Astrophysics and the Evolution of the Universe

Leonard S Kisslinger

• Publisher: WSPC
• Year: 2016
• eBook ISBN: 9789813147126
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Computer Science General

The aim of this book is to teach undergraduate college or university students, and adults interested in astronomy and astrophysics, the basic mathematics and physics concepts needed to understand the evolution of the universe, and based on this to teac

Chapter 1

Physics Concepts Needed for Astrophysics

In this first chapter, after a brief overview of some basic physics concepts we review the concepts of position, velocity, and acceleration as vectors, needed for the treatment of topics such as the size and rate of expansion of the universe. We then discuss force, Newton’s Law of Motion, and the force of gravity, and review the concept of energy and temperature as a form of energy. As we discuss in later chapters, knowing the temperature of the universe at different times is essential to understand the evolution of the universe. Finally we briefly introduce Dark Energy.

From Big Bang to now.

The figure shows the evolution of the universe from the very early time, when inflation took place, through cosmological phase transitions EWPT (particles got masses) and QCDPT (neutrons and protons form), emitted the Cosmic Microwave Background Radiation (CMBR) from which we learn the constituents of the universe, to the present time with stars and galaxies. We will explore all of these events in this book.

1. Overview of Some Basic Physics Concepts

The basic concepts reviewed in this chapter are treated in greater detail in some textbooks, such as Blatt [1], Halliday and Resnick, or some more recent texts.

1.1. Time, Position, Distance, Velocity, Acceleration, Force, Newton’s Law of Motion, Energy, Temperature

1.1.1. Time = t, Position = r, Distance, Velocity

Calling time = t and position = r, at time = t₁ an object is at position r₁, and at time t₂ at position r₂. Let us define the difference in time as ∆t, and the difference between positions as distance:

Velocity = v, speed in one spatial dimension, is the distance an object moves in a time difference divided by the time difference, in the limit as the time difference becomes very small:

That is, v is the rate of change of position with respect to time. As we shall see in the next section, velocity is a vector, with magnitude and direction, and the quantity v = speed is the magnitude of the velocity.

1.1.2. Acceleration, Force, and Newton’s Law of Motion

If v₁, v₂ are speeds at t₁,t₂, then acceleration = a is the rate of change of speed with respect to time:

Force = F causes an object to move. That is, it changes its speed. From the definitions above, force causes acceleration.

NEWTON’S LAW OF MOTION: if a force F acts on an object with mass m, then m has acceleration = a, which is

Newton’s Law of Motion, which we study in detail in Section 3, is one of the most important principles in science.

1.1.3. Work and Energy

Work: If a force is exerted on an object and it moves a distance = d, then the force does work = W = force times distance. If work is exerted on a mass m, m gets energy, E, equal to the work:

W = E.

The types of energy are:

KINETIC ENERGY	=	energy of motion.
POTENTIAL ENERGY	=	stored energy.
HEAT ENERGY	=	energy of a substance due to its components, such as atoms, moving. A type of internal kinetic energy.

TEMPERATURE = T of an object is a measurement of its heat energy, with heat energy = kT, where k is Boltzman’s constant. As we shall see in later chapters, T is a very important property when we explore the evolution of the universe.

We shall study energy in detail later in this chapter.

1.2. Units of Time, Distance, Velocity, Acceleration, Force, Energy, Temperature

1.2.1. Powers of Ten

Before we discuss the units, we need to define the powers of ten.

1.2.2. Units of Time, Distance, Velocity, and Acceleration

The unit of time is second = sec = s

1 minute	=	60s
1 hour	=	60 minutes = 60 × 60 s = 3,600 s = 3.6 × 10^3 s
1 year	=	365 days = 365 × 24 × 3,600 s = 31,536,000 s
	=	3.1536 × 10^7 s ≃ 3.15 × 10^7 s

The unit of distance or position i...

Table of contents

• Cover Page
• Title Page
• Copyright
• Contents
• Preface
• Chapter 1. Physics Concepts Needed for Astrophysics
• Chapter 2. Forces and Particles
• Chapter 3. Hubble’s Law: Expansion of the Universe
• Chapter 4. Stars, Galaxies, Etc.
• Chapter 5. Neutrino Oscillations, Symmetries, and Pulsar Kicks
• Chapter 6. Einstein’s Special and General Theories of Relativity
• Chapter 7. Radius and Temperature of the Universe from the General Theory of Relativity
• Chapter 8. Cosmic Microwave Background Radiation (CMBR)
• Chapter 9. Electroweak Phase Transition (EWPT)
• Chapter 10. Quantum Chromodynamic Phase Transition (QCDPT)
• 11. Gravitational Waves
• Solutions to Problems
• Appendix: Vector Calculus and Maxwell’s Equations
• Index