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Chapter 1: Problem 47

ssM An astronomical unit (AU) is the average distance between Earth and the Sun, approximately \(1.50 \times 10^{8} \mathrm{~km} .\) The speed of light is about \(3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}\). Express the speed of light in astronomical units per minute.

Short Answer

Expert verified
The speed of light is 0.12 AU/min.

Step by step solution

01

Convert Speed Units

First, convert the speed of light from meters per second to kilometers per second. Since there are 1000 meters in a kilometer, divide the speed by 1000: \[ \text{Speed of light: } \frac{3.0 \times 10^8 \, \text{m/s}}{1000} = 3.0 \times 10^5 \, \text{km/s} \].
02

Calculate Speed in AU per Second

Determine how many kilometers are in one astronomical unit: \[ 1 \, \text{AU} = 1.50 \times 10^8 \, \text{km} \].Now calculate how many AUs the light travels per second by dividing the speed in km/s by the number of km per AU: \[ \frac{3.0 \times 10^5 \, \text{km/s}}{1.50 \times 10^8 \, \text{km/AU}} = 2 \times 10^{-3} \, \text{AU/s} \].
03

Convert to AU per Minute

Since there are 60 seconds in a minute, multiply the result by 60 to convert the speed to AU per minute: \[ 2 \times 10^{-3} \, \text{AU/s} \times 60 \, \text{s/min} = 0.12 \, \text{AU/min} \].

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Key Concepts

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

Speed of Light
The speed of light is a fundamental constant in physics, denoted by the symbol \( c \). It represents the maximum speed at which information travels through a vacuum. This speed is approximately \( 3.0 \times 10^{8} \) meters per second. In simpler terms, light can travel around the Earth about 7.5 times in one second.
  • Light speed is essential for understanding various phenomena in physics and astronomy.
  • It plays a critical role in Einstein's theory of relativity, affecting how time and space are perceived.
Understanding the speed of light helps astronomers determine distances in space and measure how long it takes light to travel from astronomical bodies to Earth.
Unit Conversion
Unit conversion is the process of transforming a measurement from one unit to another. It helps to make measurements compatible and understandable across different systems.
For the speed of light, unit conversion is vital, especially when astronomers use different units for different scales.
  • To convert meters per second to kilometers per second, divide by 1,000 (since 1 kilometer is 1,000 meters).
  • To express measurements in astronomical units (AU), compare them to the average Earth-to-Sun distance.
This practice ensures accuracy and consistency when calculating and interpreting astronomical data, allowing clearer communication of distances and speeds.
Distance Measurement
In astronomy, measuring distances accurately is crucial for understanding our universe. Popular units like kilometers or miles become impractical for vast cosmic distances. Instead, astronomers use the astronomical unit (AU) to simplify these large numbers.
  • One AU is the average distance from the Earth to the Sun, approximately \( 1.50 \times 10^{8} \) kilometers.
  • It's a helpful standard for comparing distances within our solar system and beyond.
Such units allow scientists to calculate how far planets or stars are from each other, enabling them to comprehend their arrangement and movement through space.
Astronomy Basics
Astronomy is a natural science that endeavors to understand celestial objects and phenomena outside Earth's atmosphere. Understanding fundamental concepts like distance and speed of light is essential for studying the universe.
  • Core basics of astronomy include terms like astronomical units, light years, and parsecs which help in understanding cosmic scales.
  • These measures assist in estimating spatial relationships among heavenly bodies, providing insights into their behavior and properties.
By grasping these basics, astronomy becomes more accessible and less abstract, allowing students and enthusiasts to appreciate the grandeur of space and its intricate workings.

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Most popular questions from this chapter

A traditional unit of length in Japan is the ken \((1 \mathrm{ken}=\) \(1.97 \mathrm{~m}\) ). What are the ratios of (a) square kens to square meters and (b) cubic kens to cubic meters? What is the volume of a cylindrical water tank of height \(5.50\) kens and radius \(3.00\) kens in (c) cubic kens and (d) cubic meters?

The micrometer \((1 \mu \mathrm{m})\) is often called the micron. (a) How many microns make up \(1.0 \mathrm{~km}\) ? (b) What fraction of a centimeter equals \(1.0 \mu \mathrm{m} ?(\mathrm{c})\) How many microns are in \(1.0 \mathrm{yd}\) ?

yuring heavy rain, a section of a mountainside measuring \(2.5 \mathrm{~km}\) horizontally, \(0.80 \mathrm{~km}\) up along the slope, and \(2.0 \mathrm{~m}\) deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring \(0.40 \mathrm{~km} \times 0.40 \mathrm{~km}\) and that mud has a density of \(1900 \mathrm{~kg} / \mathrm{m}^{3}\). What is the mass of the mud sitting above a \(4.0 \mathrm{~m}^{2}\) area of the valley floor?

Until 1883 , every city and town in the United States kept its own local time. Today, travelers reset their watches only when the time change equals \(1.0 \mathrm{~h}\). How far, on the average, must you travel in degrees of longitude between the time-zone boundaries at which your watch must be reset by \(1.0 \mathrm{~h} ?\) (Hint: Earth rotates \(360^{\circ}\) in about \(24 \mathrm{~h}\).)

Earth has a mass of \(5.98 \times 10^{24} \mathrm{~kg}\). The average mass of the atoms that make up Earth is \(40 \mathrm{u}\). How many atoms are there in Earth?
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