Understanding the nature of orbits has been a fundamental aspect of astronomy and astrophysics for centuries. One common question is why orbits, be they those of planets around stars or planets around planets, are not perfect circles.
Orbits are not circular because of the gravitational influence of other celestial bodies. The balance between the central object’s gravitational force and the orbiting object’s centrifugal force determines the orbit’s shape.
This article will examine the reasons behind the elliptical nature of orbits and the interplay between gravitational forces and orbital mechanics.
Celestial Mechanics And Kepler’s Laws
To understand why orbits are not circular, we first need to delve into the basics of celestial mechanics. Celestial mechanics deals with the motion of celestial objects, such as planets, moons, and stars.
The astronomer and mathematician Johannes Kepler’s contributions, laid the groundwork for our current understanding of orbital motions. Kepler’s three laws of planetary motion explain the behavior of celestial bodies in orbit around one another.
These laws have since been generalized to cover any two objects orbiting each other due to gravity.
Kepler’s First Law: The Law Of Ellipses
Kepler’s first law states that the orbit of a planet around the Sun (or any object around another object) is an ellipse, with the larger object at one of the ellipse’s two foci.
An ellipse is a geometric shape resembling a squashed circle or an oval, characterized by two foci. The sum of the distances between any two foci and any point on the ellipse is always constant.
Kepler’s Second Law: The Law Of Equal Areas
The second law states that a line connecting the orbiting object and the larger object sweeps out equal areas in equal periods. It means that the orbiting object moves faster when it is closer to the larger object and slower when it is farther away.
The conservation of angular momentum has caused it.
Kepler’s Third Law: The Harmonic Law
The third law relates the square of the orbital period to the cube of the semi-major axis of the ellipse. Objects orbiting farther away from the larger object take longer to complete one orbit.
The Role Of Gravity In Shaping Orbits
Gravity is the primary force that governs the motion of celestial bodies. The gravitational force between two objects depends on their masses and distance.
Centripetal Force And Orbital Velocity
The gravitational force serves as the centripetal force, which keeps an object in orbit traveling along a curving path. The gravitational and centripetal forces must be equal for a stable orbit.
The Interplay Of Gravitational And Centripetal Forces
The balance between gravitational and centripetal forces determines the shape of an orbit. If the orbiting object’s velocity is too low, the gravitational force will cause it to spiral inward and collide with the larger object.
If the velocity is too high, the object will escape the gravitational pull and fly into space.
To achieve a stable, circular orbit, the object’s velocity must be precisely what is needed to balance the gravitational force. However, their initial velocities and positions do not result in perfect circles for most celestial bodies.
Instead, they form elliptical orbits that balance the gravitational and centripetal forces throughout the orbit.
Watch this video to learn why orbits are elliptical:
Why Are Orbits Elliptical? | Intuitive Proof
Energy And Orbital Shape
Another way to understand the elliptical nature of orbits is to consider the total energy of the orbiting system. The total energy consists of kinetic energy (due to motion) and gravitational potential energy (due to the attractive force between the objects).
In a stable orbit, the total energy remains constant.
Kinetic Energy
The kinetic energy of an object in motion is a fundamental parameter that determines the shape of its orbit. The kinetic energy is directly proportional to the mass of an object and the square of the object’s velocity. Therefore, an object’s kinetic energy increases with increasing mass or velocity.
In an elliptical orbit, the object moves faster when it is closer to the central object and slower when it is further away. As a result, the object’s kinetic energy varies throughout its orbit, with the highest kinetic energy occurring at the closest point to the central object.
Gravitational Potential Energy
Another important factor that influences how an orbit is shaped is the gravitational potential energy between two objects. The gravitational potential energy varies with the separation between the two objects in direct proportion.
Therefore, the closer the objects are, their gravitational potential energy is higher.
The gravitational potential energy of the system changes during the course of an elliptical orbit due to variations in the distance between the orbiting object and the central object.
When the orbiting object is closest to the central object, the gravitational potential energy is at its lowest, and it is at its highest when it is farthest from the central object.
Total Energy
The system’s total energy (E) is the sum of the kinetic and potential energy. For a stable orbit, the total energy must remain constant. It means that as the object moves closer to the larger object, its gravitational potential energy increases, and its kinetic energy decreases.
As it moves farther away, the opposite occurs.
The total energy of the system determines the shape of the orbit. If the total energy is negative, the orbit is bound, and the object will continue to orbit the larger object. The object will escape the gravitational pull and fly into space if the total energy is positive.
If the total energy is zero, the orbit is circular.
In most cases, the system’s total energy is negative but not zero, resulting in an elliptical orbit. The initial velocity and position of the orbiting object determine the shape of the ellipse.
Conclusion
The elliptical shape of orbits is due to the interaction between gravitational and centripetal forces and the system’s total energy.
Although a stable circular orbit is feasible, most cosmic objects follow an elliptical path due to their initial velocities and positions.
