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David McNamara and Gianfranco Vidali, "Kepler's Second Law – Java Interactive Tutorial", an interactive Java applet that aids in the understanding of Kepler's Second Law. Cain, Gay (May 10, 2010), Astronomy Cast, "Ep. 189: Johannes Kepler and His Laws of Planetary Motion"
This is Kepler's second law of planetary motion. The square of this quotient is proportional to the parameter (that is, the latus rectum) of the orbit and the sum of the mass of the Sun and the body. This is a modified form of Kepler's third law. He next defines: 2p as the parameter (i.e., the latus rectum) of a body's orbit,
Kepler's laws apply only in the limited case of the two-body problem. Voltaire and Émilie du Châtelet were the first to call them "Kepler's laws". Nearly a century later, Isaac Newton had formulated his three laws of motion. In particular, Newton's second law states that a force F applied to a mass m produces an acceleration a given by the ...
Mathematically, the second epicycle and the equant produce nearly the same results, and many Copernican astronomers before Kepler continued using the equant, as the mathematical calculations were easier. Copernicus' epicycles were also much smaller than Ptolemy's, and were required because the planets in his model moved in perfect circles.
Thus, the areal velocity is constant for a particle acted upon by any type of central force; this is Kepler's second law. [13] Conversely, if the motion under a conservative force F is planar and has constant areal velocity for all initial conditions of the radius r and velocity v, then the azimuthal acceleration a φ is always zero.
The second section establishes relationships between centripetal forces and the law of areas now known as Kepler's second law (Propositions 1–3), [21] and relates circular velocity and radius of path-curvature to radial force [22] (Proposition 4), and relationships between centripetal forces varying as the inverse-square of the distance to ...
Geometric diagram for Newton's proof of Kepler's second law. 1602-1608 – Galileo Galilei experiments with pendulum motion and inclined planes; deduces his law of free fall; and discovers that projectiles travel along parabolic trajectories. [3] 1609 – Johannes Kepler announces his first two laws of planetary motion. [4]
Next Newton proves his "Theorema II" which shows that if Kepler's second law results, then the force involved must be along the line between the two bodies. In other words, Newton proves what today might be called the "inverse Kepler problem": the orbit characteristics require the force to depend on the inverse square of the distance. [3]: 107