Elliptic orbit

In astrodynamics or celestial mechanics, an elliptical orbit is a special type of path that objects follow when they move around another object due to gravity. These orbits are shaped like slightly stretched circles, and they can range from almost perfect circles to very long, thin ovals. The measure of how stretched the orbit is called eccentricity, and for an elliptical orbit, this number is always less than 1. When the eccentricity is exactly 0, the orbit is a perfect circle, which is a special case of an elliptical orbit.

In simple situations where two objects are moving under each other's gravity, both objects follow elliptical orbits around a common center called the barycenter. They complete these orbits in the same amount of time, known as the orbital period. This means that if you were to look at one object from the other, the path would also look like an ellipse.

In our solar system, the planets generally follow nearly circular elliptical orbits around the sun because the sun is so much more massive than the planets. However, some objects, like comets, have highly stretched elliptical orbits. For example, Halley's Comet has an orbit that is very long and thin. Similarly, man-made satellites can also follow elliptical paths, such as Hohmann transfer orbits, Molniya orbits, and tundra orbits, which are used for specific space missions.

Velocity

The speed of an object moving in an elliptical orbit can be found using a special math formula called the vis-viva equation. This formula helps us understand how fast a planet or satellite moves depending on its distance from the object it is orbiting and the size of its orbit.

The formula uses a few important values: the distance between the objects, the size of the orbit's longest axis, and a special number that depends on the masses of the two objects involved. This helps scientists predict the motion of planets, moons, and spacecraft in space.

Main article: vis-viva equation

Orbital period

The orbital period is the time it takes for an object to travel once around its orbit. For objects moving in an elliptical orbit, this period can be calculated using a simple formula that depends on the size of the orbit and the gravitational pull of the body it is orbiting.

Importantly, the time it takes to complete one orbit is the same as it would be for a circular orbit with the same size. This means that no matter how stretched out the orbit is, the time to complete one full trip stays the same if the overall size does not change. This idea is part of Kepler's third law.

Main article: Orbital period

Energy

In space, objects moving around a planet or star have a special kind of energy called specific orbital energy. For an elliptical orbit — the path many planets and moons follow — this energy is always negative. This means the object is bound to the planet or star and can’t escape.

We can describe this energy using a simple idea called the semi major axis, which is the longest distance across the orbit. The total energy of the orbit depends on this distance and the masses of the two objects. The closer the orbit, the more negative the energy, showing a stronger bond between the objects.

Flight path angle

The flight path angle is the angle between an object's speed and the horizontal direction as it moves around another object in space. It helps us understand the shape and direction of the orbit.

This angle changes depending on where the object is in its orbit and how stretched out, or eccentric, the orbit is. By studying this angle, scientists can predict the object's path and movement around the central body it orbits.

Equation of motion

Main article: Orbit equation

An orbit equation describes the path of an object moving around a central body, such as a planet around the Sun. If the orbit's shape is not a perfect circle but still closed and repeated, it is called an elliptical orbit. This happens when the orbit's eccentricity is less than 1.

To understand the motion, scientists use the object's starting position and speed. They also assume the central body, like the Sun, stays at a fixed point. With these starting details, they can calculate the orbit's shape and how the object will move over time.

Orbital parameters

The position and speed of an object moving around another object can be described using special coordinates called Cartesian coordinates. These coordinates, along with the object's speed in each direction, help us understand the object's path. Together, these six pieces of information are known as orbital state vectors. They can tell us the full path of the orbiting object.

Another way to describe an orbit uses six different numbers called orbital elements. Both methods help scientists predict how objects move in space.

Solar System

In the Solar System, planets, asteroids, most comets, and some pieces of space debris move in paths called elliptical orbits around the Sun. These orbits are not perfect circles but are slightly stretched out. The chart showing the closest and farthest points of planets, dwarf planets, and Halley's Comet illustrates how stretched these paths can be. Earth and Venus have almost circular paths, while Halley's Comet and Eris have much more stretched paths.

Radial elliptic trajectory

A radial trajectory can be thought of as a special kind of stretched-out ellipse where the smaller part of the shape is zero. Even though it looks a bit like a parabola, it is not one. Most of the rules that apply to normal oval orbits still work here, but the path does not loop back on itself—it stays open. This kind of path happens when two objects start very close, move apart, and then come back together again.

This type of orbit also appears when an object is simply dropped, assuming there is no air pushing against it.

History

The Babylonians noticed that the Sun did not move at the same speed along its path in the sky. They did not know why, but we now understand this happens because the Earth moves in an oval-shaped path called an elliptic orbit around the Sun. The Earth moves faster when it is closest to the Sun at a point called perihelion and slower when it is farthest away at aphelion.

In the 1600s, Johannes Kepler discovered that the planets travel around the Sun in oval paths, with the Sun at one end of the oval. He called this his first law of how planets move. Later, Isaac Newton explained this using his ideas about the force that pulls objects together, called the law of universal gravitation.