Elliptical Motion Example

The elliptical motion is the one in which a body traces an ellipse on the path. It is necessary, for a better understanding, to define the concept of the ellipse.

An Ellipse, in analytical geometry, is the geometric figure generated by a set of points for which the sum of the distances to two other fixed points is constant.

If a circle is the set of points that are the same distance from a single point called the Center, the ellipse is a more elongated figure with two fixed points inside it, which are called Foci. The foci can be designated as A and B. And finally, the distances a and b will form a constant sum, taking as a starting point each point of the ellipse.

And if the ellipse is divided into two axes of symmetry, one vertical and the other horizontal, the Major axis and the minor axis will be formed. Both axes are perpendicular, and they meet at the Center of the Ellipse.

The farthest points on the ellipse are the Vertices, which are the tightest curvatures in the figure.

The semi-axes r and s are defined below. The semi-axis r is the distance from the vertex to the center. The semi-axis s is the distance from the top, or the valley of the ellipse, to the center.

Based on the values ​​of the semi-axes, it is possible to calculate an approximation to the value of the perimeter of the Ellipse, which will serve to determine the total travel in the elliptical movement.

For the explanation of the elliptical movement, we will resort to the examples, to discover its nature in the diversity of cases in which it manifests itself.

Examples of Elliptical Motion

Translational movement of the earth

The Translation Movement of Planet Earth describes an elliptical path around the Sun, in a period of approximately 365 days. Due to the variation in proximity to the star, the four seasons are generated. The entire trajectory is 930 million kilometers long, which represents little more than six times the mean distance of the Earth from the Sun, which is 150 million Kilometres. This last measure is known as the Astronomical Unit. Based on the duration of the Year and the total distance traveled of the 930 million Kilometers, the estimates a speed of displacement of the Earth of 29.49 Kilometers every second, in its movement elliptical.

When the Earth is at the closest point to the Sun, it is called Perihelion, and it takes place in January. And when the planet moves away to a maximum point, the moment is called Aphelion, manifesting this in July. The elliptical path of the Planet is called Orbit, and in this figure, the Sun is located in one of the Foci.

Pendulums

When a pendulum moves on a plane, generates an elliptical trajectory in each oscillation, which is varying its final point, generating a flourish, in exact forms, and visible if it is traced with ink.

The elliptical motion of the pendulum is influenced by the gravitational and magnetic fields of planet Earth, and even by the subtle and almost undetectable rotational motion. That is why the elliptical path is always changing by some sexagesimal degrees, and it is not highlighted in the same place.

If allowed to move indefinitely without additional momentum, the pendulum will slow down and range, tracing smaller ellipses, until it comes to rest.

Circular motion of an object

It is possible to assume that the circular motion is a type of elliptical motion, but with a Center that encompasses the two foci to which an ellipse is associated.

When an object is attached to the end of a string and it begins to move in the air with centrifugal force, leaving the string taut, the path described is circular because the length of the string is constant, and the center of the movement is the hand that is generating the movement.