4 December 2023 Elliptical motion is a fundamental concept of physics describing the movement of objects in an oval or elliptical path. This type of motion is common in many real-world applications, from the orbits of planets around the sun to the motion of electrons in atoms.

Understanding classification and the concept of elliptical motion is essential to many fields of study, such as astronomy, engineering and physics.

In this post, we will explore what is elliptical motion and how does it work. We will cover the different types of elliptical motion, including elliptical orbits and elliptical paths. In addition, we will delve into the mathematical formulas and equations that help describe and predict elliptical motion.

The idea is that you have a firm understanding of the concept of elliptical motion and its real world application. If you are a student, scientist or just curious about the mechanics of movement, this post will provide you with the necessary knowledge to understand the classification and concept of elliptical movement.

## Definition of elliptical motion

Elliptical motion, also known as elliptical motion, is a recurring pattern of movement or trajectory that follows an elliptical trajectory. It is often observed in various physical systems and mechanisms, including planetary orbits, pendulums, and celestial bodies.

In physics, elliptical motion is commonly defined as the path followed by an object moving around two or more centers of attraction, subject to the influences of various forces, such as centripetal force and gravity.

The shape of the elliptical path is determined by the relationship between distances from the center of attraction to the two foci of the ellipse. The concept of elliptical motion is fundamental in modern physics, since it helps to understand the dynamics of many natural phenomena and the movement of objects in different systems.

## When can you say that a movement is elliptical?

elliptical movement can be identified by its unique properties: is periodic, which means that the object returns to its starting point after a certain period of time; it is not uniform, which means that the object moves faster at some points and slower at others; and follows a closed path that is symmetric about two fixed points called foci.

To classify a motion as elliptical, must have these characteristics. The concept of elliptical motion is fundamental in many areas of physics, such as celestial mechanics, where the orbits of the planets are elliptical, and in the study of wave motion and optics, where the concept of elliptical polarization is used to describe the light behaviour.

Understanding the classification and concept of elliptical motion is essential to understand the principles of physics and its applications in various fields.

## How is elliptical motion calculated? – Formula

It is a type of movement in which an object moves following an elliptical path. This motion is characterized by the object moving at variable speeds along its path, with its highest speed at points closest to the center of the elliptical path, and its slowest speed at points furthest from the center.

To calculate the speed and position of an elliptical moving object, physicists use a formula that takes into account the mass of the object, the intensity of the Gravitational force acting on it and the eccentricity of its elliptical trajectory.

The formula is derived from Kepler’s laws of planetary motion and is known as vis-viva equation. It establishes that the velocity of an object in elliptical motion is proportional to the square root of the product of the gravitational constant and the sum of the masses of the object and the central body, divided by the semi-major axis of the elliptical trajectory.

This formula is essential for calculate the movement of planetscomets and other celestial bodies in our solar system.

## What types of elliptical movements exist?

In the field of physics there are two types of elliptical movements:

uniform elliptical motion

In this type of motion, an object moves in an elliptical path. with a constant speed. The tangential speed of the object is constant, which means that the object moves at the same speed along the ellipse.

The distance between the object and the focus of the ellipse is also constant. A common example of uniform elliptical motion is the Earth’s orbit around the Sun. The Earth moves in an elliptical path around the Sun with a constant velocity.

The distance between the Earth and the Sun varies along the ellipse, but the tangential velocity of the Earth is constant. This movement is uniform since the speed of the Earth is constant and the ellipse is a regular geometric figure with two foci.

This type of movement is the result of the gravitational interaction between the Earth and the Sun. The gravitational force of the Sun is responsible for keeping the Earth in its elliptical orbit.

nonuniform elliptical motion

In this type of motion, an object moves in an elliptical path, but its speed is constantly changing. The tangential speed of the object is not constant, which means that the object moves at different speeds along the ellipse.

The distance between the object and the focus of the ellipse also changes. A common example of this type of motion is the motion of a satellite in a low orbit around the Earth, where the velocity of the satellite varies due to air resistance.

This type of movement is not uniform because the speed of the satellite is not constant, but it changes as you move along the ellipse. The Earth’s gravitational force is responsible for keeping the satellite in its elliptical orbit, while air resistance exerts a force that changes the speed of the satellite along the ellipse.

In both types of elliptical movements, the gravitational force is responsible for keep the object on its elliptical trajectory. The gravitational force is a central force that acts between two objects due to their mass, and it always points towards the objects center of mass.

## What characteristics do elliptical movements have?

The characteristics of elliptical movements can be described by their shape, speed, direction and energy.

• The elliptical path is defined as a closed curve resembling an elongated circle or oval shape, with two foci located at different points within the curve.
• The speed of the elliptical movement is not constantbut it varies as the object moves along the trajectory, producing the greatest speed at the perigee, or point closest to the foci.
• The direction of movement also changes as the object moves along the curve, the steering angle varying depending on the object’s location on the path.
• elliptical movement can have varying amounts of energy at different points of the trajectory, the total energy of the object remaining constant throughout the movement.

## Examples of elliptical movements

Examples of elliptical motion can be found in various contexts, such as astronomy, mechanics and electricity. In astronomy, the planets and comets follow elliptical orbits around the sun, with different degrees of eccentricity.

in mechanics, a simple pendulum presents an elliptical movement when its amplitude exceeds a critical value. In electricity, the polarization of light waves can be described as a type of elliptical motion, in which different states of polarization correspond to different orientations of the ellipse.

In general, elliptical motion is a fundamental concept in both physics and engineering, and its classification and understanding are essential for many applications.

### Parabolic shot

A parabolic shot is one of many elliptical motion shapes that can occur in physics. This type of motion occurs when an object is thrown at an angle and follows a parabolic path due to the gravitational pull of the Earth.

The trajectory of the object comes determined by the initial velocity and the launch angle, as well as by the gravitational force acting on it. This type of motion is commonly seen in projectile motion, for example in sports like basketball and golf, where understanding the parabolic trajectory can help players accurately aim their shots.

The concept of parabolic motion is important in physics, as it helps to explain the behavior of objects in motion and their interactions with the environment.

### The translation of the earth

The translation of the Earth refers to the movement of the Earth when it orbits the Sun. This movement is considered an elliptical movement in physics, which means that it follows an ellipse-shaped path.

The elliptical path of the Earth is characterized by two points called fociin one of which is the Sun. As the Earth moves along its elliptical path, it experiences changes in its speed and distance from the Sun.

This movement plays a crucial role in the weather determination and the seasons of the Earth, as well as in the behavior of the tides and other astronomical phenomena. Understanding the concept of elliptical motion and its various classifications is crucial not only in physics, but also in other areas such as astronomy, engineering, and mathematics.

### A swing

An elliptical motion refers to a type of motion that occurs in a slightly oval trajectory, also known as an ellipse. A common example of elliptical motion can be seen in a swing, where the motion of the seat travels back and forth in an elliptical path.

The swing hangs from two parallel chains, and when a person sits on the seat, the force of gravity pull the swing to the ground. When the swing starts to move, its movement follows a path in the air that resembles an ellipse.

This motion continues until the force of friction and air resistance stop the movement of the swing and they stop it. The physics behind elliptical motion is complex, but understanding the concept can help us better understand the motions of objects in the world around us.

This type of movement finds applications in various fields of engineering and science, from movements of robotic arms to trajectories of satellite orbits. In engineering, elliptical motion is used in the design of cam mechanisms, in which a follower follows an elliptical path traced by a cam, resulting in the required motion.

This type of movement is also used in the design of linkage mechanisms, gears and crankshafts. In the field of physics, elliptical motion is used to describe the motion of celestial bodies, such as the elliptical orbits of planets around the sun.

It is also used to describe the movement of objects in the field of astronomy, like the elliptical orbits of stars around a galactic center. Furthermore, the concept of elliptical motion has applications in sports science, where athletes use elliptical trainers to simulate jogging and stair climbing while minimizing impact on the body.

The versatility of the elliptical motion makes it a valuable concept and widely used in various fields of research and development.

Understanding and classifying the different types of elliptical motions is important for physicists, as it allows them to accurately model and predict the behavior of physical systems. Whether you are a student or a researcher, understanding the concept of elliptical motion can help you make sense of various natural phenomena and contribute to advances in the field of physics.