Space Flight Dynamics
Space Flight Dynamics is a welcome addition to the field, ideally suited for upper-level undergraduate and graduate students studying aerospace engineering. Craig A. Kluever is C. W. LaPierre Professor of Mechanical and Aerospace Engineering, University of Missouri-Columbia, USA. He has industry experience as an aerospace engineer on the Space Shuttle program and has performed extensive research at the University of Missouri in collaboration with NASA involving trajectory optimization, space mission design, entry flight mechanics, and guidance and control of aerospace vehicles.
Space Flight Dynamics
Before we begin our technical discussion of space flight dynamics, this first chapter will provide a condensed historical overview of the principle contributors and events associated with the development of what we now commonly refer to as space flight . We may define space flight as sending a human-made satellite or spacecraft to an Earth orbit or to another celestial body such as the moon, an asteroid, or a planet. Of course, our present ability to launch and operate satellites in orbit depends on knowledge of the physical laws that govern orbital motion. This brief chapter presents the major developments in astronomy, celestial mechanics, and space flight in chronological order so that we can gain some historical perspective.
1.2 Early Modern Period
The fields of astronomy and celestial mechanics (the study of the motion of planets and their moons) have attracted the attention of the great scientific and mathematical minds. We may define the early modern period by the years spanning roughly 1500-1800. This time frame begins with the late Middle Ages and includes the Renaissance and Age of Discovery. Figure 1.1 shows a timeline of the important figures in the development of celestial mechanics during the early modern period. The astute reader will, of course, recognize these illuminous figures for their contributions to mathematics (Newton, Euler, Lagrange, Laplace, Gauss), physics (Newton, Galileo), dynamics (Kepler, Newton, Euler, Lagrange), and statistics (Gauss). We will briefly describe each figure's contribution to astronomy and celestial mechanics.
Figure 1.1 Timeline of significant figures in the Early Modern Period.
The first major figure is Nicolaus Copernicus (1473-1543), a Polish astronomer and mathematician who developed a solar-system model with the sun as the central body. Galileo Galilei (1546-1642) was an Italian astronomer and mathematician who defended Copernicus' sun-centered (or "heliocentric") solar system. Because of his heliocentric view, Galileo was put on trial by the Roman Inquisition for heresy and spent the remainder of his life under house arrest.
Johann Kepler (1571-1630) developed the fundamental laws for planetary motion based on astronomical observations of the planet Mars compiled by the Danish nobleman Tycho Brahe (1546-1601). Kepler's three laws are:
The orbit of a planet is an ellipse, with the sun located at a focus.
The radial line from the sun to the planet sweeps out equal areas during equal time intervals.
The square of a planet's orbital period for one revolution is proportional to the cube of the planet's "mean distance" from the sun.
The third law notes the planet's "mean distance" from the sun. In Chapter 2 we will define this "mean distance" as one-half of the length of the major axis of an ellipse. Kepler published his first two laws of planetary motion in 1609 and his third law in 1619. Kepler developed an expression for the time-of-flight between two points in an orbit; this expression is now known as Kepler's equation .
Isaac Newton (1642-1727) was an English astronomer, mathematician, and physicist who developed calculus and formulated the laws of motion and universal gravitation. Newton's three laws of motion are:
A body remains at rest or moves with a constant velocity unless acted upon by a force.
The vector sum of the forces acting on a body is equal to the mass of the body multiplied by its absolute acceleration vector (i.e., ).
When a body exerts a force on a second body, the second body exerts an equal-and-opposite force on the first body.
The first and second laws hold relative to a fixed or inertial reference frame. Newton published the three laws of motion in Prin