In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits and epicycles with elliptical trajectories, and explaining how planetary velocities vary. The three laws state that:
- The orbit of a planet is an ellipse with the Sun at one of the two foci.
- A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
- The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit.
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics to astronomical objects, such as stars and planets, to produce ephemeris data.
In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets. In particular it explained the apparent retrograde motion of the five planets known at the time. Secondarily, it also explained changes in the apparent distances of the planets from the Earth.
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control.
David Louis Goodstein is an American physicist and educator. From 1988 to 2007 he served as Vice-provost of the California Institute of Technology (Caltech), where he is also a professor of physics and applied physics, as well as the Frank J. Gilloon Distinguished Teaching and Service Professor.
In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1. In a wider sense, it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1.
In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a rosette orbit through the Galaxy.
A hodograph is a diagram that gives a vectorial visual representation of the movement of a body or a fluid. It is the locus of one end of a variable vector, with the other end fixed. The position of any plotted data on such a diagram is proportional to the velocity of the moving particle. It is also called a velocity diagram. It appears to have been used by James Bradley, but its practical development is mainly from Sir William Rowan Hamilton, who published an account of it in the Proceedings of the Royal Irish Academy in 1846.
Astronomia nova is a book, published in 1609, that contains the results of the astronomer Johannes Kepler's ten-year-long investigation of the motion of Mars.
De motu corporum in gyrum is the presumed title of a manuscript by Isaac Newton sent to Edmond Halley in November 1684. The manuscript was prompted by a visit from Halley earlier that year when he had questioned Newton about problems then occupying the minds of Halley and his scientific circle in London, including Sir Christopher Wren and Robert Hooke.
The Copernican Revolution was the paradigm shift from the Ptolemaic model of the heavens, which described the cosmos as having Earth stationary at the center of the universe, to the heliocentric model with the Sun at the center of the Solar System. This revolution consisted of two phases; the first being extremely mathematical in nature and the second phase starting in 1610 with the publication of a pamphlet by Galileo. Beginning with the publication of Nicolaus Copernicus’s De revolutionibus orbium coelestium, contributions to the “revolution” continued until finally ending with Isaac Newton’s work over a century later.
In astronomy, the variation of the Moon is one of the principal perturbations in the motion of the Moon.
The Mechanical Universe...And Beyond is a 52-part telecourse, filmed at the California Institute of Technology, that introduces university level physics, covering topics from Copernicus to quantum mechanics. The 1985-86 series was produced by Caltech and INTELECOM, a nonprofit consortium of California community colleges now known as Intelecom Learning, with financial support from Annenberg/CPB. The series, which aired on PBS affiliate stations before being distributed on LaserDisc and eventually YouTube, is known for its use of computer animation.
The two-body problem in general relativity is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun. Solutions are also used to describe the motion of binary stars around each other, and estimate their gradual loss of energy through gravitational radiation.
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle.
Ismaël Boulliau was a 17th-century French astronomer and mathematician who was also interested in history, theology, classical studies, and philology. He was an active member of the Republic of Letters, an intellectual community that exchanged ideas. An early defender of the ideas of Copernicus, Kepler and Galileo, Ismael Bullialdus has been called "the most noted astronomer of his generation". One of his books is Astronomia Philolaica (1645).
The Feynman Lectures on Physics is a physics textbook based on some lectures by Richard Feynman, a Nobel laureate who has sometimes been called "The Great Explainer". The lectures were presented before undergraduate students at the California Institute of Technology (Caltech), during 1961–1963. The book's co-authors are Feynman, Robert B. Leighton, and Matthew Sands.
Judith Ronnie Goodstein is an American historian of science, historian of mathematics, archivist, and book author. She worked for many years at the California Institute of Technology (Caltech), where she is University Archivist Emeritus.
