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Chapter 1: Problem 47

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 approximately 0.12 AU/min.

Step by step solution

01

Understand Unit Conversion

To express the speed of light in astronomical units per minute, we need to convert from meters per second to kilometers per minute first, and then to astronomical units per minute.
02

Convert Speed of Light to Kilometers per Minute

First, convert the speed of light from meters per second to kilometers per second by dividing by 1000. \[ 3.0 \times 10^{8} \text{ m/s} = 3.0 \times 10^{5} \text{ km/s} \]Next, multiply by 60 to convert from kilometers per second to kilometers per minute. \[ 3.0 \times 10^{5} \text{ km/s} \times 60 = 1.8 \times 10^{7} \text{ km/min} \]
03

Convert Kilometers per Minute to Astronomical Units per Minute

Now, convert kilometers per minute to astronomical units per minute by dividing by the number of kilometers in one astronomical unit.\[ \frac{1.8 \times 10^{7} \text{ km/min}}{1.5 \times 10^{8} \text{ km/AU}} \approx 0.12 \text{ AU/min} \]

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Key Concepts

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

Astronomical Unit
The concept of an astronomical unit, often abbreviated as AU, is a crucial measure in astronomy. It represents the average distance from the Earth to the Sun.
This measurement is approximately equal to \(1.50 \times 10^{8}\) kilometers. The AU is a useful unit because it provides a practical means of measuring vast distances in space in a more relatable context.
  • Astronomical units help astronomers avoid the unwieldy numbers that would otherwise be necessary when discussing distances in the solar system.
  • By using AU, scientists can easily communicate and understand distances between objects like planets, asteroids, and other celestial bodies.
Understanding AU is foundational for any astronomy enthusiast or scholar, as it helps simplify discussions of the scale of our solar system.
Speed of Light
The speed of light is a fundamental constant in physics, symbolized as 'c'. Its value is around \(3.0 \times 10^{8}\) meters per second. This speed is immensely fast, allowing light to travel incredible distances in the universe in short periods.
  • The speed of light underlines the maximum speed at which all energy, matter, and information in the universe can travel.
  • It also plays a critical role in understanding the theory of relativity developed by Albert Einstein, impacting how we perceive time and space.
When it comes to unit conversions, expressing the speed of light in different units, like kilometers per minute or astronomical units per minute, helps apply this knowledge to various scientific contexts. This allows scientists to better relate this constant speed to other measures and calculations.
Kilometer Conversion
Kilometer conversion is an essential skill for converting between various measurement systems.
Considering the context of the original problem, you first convert meters to kilometers by dividing the amount by 1000, which simplifies understanding and computing large distances like those involved with the speed of light.
  • For example, \(3.0 \times 10^{8}\) meters per second is converted to \(3.0 \times 10^{5}\) kilometers per second by dividing by 1000.
  • After this, to change kilometers per second to kilometers per minute, you multiply by 60, since there are 60 seconds in a minute.
Such conversions are vital in making measurements more comprehensible and manageable in scientific and everyday contexts, ensuring accuracy in calculations and practical applications.

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Most popular questions from this chapter

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 \(24 \mathrm{~h} .)\)

A person on a diet might lose \(2.3 \mathrm{~kg}\) per week. Express the mass loss rate in milligrams per second, as if the dieter could sense the second- by-second loss.

A unit of area often used in measuring land areas is the hectare, defined as \(10^{4} \mathrm{~m}^{2}\). An open-pit coal mine consumes 75 hectares of land, down to a depth of \(26 \mathrm{~m},\) each year. What volume of earth, in cubic kilometers, is removed in this time?

On a spending spree in Malaysia, you buy an ox with a weight of 28.9 piculs in the local unit of weights: 1 picul \(=100\) gins, 1 gin \(=16\) tahils, 1 tahil \(=10\) chees, and 1 chee \(=10\) hoons. The weight of 1 hoon corresponds to a mass of \(0.3779 \mathrm{~g}\). When you arrange to ship the ox home to your astonished family, how much mass in kilograms must you declare on the shipping manifest? (Hint: Set up multiple chain-link conversions.)

A ton is a measure of volume frequently used in shipping, but that use requires some care because there are at least three types of tons: A displacement ton is equal to 7 barrels bulk, a freight ton is equal to 8 barrels bulk, and a register ton is equal to 20 barrels bulk. A barrel bulk is another measure of volume: 1 barrel bulk \(=0.1415 \mathrm{~m}^{3} .\) Suppose you spot a shipping order for "73 tons" of M\&M candies, and you are certain that the client who sent the order intended "ton" to refer to volume (instead of weight or mass, as discussed in Chapter 5 ). If the client actually meant displacement tons, how many extra U.S. bushels of the candies will you erroneously ship if you interpret the order as (a) 73 freight tons and (b) 73 register tons? \(\left(1 \mathrm{~m}^{3}=28.378\right.\) U.S. bushels. \()\)
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