### Orbital and Speed Calculations**a) Orbital Speed of the Earth**- Assume that the Earth follows a perfectly circular orbit around the Sun, with a radius of 1 AU (Astronomical Unit). It takes one year for the Earth to complete an orbit. Calculate the average speed of the Earth in its orbit and provide the answer in kilometers per second.**b) Highway Speed Conversion**- The typical speed limit for a car on an Illinois highway is 75 miles per hour. Convert this speed to kilometers per second.**c) Comparison of Speeds**1. Compare the speed of Earth to the speed of the car found in part (b). 2. First, determine the difference between them (subtract).3. Then, determine their ratio (divide).4. Discuss which of these methods provides a better way of comparing the numbers, and why. Which method best emphasizes the magnitude of the difference between these speeds?### Possibly Useful Equations/Relations- **Distance Calculation:** Distance = Speed × Time = v × t- **Circle Circumference:** Circumference = π × Diameter = π × D- **Diameter Calculation:** Diameter = 2 × Radius = 2 × R### Units and Abbreviations- **m:** meter (distance)- **cm:** centimeter (distance)- **km:** kilometer (distance)- **AU:** Astronomical Unit (distance)- **s:** second (time)- **yr:** year (time)### Relevant Numbers- **Speed of Light:** 3 × 10⁸ m/s- **Light Year Distance:** 1 lightyear = distance light travels in one year = 9.5 × 10¹² km- **Astronomical Unit:** 1 AU = 150,000,000 km = 1.5 × 10⁸ km- **Conversion Factors:** - 1 inch = 2.54 cm - 1 m = 100 cm - 1 m = 0.001 km - 1 mile = 1.6 km - 1 mile = 5280 feet - 1 foot = 12 inchesUse these equations, units, and conversion factors to solve the problems and analyze the speeds effectively.

Answered: 1) Assume that the Earth follows a…

Applications and Investigations in Earth Science (9th Edition)

9th Edition

ISBN:9780134746241

Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Chapter1: The Study Of Minerals

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### Orbital and Speed Calculations

**a) Orbital Speed of the Earth**
- Assume that the Earth follows a perfectly circular orbit around the Sun, with a radius of 1 AU (Astronomical Unit). It takes one year for the Earth to complete an orbit. Calculate the average speed of the Earth in its orbit and provide the answer in kilometers per second.

**b) Highway Speed Conversion**
- The typical speed limit for a car on an Illinois highway is 75 miles per hour. Convert this speed to kilometers per second.

**c) Comparison of Speeds**
1. Compare the speed of Earth to the speed of the car found in part (b).
2. First, determine the difference between them (subtract).
3. Then, determine their ratio (divide).
4. Discuss which of these methods provides a better way of comparing the numbers, and why. Which method best emphasizes the magnitude of the difference between these speeds?

### Possibly Useful Equations/Relations
- **Distance Calculation:** Distance = Speed × Time = v × t
- **Circle Circumference:** Circumference = π × Diameter = π × D
- **Diameter Calculation:** Diameter = 2 × Radius = 2 × R

### Units and Abbreviations
- **m:** meter (distance)
- **cm:** centimeter (distance)
- **km:** kilometer (distance)
- **AU:** Astronomical Unit (distance)
- **s:** second (time)
- **yr:** year (time)

### Relevant Numbers
- **Speed of Light:** 3 × 10⁸ m/s
- **Light Year Distance:** 1 lightyear = distance light travels in one year = 9.5 × 10¹² km
- **Astronomical Unit:** 1 AU = 150,000,000 km = 1.5 × 10⁸ km
- **Conversion Factors:**
- 1 inch = 2.54 cm
- 1 m = 100 cm
- 1 m = 0.001 km
- 1 mile = 1.6 km
- 1 mile = 5280 feet
- 1 foot = 12 inches

Use these equations, units, and conversion factors to solve the problems and analyze the speeds effectively.

Expert Solution

Step 1: Introduction

Answer a)

It is given that,

the radius of the Earth, r = 1 AU

1 AU = 1.5 x 10⁸ km = 1.5 x 10¹¹ meters

The radius of the Earth, r = 1.5 x 10¹¹ meters

time taken for Earth to orbit around the Sun, time = 1 year

time = (365 x 24 x 60 x 60) Seconds = 3.156 x 10⁷ seconds

So, time taken for Earth to orbit around the Sun, time = 3.156 x 10⁷ seconds

The average speed of the Earth can be calculated using the formula:

V = 2πr/T

V = (2 x 3.14 x 1.5 x 10¹¹)/( 3.156 x 10⁷)

V = 2.98 x 10⁴ m/sec

Or, V = 29.8 km/sec

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