/*! 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 84 In January \(2006,\) the New Hor... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

In January \(2006,\) the New Horizons space probe was launched from Earth with the mission to perform a flyby study of Pluto. The arrival at the dwarf planet was estimated to happen after nine years, in 2015 . The distance between Earth and Pluto varies depending on the location of the planets in their orbits, but at their closest, the distance is 4.2 billion kilometers \((2.6\) billion miles). Calculate the minimum amount of time it takes for a transmitted signal from Pluto to reach the Earth.

Short Answer

Expert verified
About 3 hours and 53 minutes.

Step by step solution

01

Understand the Problem

We need to determine the minimum amount of time it takes for a signal to travel from Pluto to Earth at their closest distance of 4.2 billion kilometers. The speed of light, which is the speed at which signals travel, is approximately 299,792 kilometers per second.
02

Apply the Formula for Time

The formula to calculate the time it takes for light to travel a certain distance is given by \[\text{Time} = \frac{\text{Distance}}{\text{Speed of light}}\]Here, the distance between Pluto and Earth is 4.2 billion kilometers, and the speed of light is 299,792 kilometers per second.
03

Calculate the Time

Substitute the values into the formula:\[\text{Time} = \frac{4,200,000,000}{299,792} \approx 14007.18 \text{ seconds}\]
04

Convert Seconds to a More Understandable Unit

To convert the time from seconds to minutes, divide by 60:\[\text{Time in minutes} = \frac{14007.18}{60} \approx 233.45 \text{ minutes}\]This is roughly 3 hours and 53 minutes.

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 91Ó°ÊÓ!

Key Concepts

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

Signal Transmission
Have you ever wondered how signals travel through space? The speed at which signals are transmitted is determined by the speed of light, which is extremely fast. In scientific terms, it measures approximately 299,792 kilometers per second. This jaw-dropping speed allows us to send and receive data across vast distances in relatively short periods. For instance, when NASA communicates with distant probes exploring our solar system, these signals zip through space at the speed of light.
  • The speed of light is a universal physical constant.
  • Signals in space travel without any significant interference.
  • Light travels about 299,792 kilometers, or roughly 186,282 miles, each second.
Signals need to overcome large distances between celestial bodies, as demonstrated in the case of the New Horizons probe receiving commands from Earth. Despite these vast spaces, light's unfathomable speed reduces the waiting time to a manageable length. Thus, understanding signal transmission is vital for effective communication in space exploration.
Space Exploration
Exploring the vastness of space is one of humanity's most thrilling pursuits. Space missions, like NASA's New Horizons, expand our understanding of the solar system and beyond. Launched in 2006, New Horizons embarked on a mission to see Pluto up close, a journey that took almost a decade.
  • Space missions involve meticulous planning and long travel times.
  • They provide invaluable scientific data about planets, moons, and other celestial bodies.
  • Spacecraft like New Horizons travel through space using the momentum and gravity of celestial bodies.
Though traveling in space might seem slow compared to the speed of light, these missions are unparalleled achievements. They require solving complex problems related to distance, time, and cosmic phenomena. Space exploration not only quenches our thirst for knowledge but also drives technological advancements and international collaborations.
Planetary Distances
Understanding the distances between celestial bodies is crucial in both astronomy and space missions. For example, distance variations between Earth and Pluto can significantly alter the time it takes for a signal to travel between them. When Pluto and Earth are at their closest, they are still about 4.2 billion kilometers apart.
  • Distances in space are often measured in astronomical units (AU) or light years.
  • The Earth and Pluto distance varies due to their elliptical orbits.
  • When they are at their farthest, the distance can exceed 7 billion kilometers.
By calculating these distances accurately, scientists can determine travel times for spacecraft communications and plan mission details with precision. It highlights the vastness of our solar system and underscores the power of scientific advancements that allow us to bridge these enormous spans.

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

If human height were quantized in 1 -cm increments, what would happen to the height of a child as she grows up: (i) the child's height would never change, (ii) the child's height would continuously increase, (iii) the child's height would increase in jumps of \(6 \mathrm{~cm},\) or (iv) the child's height would increase in "jumps" of \(1 \mathrm{~cm}\) at a time?

The watt is the derived SI unit of power, the measure of energy per unit time: \(1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}\). A semiconductor laser in a DVD player has an output wavelength of \(650 \mathrm{nm}\) and a power level of \(5.0 \mathrm{~mW}\). How many photons strike the DVD surface during the playing of a DVD 90 minutes in length?

The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists' understanding of the nature of matter. (a) How did Rutherford's experiments on the scattering of \(\alpha\) particles by a gold foil set the stage for Bohr's theory of the hydrogen atom? (b) In what ways is de Broglie's hypothesis, as it applies to electrons, consistent with J. J. Thomson's conclusion that the electron has mass? In what sense is it consistent with proposals preceding Thomson's work that the cathode rays are a wave phenomenon?

Sketch the shape and orientation of the following types of orbitals: \((\mathbf{a}) s,(\mathbf{b}) p_{z},(\mathbf{c}) d_{x y}\).

Certain elements emit light of a specific wavelength when they are burned or heated in a non-luminous flame. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for a few of the elements are given in the following table: $$\begin{array}{llll} \hline \mathrm{Ag} & 328.1 \mathrm{nm} & \mathrm{Fe} & 372.0 \mathrm{nm} \\ \mathrm{Au} & 267.6 \mathrm{nm} & \mathrm{K} & 404.7 \mathrm{nm} \\ \mathrm{Ba} & 455.4 \mathrm{nm} & \mathrm{Mg} & 285.2 \mathrm{nm} \\ \mathrm{Ca} & 422.7 \mathrm{nm} & \mathrm{Na} & 589.6 \mathrm{nm} \\ \mathrm{Cu} & 324.8 \mathrm{nm} & \mathrm{Ni} & 341.5 \mathrm{nm} \\ \hline \end{array}$$ (a) Determine which of these emissions occur in the ultraviolet part of the spectrum. (b) Which emission has the highest frequency and which one has the lowest frequency? (c) When burned, a sample of an unknown substance is found to emit light of frequency \(6.58 \times 10^{14} \mathrm{~s}^{-1} .\) Which of these elements is probably in the sample?

See all solutions

Recommended explanations on Chemistry Textbooks

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.