 years older when he reaches Vega than he was when he started the trip.

Step by step solution

01

Calculate the time for the traveler to reach Vega

First, we calculate the time it takes for the traveler to reach Vega as observed on Earth. This can be done by simply dividing the distance to Vega by the speed of the spaceship. \(T = D/v = 26.0 / 0.988 = 26.3\) years
02

Calculate the time for the message to reach Earth

Secondly, we calculate the time it takes for the message from the traveler to reach Earth. This is simply the distance to Vega divided by the speed of light (since the message travels at the speed of light). \(T_m = D/c = 26.0/1 = 26.0\) years
03

Calculate the total time for both the traveler to reach Vega and the message to reach Earth

The total time as observed on Earth is the sum of the time it takes for the traveler to reach Vega and the time it takes for the message to reach Earth. \(T_{total} = T + T_m = 26.3 + 26.0 = 52.3\) years
04

Calculate the time elapsed on the spaceship

The time elapsed on the spaceship (as experienced by the traveler) can be calculated using the time dilation formula: \[ T_0 = T * \sqrt{1 - (v^2/c^2)} = 26.3 * \sqrt{1 - (0.988^2)} = 6.98\] years
05

Calculate the age difference

The age difference as calculated by the Earth observers is simply the time elapsed on Earth (the time it took for the traveler to reach Vega) minus the time elapsed on the spaceship (as experienced by the traveler). This gives: \[ Age\,Difference = T - T_0 = 26.3 - 6.98 = 19.32\] years.

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

Calculate the speed parameter \(\beta\) of a particle with a momentum of \(12.5 \mathrm{MeV} / c\) if the particle is \((a)\) an electron and \((b)\) a proton.

A rod lies parallel to the \(x\) axis of reference frame \(S\), moving along this axis at a speed of \(0.632 c .\) Its rest length is \(1.68 \mathrm{~m}\). What will be its measured length in frame \(S ?\)

Find the speed parameter \(\beta\) and the Lorentz factor \(\gamma\) for a particle whose kinetic energy is \(10 \mathrm{MeV}\) if the particle is \((a)\) an electron, \((b)\) a proton, and \((c)\) an alpha particle.

A spaceship whose rest length is \(358 \mathrm{~m}\) has a speed of \(0.728 c\) with respect to a certain reference frame. A micrometeorite, with a speed of \(0.817 c\) in this frame, passes the spaceship on an antiparallel track. How long does it take this micrometeorite to pass the spaceship?

Observer \(S\) assigns to an event the coordinates \(x=100 \mathrm{~km}\), \(t=200 \mu \mathrm{s}\). Find the coordinates of this event in frame \(S^{\prime}\), which moves in the direction of increasing \(x\) with speed \(0.950 c\). Assume that \(x=x^{\prime}\) at \(t=t^{\prime}=0\).
See all solutions

Recommended explanations on Physics Textbooks

Force

Read Explanation

Engineering Physics

Read Explanation

Electricity

Read Explanation

Astrophysics

Read Explanation

Physical Quantities And Units

Read Explanation

Particle Model of Matter

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