PROBLEMS

for

Introduction to Planetary Science;

The Geological Perspective

by

Gunter Faure and Teresa M. Mensing

The Ohio State University

Published by Springer, P.O. Box 17,

3300 AA Dordrecht, The Netherlands

2007

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Chapter 1: The Urge to Explore

1. Select one of the several polar explorers and write a short report about him (2 pages doublespaced). Identify what aspect of planning and execution led to success or failure of the expedition: 1. Roald Amundsen

2. Robert F. Scott

3. Ernest Shackleton

4. Fridtjof Nansen

5. Lauge Koch

6. Peter Freuchen

Attributes that are necessary for success:

1. Adequate supplies and equipment

2. Experience gained during prior expeditions

3. Leadership qualities

4. Wide range of skills necessary for survival

5. Adaptation to the environment

6. Selection of compatible companions

7. Strong motivation

8. Careful planning based on experience

9. Realistic expectations

10. Willingness to admit defeat

11. Careful risk management

12. Good luck

2. Solve the equation

first for the velocity (v) and then for the orbital radius (r)

3. Calculate the velocity of the Earth in its orbit around the Sun.

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M = 1.99 × 1030 kg (mass of the Sun) r = 149.6 × 109 m (radius of the orbit of the Earth)

G = 6.67 × 10-11 Nm2/kg2 (gravitational constant) v = velocity

4. What important assumption underlies the calculation in problem 3 above?

The orbit of the Earth around the Sun is a circle.

5. Calculate the average orbital velocity of the Earth given that: r = 149.6 × 106 km (radius of the orbit of the Earth) p = 365.25 days (time required for the Earth to complete one orbit around the Sun)

C = 2Br (circumference of a circle)

B = 3.14

Express the velocity in km/s

v = 2.5721 × 106 km/day

6. Does the good agreement of the orbital velocities obtained in problems 3 and 5 above prove

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No, both calculations assume that the orbit of the Earth is a circle.

Chapter 2: From Speculation to Understanding

1. Express 1 kilometer in terms of millimeters

1 km = 1000 m = 1000 × 100 cm = 1000 × 100 × 10 mm

1 km = 106 mm

2. Convert 1 lightyear into the corresponding number of astronomical units.

1 AU = 149.6 × 106 km

1 ly = 9.46 × 1012km

1 ly = 6.3235 × 104 = 63,235 AU

3. How long would it take a spacecraft to reach the star Proxima Centauri assuming that the speed of the spacecraft is 1000 km/s and that the distance to Proxima Centauri is 4.2 ly?

Express the result in sidereal years.

distance = 4.2 ly = 4.2 × 9.46 × 1012 km velocity = 1000 km/s

Traveltime to Proxima Centauri: 1259 years (What does that mean?)

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4. Derive an equation for the conversion of temperatures on the Fahrenheit to the Kelvin scale

(1)

C = K - 273.15

(2)

From equation (1);

Substitute equation (2) for C

Test: Let T = 32°F

5. Write a brief essay about the life and scientific contributions of one of the following pioneers of astronomy.

a. Galileo Galilei

b. Johannes Kepler

c. Isaac Newton

d. Albert Einstein

e. Edwin Hubble

f. Carl Sagan

Consider these and other aspects:

1. Education

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2. Evidence of unusual talent as a child

3. Support from colleagues

4. Support from contemporary society

5. Motivation

6. Problem to be solved

7. Available data

8. Reasoning to reach conclusions

9. Recognition for achievement

10. Perseverance in the face of adversity

11. Vindication or despair

Chapter 3: The Planets of the Solar System

1. Calculate the volume of the Earth (VE) and the Sun (VS) and compare them to each other by dividing the volume of the Sun by the volume of the Earth. Express the result in words.

Radius of the Sun: 695,700 km

Radius of the Earth: 6378 km

Volume of a sphere =

Volume of the Sun

VS = 1.4097 × 1018 km3

Volume of the Earth

VE = 1.0862 × 1012 km3

VS = 1.297 × 106 VE

The Volume of the Sun is one million two hundred ninety seven times larger than the volume of the Earth.

2. Express the average distance between the Sun and the Earth as a percent of the average