Lecture

Eccentric Anomaly: Circular Non-Uniform

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

ENV-542: Advanced satellite positioning

All fundamental principles behind modern satellite positioning to acquire, track and evaluate direct and indirect satellite signals and process them in relation to example applications: Earth monitoring (landslides,...), high precision positioning (autom ...

Description

This lecture covers the concept of eccentric anomaly in circular non-uniform orbits, explaining the relationship between the eccentric anomaly and mean anomaly. It delves into the mathematical expressions involving the eccentric anomaly and its applications in determining positions in orbits.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Ontological neighbourhood

Astronomy

Astrodynamics: Topics in astrodynamics

Related concepts (18)

Mean anomaly

In celestial mechanics, the mean anomaly is the fraction of an elliptical orbit's period that has elapsed since the orbiting body passed periapsis, expressed as an angle which can be used in calculating the position of that body in the classical two-body problem. It is the angular distance from the pericenter which a fictitious body would have if it moved in a circular orbit, with constant speed, in the same orbital period as the actual body in its elliptical orbit. Define T as the time required for a particular body to complete one orbit.

Eccentric anomaly

In orbital mechanics, the eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit. The eccentric anomaly is one of three angular parameters ("anomalies") that define a position along an orbit, the other two being the true anomaly and the mean anomaly. Consider the ellipse with equation given by: where a is the semi-major axis and b is the semi-minor axis. For a point on the ellipse, P = P(x, y), representing the position of an orbiting body in an elliptical orbit, the eccentric anomaly is the angle E in the figure.

True anomaly

In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse (the point around which the object orbits). The true anomaly is usually denoted by the Greek letters ν or θ, or the Latin letter f, and is usually restricted to the range 0–360° (0–2π^c).

Orbital mechanics

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. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets.

Circular orbit

A circular orbit is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle. In this case, not only the distance, but also the speed, angular speed, potential and kinetic energy are constant. There is no periapsis or apoapsis. This orbit has no radial version. Listed below is a circular orbit in astrodynamics or celestial mechanics under standard assumptions. Here the centripetal force is the gravitational force, and the axis mentioned above is the line through the center of the central mass perpendicular to the orbital plane.

Related lectures (54)

Elliptical Orbits: Examples and Formulas MOOC: Space Mission Design and Operations

Covers examples and formulas related to elliptical orbits and how to determine parameters of an elliptical orbit using known points.

Orbital Parameters and Calendars MOOC: Space Mission Design and Operations

Explains classical orbital parameters, spacecraft's state vector, and Gregorian vs. Julian days.

Crew-7 Return and Space Mission Design Overview

Discusses Crew-7's return from the ISS and key principles of space mission design.

Orbital Motion: Circular and Elliptical MOOC: Space Mission Design and Operations

Covers circular and elliptical orbits, orbital period, velocity, energy, and angular momentum.

Space Mission Design: Starship Test and Rendezvous Techniques