Vectors (mathematics and physics)
In celestial mechanics, the eccentricity vector of a Kepler orbit is the dimensionless vector with direction pointing from apoapsis to periapsis and with magnitude equal to the orbit's scalar eccentricity. For Kepler orbits the eccentricity vector is a constant of motion. Its main use is in the analysis of almost circular orbits, as perturbing (non-Keplerian) forces on an actual orbit will cause the osculating eccentricity vector to change continuously. For the eccentricity and argument of periapsis parameters, eccentricity zero (circular orbit) corresponds to a singularity. The magnitude of the eccentricity vector represents the eccentricity of the orbit. Note that the velocity and position vectors need to be relative to the inertial frame of the central body. (Wikipedia).
Teach Astronomy - Orbit Eccentricity
http://www.teachastronomy.com/ Orbital eccentricity is the amount by which an orbit deviates from a circle. Mathematically it's defined as the distance between the two foci of an elliptical orbit divided by the major axis. A circle has an ellipticity, denoted by the little symbol "e", of
From playlist 10. The Solar System
Physics - Mechanics: Gravity (11 of 20) Eccentricity Of A Planet's Orbits
Visit http://ilectureonline.com for more math and science lectures! In this video I will show you how to calculate the eccentricity of a planets orbit using Keppler's 1st law.
From playlist PHYSICS 18 GRAVITY
This calculus 2 video tutorial provides a basic introduction into the eccentricity of an ellipse. It explains how to calculate the eccentricity of an ellipse from a standard equation. The eccentricity is close to zero for ellipses that are nearly circular and close to 1 for elongated ell
From playlist New Calculus Video Playlist
Astrophysics: Binary Star System (16 of 40) Elliptical Orbits: A Closer Look
Visit http://ilectureonline.com for more math and science lectures! In this video I will derive the 2 general equation for calculating the eccentricity of a planet around a sun. Next video in this series can be found at: https://youtu.be/2okz-VGkeAI
From playlist ASTROPHYSICS 1 BINARY SYSTEMS & KEPLER'S LAWS
Astronomy - Ch. 7: The Solar Sys - Comparative Planetology (15 of 33) Planet Orbital Eccentricity
Visit http://ilectureonline.com for more math and science lectures! In this video I will discuss the various orbital eccentricities of the planets in our Solar System. Next video in this series can be seen at: http://youtu.be/igAZ0bSyi2c
From playlist ASTRONOMY 7B THE SOLAR SYSTEM - COMPARATIVE PLANETOLOGY
Given the center, b and eccentricity find the equation of a hyperbola
Learn how to write the equation of hyperbolas given the characteristics of the hyperbolas. The standard form of the equation of a hyperbola is of the form: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1 for horizontal hyperbola or (y - k)^2 / a^2 - (x - h)^2 / b^2 = 1 for vertical hyperbola. The c
From playlist The Hyperbola in Conic Sections
Introduction to Cylindrical Coordinates
This video introduces cylindrical coordinates and shows how to convert between cylindrical coordinates and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
In this video, I use the orbit equation to determine the range of values of the eccentricity for circular, elliptical, parabolic, and hyberbolic orbits, and find the minimum and maximum radii for each type of orbit, where pertinent.
From playlist Intermediate Classical Mechanics
Definition of spherical coordinates | Lecture 33 | Vector Calculus for Engineers
We define the relationship between Cartesian coordinates and spherical coordinates; the position vector in spherical coordinates; the volume element in spherical coordinates; the unit vectors; and how to differentiate the spherical coordinate unit vectors. Join me on Coursera: https://www
From playlist Vector Calculus for Engineers
Geometric Algebra Applications - Kepler Problem (Part 2)
In this video, we show that the trajectories of masses moving under an inverse-square law are conic sections using geometric algebra. We will not be solving any differential equations, but instead showing that a special vector, the Laplace-Runge-Lenz vector, is a conserved quantity of moti
From playlist Math
The Kepler Problem (part 1 - 2)
In this first part of a multi-video series, I describe the six orbital elements defining a two-body trajectory in 3D space and explain how to solve for said elements given an object's state vectors, or position and velocity. Check out the three.js sandbox here: https://rtoole13.github.io/
From playlist Summer of Math Exposition Youtube Videos
Gravity: Newtonian, post-Newtonian, Relativistic (Lecture 3) by Clifford M Will
DATES Monday 25 Jul, 2016 - Friday 05 Aug, 2016 VENUE Madhava Lecture Hall, ICTS Bangalore APPLY Over the last three years ICTS has been organizing successful summer/winter schools on various topics of gravitational-wave (GW) physics and astronomy. Each school from this series aimed at foc
From playlist Summer School on Gravitational-Wave Astronomy
Lecture 7 | Modern Physics: Quantum Mechanics (Stanford)
Lecture 7 of Leonard Susskind's Modern Physics course concentrating on Quantum Mechanics. Recorded February 25, 2008 at Stanford University. This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of mod
From playlist Course | Modern Physics: Quantum Mechanics
Bizarre orbits of minor planets beyond Neptune - Ann Marie Madigan(SETI Talk)
The major planets in our solar system are on nearly circular orbits in a well-defined disk plane. The minor planets, however, take very different paths around the sun. Many minor planets are on orbits that tilt 30 degrees or more out of this disk plane; bizarrely, as Dr. Madgian will descr
From playlist Oumuamua: Extrasolar Asteroid Playlist
What Is General Relativity? Lesson 28: The Classical Central Force Problem - Orbit shape
What Is General Relativity? Lesson 28: The Classical Central Force Problem - Orbit shape Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX and discussing the material on the forums: https://www.patreon.com/XYLYXYLYX
From playlist What is General Relativity?
Geometric Algebra Applications - Kepler Problem (Part 3)
In this video, we will finish our discussion of the Kepler problem by deriving Kepler's 3rd Law, total energy, the Vis-Viva equation, and the Virial Theorem. Along the way, we'll review some facts about the ellipse and observe the total energies for the different conic sections. Reference
From playlist Math
Feynman's Lost Lecture (ft. 3Blue1Brown)
Check out Grant’s channel: 3blue1brown: https://www.youtube.com/3blue1brown This video recounts a lecture by Richard Feynman giving an elementary demonstration of why planets orbit in ellipses. See the excellent book by Judith and David Goodstein, "Feynman's lost lecture”, for the full s
From playlist Feynman's Lectures
Arc Length: Perimeter of an Ellipse | Lecture 36 | Vector Calculus for Engineers
How to compute the perimeter of an ellipse by calculating an arc length from a line integral. The formula for the perimeter is a complete elliptic integral of the second kind. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture notes at http://www.math.
From playlist Vector Calculus for Engineers
Finding the Eccentricity of the Conic Section x^2 - 4y^2 = 8
Finding the Eccentricity of the Conic Section x^2 - 4y^2 = 8. This is a hyperbola. Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
From playlist Conics
Network Analysis. Lecture 5. Centrality measures.
Node centrality metrics, degree centrality, closeness centrality, betweenness centrality, eigenvector centrality. Katz status index and Bonacich centrality, alpha centrality. Spearman rho and Kendall-Tau ranking distance. Lecture slides: http://www.leonidzhukov.net/hse/2015/networks/lect
From playlist Structural Analysis and Visualization of Networks.