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Chapter 1: Problem 5

An astronomical unit (AU) is the average distance of Earth from 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 terms of astronomical units per minute.

Short Answer

Expert verified
The speed of light is 0.12 AU per minute.

Step by step solution

01

- Convert kilometers to meters

First, convert the distance of one astronomical unit from kilometers to meters. Since 1 km = 1000 m, we have: \[ 1 \text{ AU} = 1.50 \times 10^8 \text{ km} = 1.50 \times 10^8 \times 10^3 \text{ m} = 1.50 \times 10^{11} \text{ m} \]
02

- Calculate the speed of light in meters per minute

Next, convert the speed of light from meters per second to meters per minute. Since there are 60 seconds in a minute, multiply the speed of light by 60: \[ \text{Speed of light} = 3.0 \times 10^8 \text{ m/s} \] \[ \text{Speed of light in m/min} = 3.0 \times 10^8 \text{ m/s} \times 60 \text{ s/min} = 1.8 \times 10^{10} \text{ m/min} \]
03

- Express the speed of light in AU per minute

Finally, convert the speed from meters per minute to astronomical units per minute by dividing the speed in meters per minute by the distance of one astronomical unit: \[ \text{Speed of light in AU/min} = \frac{1.8 \times 10^{10} \text{ m/min}}{1.50 \times 10^{11} \text{ m}} \] \[ \text{Speed of light in AU/min} = 0.12 \text{ AU/min} \]

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Key Concepts

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

astronomical unit
An astronomical unit (AU) is a fundamental concept in astronomy. It represents the average distance from the Earth to the Sun, which is about \(1.50 \times 10^8\) kilometers. This measurement helps astronomers and scientists communicate immense distances within our solar system more easily.
Understanding the concept of AU is crucial for various scientific and practical applications such as:
  • Measuring distances between celestial bodies
  • Calculating orbital parameters
  • Understanding scale within the solar system
  • Translating vast distances into more comprehensible units
Learning about AU also helps in visualizing the scale of the universe better. Instead of dealing with impractically large numbers, using AU simplifies communication and calculations.
unit conversion
Unit conversion is a crucial skill in physics and other sciences. It allows us to translate measurements from one unit to another, making calculations and comparisons easier. In the given exercise, we need to convert various units:
1. Converting kilometers to meters because the speed of light is given in meters per second.
2. Converting seconds to minutes to match the desired output measurement (AU per minute).
Let's break down how to effectively convert units:
  • Always know the conversion factors (e.g., 1 km = 1000 m, 1 minute = 60 seconds).
  • Use these factors to multiply or divide the given values to the desired units.
  • Be careful with powers of ten when dealing with scientific notation to avoid errors.
Practicing these standard conversions helps improve your problem-solving efficiency and accuracy in various scientific calculations.
physics problem-solving
Physics problem-solving involves using mathematical tools and scientific principles to find solutions to real-world problems. In the exercise provided, we follow a step-by-step process to convert the speed of light to astronomical units per minute. The steps include:
  • Identify the given values (distance of AU and speed of light).
  • Convert these values into compatible units (kilometers to meters, seconds to minutes).
  • Apply necessary mathematical operations to find the desired output (speed of light in AU/min).
To excel in physics problem-solving, it is essential to:
  • Understand the problem and break it down into manageable parts.
  • Keep track of units and conversion factors throughout the process.
  • Double-check calculations to ensure accuracy.
  • Practice regularly to enhance both conceptual understanding and computational skills.
Through consistent practice, you build a strong foundation and can approach more complex problems with confidence.

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Most popular questions from this chapter

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 \(1.0 \mu \mathrm{m}\) ? (c) How many microns are in \(1.0 \mathrm{yd}\) ?

A standard interior staircase has steps each with a rise (height) of \(19 \mathrm{~cm}\) and a run (horizontal depth) of \(23 \mathrm{~cm}\). Research suggests that the stairs would be safer for descent if the run were, instead, \(28 \mathrm{~cm}\). For a particular staircase of total height \(4.57 \mathrm{~m}\), how much farther would the staircase extend into the room at the foot of the stairs if this change in run were made?

Horses are to race over a certain English meadow for a distance of \(4.0\) furlongs. What is the race distance in units of (a) rods and (b) chains? ( 1 furlong \(=201.168 \mathrm{~m}, 1 \mathrm{rod}=5.0292 \mathrm{~m}\), and 1 chain \(=20.117 \mathrm{~m} .)\)

Muffet An old English children's rhyme states, "Little Miss Muffet sat on her tuffet, eating her curds and whey, when along came a spider who sat down beside her...." 'The spider sat down not because of the curds and whey but because Miss Muffet had a stash of 11 tuffets of dried flies. The volume measure of a tuffet is given by 1 tuffet \(=2\) pecks \(=0.50\) bushel, where 1 Imperial (British) bushel \(=36.3687\) liters (L). What was Miss Muffet's stash in (a) pecks, (b) bushels, and (c) liters?

Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of \(1 \mathrm{ft}\). A severe thunderstorm dumped \(2.0\) in. of rain in \(30 \mathrm{~min}\) on a town of area \(26 \mathrm{~km}^{2}\). What volume of water, in acre-feet, fell on the town?
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