## The Scope and Scale of Physics

1.1 The Scope and Scale of Physics

### Learning Objectives

By the end of this section, you will be able to:

- Describe the scope of physics.
- Calculate the order of magnitude of a quantity.
- Compare measurable length, mass, and timescales quantitatively.
- Describe the relationships among models, theories, and laws.

Visit this site to explore interactively the vast range of length scales in our universe. Scroll down and up the scale to view hundreds of organisms and objects, and click on the individual objects to learn more about each one.

#### Order of magnitude

The **order of magnitude** of a number is the power of 10 that most closely approximates it. Thus, the order of magnitude refers to the scale (or size) of a value.

To find the order of magnitude of a number, take the base-10 logarithm of the number and round it to the nearest integer, then the order of magnitude of the number is simply the resulting power of 10. For example, the order of magnitude of 800 is 10^{3} because log_{10}800 ≈ 2.903, which rounds to 3.

**Practice!**

Practice 1.1.1 |
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Find the order of magnitude of the following physical quantities. |

1. The mass of Earth’s atmosphere: 5.1 × 10^{18} kg |

2. The mass of the Moon’s atmosphere: 25,000 kg |

3. The mass of Earth’s hydrosphere: 1.4 × 10^{21} kg |

4. The mass of Earth: 5.97 × 10^{24} kg |

5. The mass of the Moon: 7.34 × 10^{22} kg |

6. The Earth–Moon distance (semimajor axis): 3.84 × 10^{8} m |

7. The mean Earth–Sun distance: 1.5 × 10^{11} m |

8. The equatorial radius of Earth: 6.38 × 10^{6} m |

9. The mass of an electron: 9.11 × 10^{−31} kg |

10. The mass of a proton: 1.67 × 10^{−27} kg |

11. The mass of the Sun: 1.99 × 10^{30} kg |

Answers: 1. 10^{19} 2. 10^{4} 3. 10^{21} 4. 10^{25} 5. 10^{23} 6. 10^{9} 7. 10^{11} 8. 10^{7} 9. 10^{-30} 10. 10^{-27} 11. 10^{30} |

Practice 1.1.2 |
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Use the orders of magnitude you found in the previous problem to answer the following questions to within an order of magnitude. |

1. How many electrons would it take to equal the mass of a proton? |

2. How many Earths would it take to equal the mass of the Sun? |

3. How many Earth–Moon distances would it take to cover the distance from Earth to the Sun? |

4. How many Moon atmospheres would it take to equal the mass of Earth’s atmosphere? |

5. How many moons would it take to equal the mass of Earth? |

6. How many protons would it take to equal the mass of the Sun? |

Answers: 1. 10^{3}; 2. 10^{5}; 3. 10^{2}; 4. 10^{15}; 5. 10^{2}; 6. 10^{57} |

#### Building Models

A **model** is a representation of something that is often too difficult (or impossible) to display directly. Although a model is justified by experimental tests, it is only accurate in describing certain aspects of a physical system.

A **theory** is a testable explanation for patterns in nature supported by scientific evidence and verified multiple times by various groups of researchers.

A **law** uses concise language to describe a generalized pattern in nature supported by scientific evidence and repeated experiments.

**Discuss!**

Reflect on this question and take notes on how you would answer it. Then we will share these thoughts together in a class discussion.

If two different theories describe experimental observations equally well, can one be said to be more valid than the other (assuming both use accepted rules of logic)?