Celestial mechanics
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What is celestial mechanics?
Celestial mechanics applies classical mechanics to the motion of celestial bodies influenced by various forces, most notably gravity. It is sometimes used to describe the analysis of point mass particles moving under mutual gravitational attractions, emphasizing the general orbital motions of solar system bodies.
Isaac Newton defined the laws of motion and gravity, showing that a point mass moving around a fixed force center follows an elliptical path if the initial velocity is not too large, a hyperbolic path for high initial velocities, and a parabolic path for intermediate velocities. Kepler's laws of planetary motion describe the motions of planets in the solar system.
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What kinds of objects does celestial mechanics study?
Celestial mechanics applies classical mechanics to celestial bodies' motions, primarily focusing on mutual gravitational attraction. It examines objects like planets, moons, and asteroids within the solar system. It also studies artificial satellites, considering atmospheric drag, radiation pressure, and electromagnetic forces.
Dynamic astronomy, a broader field, includes celestial mechanics, astrodynamics, and aspects of celestial body motion, such as rotation, tidal evolution, and mass distribution in stars and galaxies. The study of the Moon's motion, for example, has greatly contributed to the understanding of celestial mechanics and physics.
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How do gravity and motion affect planets and stars in space?
Gravity and motion intricately govern the behavior of planets and stars in space. Celestial mechanics applies classical mechanics to celestial bodies' motion, primarily focusing on mutual gravitational attraction.
Gravity
Gravity is the dominant force, dictating orbits and interactions. Isaac Newton demonstrated that a force must act on a planet to curve its path toward the Sun. Kepler's laws of planetary motion describe these movements, with planets orbiting the Sun in ellipses.
Motion
A balance between gravity and inertia dictates orbital paths. Without gravity, inertia would cause a planet to move in a straight line. The orbital velocity needed to maintain orbit depends on the mass of the central body and the distance from it.
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What is an orbit, and why do planets stay in orbit around the Sun?
An orbit is the path one body takes as it revolves around another, such as a planet around the Sun.
Planets stay in orbit due to the balance between their inertia and the Sun's gravitational pull. A planet's inertia is its tendency to keep moving in a straight line. Gravity is the force that attracts the planet towards the Sun. Without the Sun's gravity, the planet would follow a straight path into space. However, the Sun's gravity constantly pulls the planet inward, causing it to fall towards the Sun. Because of the planet's inertia, it doesn't fall directly into the Sun, but instead, it keeps missing, resulting in a circular or elliptical path around the Sun.
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What are Kepler’s laws, and what do they tell us about planetary motion?
Johannes Kepler, a German astronomer, introduced his three laws of planetary motion between 1609 and 1618, which describe how planets move in the solar system.
Kepler's laws state that:
1. Planets move in elliptical orbits with the Sun at one focus.
2. A planet's radius vector sweeps out equal areas in equal times.
3. The squares of the sidereal periods of the planets are proportional to the cubes of their average distances from the Sun.These laws apply to natural and artificial satellites, stellar systems, and extrasolar planets. Isaac Newton later used Kepler's laws to formulate his law of gravitation.
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How do scientists use celestial mechanics to predict eclipses and spacecraft paths?
Celestial mechanics, applying classical mechanics, predicts celestial body motion using gravitational forces. Isaac Newton's laws of motion form the basis, with gravity causing curved paths toward the Sun.
To predict eclipses, astronomers use the positions of the Sun and Moon relative to Earth, with computers calculating when these overlaps will occur. For spacecraft, celestial mechanics is vital for plotting trajectories. The complexities of gravitational interactions, like those in the Apollo missions, require high-speed computers to integrate motion equations and compare actual and planned paths.
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Celestial mechanics, in the broadest sense, the application of classical mechanics to the motion of celestial bodies acted on by any of several types of forces. By far the most important force experienced by these bodies, and much of the time the only important force, is that of their mutual gravitational attraction. But other forces can be important as well, such as atmospheric drag on artificial satellites, the pressure of radiation on dust particles, and even electromagnetic forces on dust particles if they are electrically charged and moving in a magnetic field.
The term celestial mechanics is sometimes assumed to refer only to the analysis developed for the motion of point mass particles moving under their mutual gravitational attractions, with emphasis on the general orbital motions of solar system bodies. The term astrodynamics is often used to refer to the celestial mechanics of artificial satellite motion. Dynamic astronomy is a much broader term, which, in addition to celestial mechanics and astrodynamics, is usually interpreted to include all aspects of celestial body motion (e.g., rotation, tidal evolution, mass and mass distribution determinations for stars and galaxies, fluid motions in nebulas, and so forth).
Historical background
Early theories
Celestial mechanics has its beginnings in early astronomy in which the motions of the Sun, the Moon, and the five planets visible to the unaided eye—Mercury, Venus, Mars, Jupiter, and Saturn—were observed and analyzed. The word planet is derived from the Greek word for wanderer, and it was natural for some cultures to elevate these objects moving against the fixed background of the sky to the status of gods; this status survives in some sense today in astrology, where the positions of the planets and Sun are thought to somehow influence the lives of individuals on Earth. The divine status of the planets and their supposed influence on human activities may have been the primary motivation for careful, continued observations of planetary motions and for the development of elaborate schemes for predicting their positions in the future.
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The Greek astronomer Ptolemy (who lived in Alexandria about 140 ce) proposed a system of planetary motion in which Earth was fixed at the centre and all the planets, the Moon, and the Sun orbited around it. As seen by an observer on Earth, the planets move across the sky at a variable rate. They even reverse their direction of motion occasionally but resume the dominant direction of motion after a while. To describe this variable motion, Ptolemy assumed that the planets revolved around small circles called epicycles at a uniform rate while the centre of the epicyclic circle orbited Earth on a large circle called a deferent. Other variations in the motion were accounted for by offsetting the centres of the deferent for each planet from Earth by a short distance. By choosing the combination of speeds and distances appropriately, Ptolemy was able to predict the motions of the planets with considerable accuracy. His scheme was adopted as absolute dogma and survived more than 1,000 years until the time of Copernicus.
Nicolaus Copernicus assumed that Earth was just another planet that orbited the Sun along with the other planets. He showed that this heliocentric (centred on the Sun) model was consistent with all observations and that it was far simpler than Ptolemy’s scheme. His belief that planetary motion had to be a combination of uniform circular motions forced him to include a series of epicycles to match the motions in the noncircular orbits. The epicycles were like terms in the Fourier series that are used to represent planetary motions today. (A Fourier series is an infinite sum of periodic terms that oscillate between positive and negative values in a smooth way, where the frequency of oscillation changes from term to term. They represent better and better approximations to other functions as more and more terms are kept.) Copernicus also determined the relative scale of his heliocentric solar system, with results that are remarkably close to the modern determination.
Tycho Brahe (1546–1601), who was born three years after Copernicus’ death and three years after the publication of the latter’s heliocentric model of the solar system, still embraced a geocentric model, but he had only the Sun and the Moon orbiting Earth and all the other planets orbiting the Sun. Although this model is mathematically equivalent to the heliocentric model of Copernicus, it represents an unnecessary complication and is physically incorrect. Tycho’s greatest contribution was the more than 20 years of celestial observations he collected; his measurements of the positions of the planets and stars had an unprecedented accuracy of approximately 2 arc minutes. (An arc minute is 1/60 of a degree.)