Celestial Mechanics
Celestial mechanics is the branch of astronomy that deals with the motions and gravitational interactions of celestial bodies, such as planets, moons, and stars. It has its roots in early astronomical observations, where ancient civilizations sought to understand and predict phenomena like eclipses, attributing divine significance to celestial events. Over time, significant advancements were made by scholars such as Ptolemy, who proposed the geocentric model, and Nicolaus Copernicus, who introduced the heliocentric model, stating that the sun is the center of the solar system.
The development of classical mechanics by Isaac Newton laid the foundation for celestial mechanics, enabling more precise calculations of celestial motion through his laws of motion and the law of universal gravitation. Key challenges in celestial mechanics include the n-body problem, which examines the complex interactions of multiple celestial bodies under the influence of gravity. Although solutions exist for simplified cases, such as the two-body and three-body problems, the unpredictability of gravitational perturbations makes more complex scenarios difficult to solve.
With advancements in technology and mathematics, scientists have improved their ability to predict celestial events, leading to significant contributions in fields like astrodynamics and lunar theory. Understanding celestial mechanics has immense practical implications, including the prediction of eclipses and the management of satellite orbits, thereby enhancing our grasp of the universe and its dynamics.
Celestial Mechanics
FIELDS OF STUDY: Astronomy; Astrophysics; Orbital Mechanics
ABSTRACT: Celestial mechanics is a subfield of classical mechanics and a branch of astronomy that studies the motion of celestial objects and the forces affecting this movement. Several types of forces can affect the orbit of bodies in space. Gravity is the main cause of orbital motion. Other forces such as atmospheric interference, radiation pressure, and electromagnetic fields affect the movement of celestial bodies.
Explaining the Motions of the Heavens
Ancient peoples viewed the stars, moon, and planets as objects of worship. They made up stories about them and believed in their power to affect conditions on Earth. Early observers were aware of the consistent motions of these objects; Mesopotamian, Egyptian, and Indus Valley civilizations understood them well enough to predict eclipses. Few astronomical observers questioned the cause of this motion, although several Greek philosophers tried to calculate precise movements of the sun, moon, and planets.
The Greek Egyptian astronomer and mathematician Ptolemy (ca. 100– ca. 170) proposed that Earth was the center of the universe and all the other planets and stars orbited around it. This theory was known as "geocentrism." Ptolemy used mathematics to calculate and predict the movement of celestial bodies. His calculations told him that planets move in epicycles, or small circles, while simultaneously orbiting Earth. Ptolemy was not certain if this was true, but he simply could not calculate a better model of planetary motion.
Ptolemy’s theories were widely accepted for many centuries before Polish mathematician Nicolaus Copernicus (1473–1543) disproved them. Copernicus held that Earth orbited the sun; therefore, the sun was the center of the solar system. This theory was called "heliocentrism." Many scholars were slow to accept heliocentric views of the universe. However, Copernicus’s mathematical calculations proved more accurate than Ptolemy’s. This breakthrough led to what is sometimes called the "Copernican revolution."
Several other key astronomical breakthroughs occurred in the years following Copernicus’s death. The celestial observations of Danish astronomer Tycho Brahe (1546–1601) greatly contributed to the accurate measurement of planet positions. Brahe’s work influenced seventeenth-century German astronomer Johannes Kepler (1571–1630), considered by many to be the father of celestial mechanics. Kepler’s laws of planetary motion state, among other things, that a planet’s orbit is shaped like an ellipse.
English physicist Isaac Newton (1643–1727) refined Kepler’s laws, working out the mathematics behind the movements of the planets. His Philosophiæ Naturalis Principia Mathematica (1687; The Mathematical Principles of Natural Philosophy, 1729) laid the foundations for classical mechanics. In it, Newton put forth three fundamental principles, now commonly referred to as Newton’s laws of motion, to explain how different forces affect the movement of any physical body. He also defined the law of universal gravitation, which played a key role in the development of celestial mechanics.
The Nature of Celestial Mechanics
Classical mechanics laid the groundwork for celestial mechanics. Further progress was made by astronomers such as Félix Tisserand (1845–1896), who compiled all known studies in the field into the compendium Traité de mécanique céleste (Treatise on celestial mechanics, 1889–1896), and physicist Albert Einstein (1879–1955), whose theory of general relativity improved on Newton’s description of gravity to allow celestial movement to be calculated with greater accuracy. Celestial mechanics, also referred to as dynamic astronomy, calculates the motion and orbit of celestial bodies by measuring the effects of gravity and other forces.
Several basic problems make up the bulk of celestial mechanics equations. All of these problems rely on Newton’s laws of classical mechanics. Most are variations on the n-body problem, which attempts to account for the overall motion of a group of n bodies that are each affected by the others’ gravitational forces. When the gravitational forces of more than one body act on a single massive body, the result is a complex series of motions called perturbation. Perturbation also happens when air resistance and atmospheric pressure disturb a celestial body. Scientists must determine the orbital properties of a group of celestial bodies and how their forces will affect one another to predict their future orbital motions. Astronomers and physicists have only solved the n-body problem for situations in which n = 2 (two-body problem) and n = 3 (three-body problem). One well-known version of the three-body problem is the orbital relationship between Earth, the moon, and the sun.
Calculating the n-Body Problem
Early mathematics did not account for the ways in which gravity affects the orbits of celestial objects. With the advent of Newton’s law of universal gravitation, mathematicians could more accurately calculate the motions of two- and three-body systems. However, the unpredictability of perturbations makes solving the n-body problem difficult in cases involving three or more bodies.
The n-body problem involves a series of equations. The first calculates the number of celestial bodies being measured. Once this is established, the next step is to calculate each body’s initial velocity, relative position and time, and mass. The motion of the bodies can be determined from the size and eccentricity of their orbits and their interactions according Newton’s law of gravitation. However, numerical calculations of celestial motion offer only indefinite predictions of future orbits, given the chaotic nature of the universe. The motion of the eight planets of the solar system is an n-body problem that incites much debate. Scientists continually try to determine whether the current movement of the solar system is ultimately stable or will eventually change motion due to altered external forces.
Impact of Celestial Mechanics
Understanding the motion of celestial bodies has allowed scientists to predict astronomical events such as eclipses. It has also contributed to the subfields of astrodynamics and lunar theory and led to a greater understanding of Earth’s ocean tides. The moon’s gravitational force is primarily responsible for Earth’s tidal evolution. As the moon’s orbit expanded over time, its effect on the tides dissipated, causing the Earth’s rotation to slow and thus lengthening Earth’s days.
Technological innovations have given scientists easier ways to calculate celestial motions. Dutch American astronomer Dirk Brouwer (1902–1966) pioneered the use of digital computers to solve orbital problems. The digital calculations proved incredibly accurate, and Brouwer’s methods were soon adopted worldwide. Computer-based problem solving enabled more accurate calculations of the orbits of artificial satellites, thus facilitating the development of satellite communications.
PRINCIPAL TERMS
- classical mechanics: the study of the motion of bodies, rooted in Isaac Newton’s physical and mathematical principles; also called Newtonian mechanics.
- eccentricity: the extent to which a celestial body’s orbit deviates from a perfect circle.
- ellipse: a shape that resembles an elongated circle; mathematically speaking, a closed conic section.
- n-body problem: a mathematical model used to determine how gravity affects the motions and interactions of a group of celestial bodies.
- Newton’s laws of motion: the three laws that describe how bodies respond to the application of force.
- perturbation: a change in the orbit of a celestial object caused by the gravitational force of another object.
- tidal evolution: the change in the rise and fall of an ocean caused by the gravitational force of a nearby celestial object.
Bibliography
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Hockey, Thomas, et al., eds. Biographical Encyclopedia of Astronomers. 2nd ed. New York: Springer, 2014. Print.
Klioner, Sergei A. "Lecture Notes on Basic Celestial Mechanics." Department of Astronomy / Lohrmann Observatory. Technical U Dresden, 2011. Web. 14 May 2015.
Matzner, Richard A., ed. Dictionary of Geophysics, Astrophysics, and Astronomy. Boca Raton: CRC, 2001. Print.
Stern, David P. "How Orbital Motion Is Calculated." From Stargazers to Starships. Author, 6 Apr. 2014. Web. 14 May 2015.