Orbit

An orbit is the path that objects in space take when they are pulled by gravity. In celestial mechanics, an orbit is the curved trajectory an object follows as it moves around something larger and more massive. This movement can be thought of as a kind of rotation around an axis that is not part of the moving body itself.

Variation of orbital eccentricity 0.0 0.2 0.4 0.6 0.8

Orbits happen all around us in space. For example, planets travel in orbits around stars, like our Earth around the Sun. A natural satellite, such as the Moon, orbits a planet, while an artificial satellite — like the ones we use for TV and phone signals — orbits around a planet, moon, or even a special point in space called a Lagrange point. Most of the time, these orbits repeat in a regular pattern and look like stretched circles called elliptic orbits. This shape was explained by Kepler's laws of planetary motion, which describe how planets move.

We can understand orbits using ideas from Newtonian mechanics, which tells us that gravity acts as a pull between objects. But for even more precise information, we use Albert Einstein's general theory of relativity. This theory says that gravity bends something called spacetime, and objects follow paths called geodesics as they move through it.

History

The Earth-centered universe according to Ptolemy; illustration by Andreas Cellarius from Harmonia Macrocosmica, 1660

Long ago, people thought planets moved in perfect circles around Earth. They imagined stars and planets attached to moving spheres. This changed when Johannes Kepler discovered that planets travel in oval shapes called ellipses. He also found that the Sun is not at the center of these paths.

Later, Isaac Newton explained that gravity keeps planets in their orbits. He showed that the time it takes for a planet to orbit the Sun depends on its distance from the Sun. We still use Newton’s ideas for many calculations today.

Planetary orbits

In a planetary system, objects such as dwarf planets, asteroids, and comets move in paths called elliptical orbits around the system's center, known as the barycenter. These orbits can be stretched out or more rounded.

When two objects orbit each other, they have points where they are closest and farthest apart. For orbits around Earth, the closest point is called perigee and the farthest is apogee. For orbits around the Sun, the closest point is perihelion and the farthest is aphelion.

Principles

An orbit happens when an object moves around another object because of gravity. We can understand this using Newton's laws of motion and his law of universal gravitation. These laws explain that objects keep moving unless something stops them, forces can make things move, and every action has an equal opposite reaction.

Imagine throwing a ball from a very high mountain. If you throw it slowly, it will drop and hit the ground. Throw it faster, and it will go farther before hitting the ground. If you throw it fast enough, the Earth will curve away as the ball falls, and the ball will keep moving around the Earth without ever hitting it. This is an orbit! The ball moves in a curved path because of Earth’s gravity. If it goes fast enough, it can stay up there forever, going around and around.

To send spacecraft into orbit, rockets first go straight up to get above the thick part of the atmosphere. Then they turn and keep burning their engines until they reach the right speed to stay in orbit. Once they have this speed, they can stay above the atmosphere and keep moving around Earth without falling back down.

Newton's laws

Newton's laws help us understand how things move in space when pulled by gravity. They tell us that gravity makes things speed up or slow down, depending on how close they are to each other. For example, the Earth orbits the Sun because of this pull.

When objects orbit each other, like planets around the Sun, their paths are usually oval-shaped, called ellipses. There are special rules called Kepler's laws that explain how these orbits work. One rule says that a planet moves faster when it is closer to the Sun and slower when it is farther away. These laws help scientists know where planets will be in their orbits.

Formulation

The orbit of an object, like a planet around a star or a moon around a planet, is a curved path shaped by gravity. This path is called an orbit because the object is pulled toward the center but also moves forward, creating a continuous loop.

Orbits follow patterns described by laws developed by scientists like Isaac Newton and Johannes Kepler. These laws help us understand how objects in space move and predict their positions over time. For example, planets orbit stars in elliptical shapes, not perfect circles, and their speeds change depending on their distance from the center.

r ¨ − r θ ˙ 2 = − μ r 2 {\displaystyle {\ddot {r}}-r{\dot {\theta }}^{2}=-{\frac {\mu }{r^{2}}}}

r θ ¨ + 2 r ˙ θ ˙ = 0 {\displaystyle r{\ddot {\theta }}+2{\dot {r}}{\dot {\theta }}=0}

r 2 θ ˙ = h {\displaystyle r^{2}{\dot {\theta }}=h}

δ 2 u δ θ 2 + u = μ h 2 {\displaystyle {\frac {\delta ^{2}u}{\delta \theta ^{2}}}+u={\frac {\mu }{h^{2}}}}

Specification

Main article: Ephemeris

Perturbations

Main article: Perturbation (astronomy)

An orbital perturbation happens when a force changes an object's path as it moves around a planet or star. These forces are usually small, but over time they can make a difference. Things that can cause perturbations include the shape of the planet not being a perfect sphere, the pull of other objects, and the friction from a planet's atmosphere.

When a force acts on an object in orbit, it can be split into three parts: one towards the center, one along the path, and one sideways. These forces can change the shape of the orbit or how fast the object moves. For example, a force along the path can make the orbit more or less stretched. Some forces can also change the angle of the orbit. Even with these changes, the orbit will still move in a smooth way.

Strange orbits

Mathematicians have found that objects can move in space in special paths that repeat in patterns that are not simple ovals. One famous example is a path shaped like a figure-eight where three objects move together. Scientists have also found ways for many objects to move in complex, interlocking circles.

However, these unusual paths are very rare in nature because the exact conditions needed for them to happen naturally are very unlikely to occur by chance.

Astrodynamics

Astrodynamics is the study of how objects like rockets and spacecraft move in space. It uses ideas from physics to help plan the paths these objects take. This helps scientists and engineers design missions and control spacecraft as they travel around planets, moons, and other objects in space.

Earth orbits

Main article: List of orbits

There are several paths that objects can take when they travel around Earth. Low Earth orbit (LEO) is the path closest to Earth, reaching up to about 2,000 kilometers above our planet. Medium Earth orbit (MEO) is a bit farther out, ranging from 2,000 to almost 36,000 kilometers.

Two special orbits are geosynchronous orbit (GSO) and geostationary orbit (GEO). These paths match Earth’s spin, taking exactly one day to go around the planet. A geostationary orbit stays over one spot on the equator, while a geosynchronous orbit can move north and south. High Earth orbit (HEO) is the farthest, sitting above 36,000 kilometers from Earth.

Scaling in gravity

The gravitational constant is a number that helps scientists understand how gravity works. It is very small: about 6.6743 × 10⁻¹¹ m³⋅kg⁻¹⋅s⁻².

When we change the size of objects but keep their density the same, their orbits look almost the same. For example, if we make everything half as big, the time it takes for objects to move in their orbits stays the same. This helps us learn how orbits work in solar systems of different sizes.