PART I
Mechanics of G Chapter 1
The Physics of Gravity
Humans exist in a gravity-dependent environment. In order to fully appreciate the physiological consequences of human exposure to high-gravitational forces, it is useful first to have a thorough understanding of what is meant by the terms gravity and acceleration, since they will be used frequently throughout this book. This chapter will examine the mathematics and physics underlying these important terms.
Mechanics
Initially, it is helpful to define some important terms in mechanics that will be used repeatedly throughout this book. Speed is the term used to denote a change in distance with respect to time. It is a scalar quantity, reflecting magnitude only. When both the magnitude and direction of change in distance with time are considered, the term velocity is used rather than speed. Velocity is a vector quantity. When velocity experiences a rate of change with respect to time, acceleration is said to have occurred. It can also be thought of as the second derivative of distance with respect to time. Acceleration is of course also a vector quantity, having both magnitude and direction. The magnitude of acceleration, and the direction in which it is applied, will be examined in more detail in Chapter 2.
The terms speed, velocity, acceleration and force (to be discussed later with Newton’s Laws of Motion) are straightforward terms. Unfortunately, in many cases they are used interchangeably and in the wrong technical sense. This is worth briefly discussing, for the sake of clarity. Speed and velocity are often used to represent the same thing, which as has been seen above, is not technically correct. One is a scalar quantity, the other is a vector. In many cases, speed is used when velocity might be the more correct term. In the lexicon of acceleration physiology, the terms force and acceleration are also very often used interchangeably. This can create some confusion on the part of readers, particularly those new to the field. The situation is made worse when the terms G force and G acceleration are used on an interchangeable basis. Ultimately, it does not matter which term is used, as long as there is some consistency. As readers will see in later sections of this chapter, the interchangeable use of force and acceleration is a by-product of one of Newton’s Laws of Motion – force and acceleration are proportional to each other. In this book, the term G force will be used to represent the force applied to a body undergoing an acceleration. This will become clearer as this chapter develops.
Gravity
While acceleration is a relatively straightforward notion, gravity is a rather more nebulous concept. While gravity is understood on an intuitive level, little is known of its actual nature. The question of just what exactly gravity is has puzzled physicists for many years (Freedman and van Nieuwenhuizen, 1978; Narlikar, 1996; Will, 1974), and remains the subject of much ongoing work (a detailed analysis of which is well beyond the scope of this book).
What is Gravity?
Current thinking, based initially on the work of the theoretical physicist Albert Einstein (1879–1955), is that gravity is a wave-form. Einstein’s General Relativity Theory predicts the existence of gravitational waves, which are considered to be ripples in (or warping of) the space–time continuum produced by violent events such as exploding stars (Wald, 1984). The Theory describes the observed gravitational attraction between such masses as being a result of warping of space and time by those very masses. As an example, Einstein’s General Relativity Theory underpins the modern understanding of black holes, an astronomic phenomenon where gravitational attraction is so strong that nothing can escape from them, not even light (Gallo and Marolf, 2009; Narlikar, 1996; Wald, 1984).
Gravitational waves have so far never been detected, but several experiments are currently underway around the world, involving the use of ground-based and space-based interferometers, as well as pulsar timing arrays (based at radiotelescope facilities such as that in Parkes, New South Wales, Australia). One of the earliest detection devices was the so-called Weber bar, developed by Joseph Weber (1919–2000). This bar, made of solid aluminium, was isolated from external vibrations. While Weber claimed to have detected gravitational waves with his device in the 1960s, repeat experiments by other researchers have failed to confirm his findings, and his claim has largely been discredited (Bartusiak, 2000). Modern forms of the Weber bar are in use for the purposes of detecting gravitational waves. These include large pieces of pure metals such as niobium which are supercooled to near absolute zero. The passage of gravitational waves through this metal sets up a series of detectable vibrations within the metal’s atoms. These efforts at detecting gravitational waves are extraordinarily difficult and complex, and have to date produced no peer-reviewed, generally accepted, concrete and empirical evidence.
The difficulty with such experiments is that gravitational waves are inherently difficult to detect. They are thought to be rare, occurring anywhere from once a decade to once a century. In addition, their physical properties make them particularly problematic. Their wavelength is thought to be very long (about 300 km), their amplitude is very small (millions of times smaller than the diameter of an atom) and their speed of travel is on an astronomical scale (they could pass through the Earth in 0.04 seconds).
According to the latest thinking in Quantum Field Theory, it is speculated that the gravitational force is mediated by the hypothetical elementary particle the ‘graviton’, similar to the role of the photon in electromagnetism (Dyson, 2013; Trippe, 2013; Vayenas and Souentie, 2012; Will, 1998). Work to detect both gravitational waves and the existence of gravitons remains ongoing.
Newton’s Universal Law of Gravitation
What is clear, however, is that gravity influences all aspects of life on Earth, as all biological, mechanical and physical processes occur within a gravitational environment. Gravity is one of the four fundamental forces in nature, and is the weakest of them all. The others are electromagnetic force, the strong nuclear force holding the nuclei of atoms together, and the weak force responsible for radioactive decay (all of which are beyond the scope of this book). Gravity influences the motion of tides, due to the intermittent influence of the gravitational pull of the Moon while in orbit around the Earth, and is responsible for the sensation of weight that humans experience on Earth.
Gravity was first comprehensively described in a scientific sense by Sir Isaac Newton (1642–1727). His classic work, Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy), was published in Latin in July, 1687. This treatise expounded the three Laws of Motion and the Universal Law of Gravitation, and made Newton internationally famous (Feynman, 1965, 1985, 1996; Goodstein and Goodstein, 1997; Kane and Sternheim, 1984; Narlikar, 1996; Westfall, 1993; White, 1997). These Laws now demand some attention, for they form the theoretical foundation for subsequent chapters of this book.
The Universal Law of Gravitation was developed by Newton as a consequence of his work on planetary motion (Feynman, 1996; Goodstein and Goodstein, 1997; Howard, 1965; Kane and Sternheim, 1984; Narlikar, 1996). This Law is a fundamentally important principle of nature, and defines gravity in mechanical terms as the force of attraction that exists between two bodies separated by a particular distance. It has as its central premise the idea that all objects in the universe attract each other in a mathematically predictable way. This attractive or gravitational force is dependent on the relative masses of the objects and the distance separating them. If two objects, of mass m and m’, are separated by a distance r, then the attractive or gravitational force between them is expressed in the following formula;
where: F = gravitational force,
G = the gravitational constant, which has been shown to have a measured value of 6.67 x 10–11N.m2.kg–2.
where: m = metre
N = Newton unit of force, where 1 Newton is defined as the force required to accelerate a 1 kilogram mass at 9.8 metres per second–2
kg = kilogram.
The value of the gravitational constant, G, was first experimentally measured by the English physicist Henry Cavendish (1731–1810). Credited with the discovery of hydrogen, Cavendish was also famous for what became known as the ‘Cavendish experiment’, where a torsion balance was used in a laboratory to measure the gravitational attraction between two objects. This experiment allowed Cavendish to determine the mass and density of the Earth, and in so doing was able to derive a value for the gravitational constant, G.
The gravitational force is directed along a line joining the centres of both objects. The magnitude of the gravitational force generated by an object is therefore a direct function of the mass of the object and an inverse function of the square of the separating distance. The greater the mass, and the closer the objects, the stronger the attractive force. A human being on the Earth’s surface is subjected to the gravitational attraction of the Earth’s mass, and the Earth in turn experiences a gravitational attraction to the human on its surface. Due to the large difference in relative mass (about 70 kg for the human, and 5.98 x 1024 kg for the Earth), the gravitational attraction of the human is negligible compared with that of the Earth (Kane and Sternheim, 1984).
From a planetary motion perspective, Newton’s Universal Law of Gravitation represented the culmination of centuries of thought. The early views on planetary motion were geocentric, in that it was thought that the planets orbited the Earth. This view was championed by Aristotle and Ptolemy. The work of the Polish astronomer and mathematician Nicholas Copernicus (1473–1543) formulated a heliocentric view of the solar system, with planets orbiting around the Sun rather than the Earth. Johannes Kepler (1571–1630) was then able to show that planetary orbits were elliptical rather than circular, and Galileo was able to provide supporting evidence from direct astronomical observations. Newton’s Universal Law of Gravitation and the three Laws of Motion were able to confirm Kepler’s Laws of Planetary Motion and effectively confirm the helicocentric nature of the solar system.
Newton’s theories were subsequently confirmed experimentally by several others, notably the French mathematician Pierre Simon Laplace (1749–1827), Urbain Jean Joseph Le Verrier (1811–77) and John Couch Adams (1819–92). Laplace’s mathematical work showed strong agreement between predicted and observed planetary motion, confirming the validity of Newton’s Law of Universal Gravitation. The Frenchman Le Verrier and the Englishman Adams are credited with the discovery of the planet Neptune, as a result of their independent work on the orbit of Uranus. This orbit did not appear to conform to Newton’s Law of Gravitation. The lack of agreement between the observed orbit of Uranus and that predicted by Newton’s Law led them to deduce the existence of another nearby planet, which was exerting a gravitational pull on Uranus. The new planet, Neptune, was duly discovered.
Newton’s Laws of Motion
Newton’s three Laws of Motion are integral to an accurate and comprehensive understanding of acceleration and its physiological consequences. Much of Newton’s work represented an evolution of thought from predecessors such as the Greek philosopher Aristotle (384–322 BC) and the Italian physicist and astronomer Galileo (1564–1642). Aristotle understood motion in a qualitative sense. His idea was that objects tended to move towards an ideal (or potential) position from their current (actual) position, and that this motion was the result of a force acting on the objects. He opined that a constant force is required on an object to produce a constant velocity. Galileo took these ideas a step further and developed the theory that a force acting on an object resulted in an acceleration of the object. In contrast to Aristotle, he believed that an object in a state of constant velocity has no force acting on it. He also considered the effects of friction in terms of opposing the applied force on an object. Newton’s significant contribution was to define the relationship between force and acceleration in a quantitative sense.
Newton’s First Law of Motion states that an object will remain in a state of rest or of uniform motion in a straight line unless acted on by a force. This force, if applied to the object, can produce a change in speed and/or direction. The object will thus experience an acceleration. For example, if an object is travelling at a certain speed and is acted on by a force that changes only its direction of travel, it is said to have been accelerated in its new direction.
Newton’s Second Law states that the force acting on a body is the product of that body’s mass and the acceleration it undergoes as a result. The equation describing this is thus;
F = m.a
where: F = force
m = mass of the body
a = acceleration
It is worth mentioning the concept of inertia at this point. The force applied to the object must overcome the object’s inherent inertia in order to achieve an acceleration. Inertia is a function of mass, which is the quantity of matter in a given object. The greater the mass, the greater is the inertia of the object. To accelerate an object of large mass by a certain amount, a larger force must be applied. Thus, an important aspect of Newton’s Second Law is that force is proportional to acceleration.
Newton’s Thi...