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

Historically, ancient thinkers used the idea of moving spheres to describe how planets moved across the sky. They believed stars and planets were attached to perfect, moving spheres around Earth. This changed when Johannes Kepler discovered that planets travel in oval-shaped paths called ellipses, not perfect circles, and 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 go around the Sun relates to its distance from the Sun. Even today, we use Newton’s ideas for most calculations, though modern science has added more details about how gravity works.

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, and they change slowly over time due to the pull of gravity from other objects.

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. These points help us understand how objects move in space.

Principles

An orbit happens when an object moves around another object due to gravity. We can understand this by thinking about Newton's laws of motion and his law of universal gravitation. These laws tell us that objects keep moving unless a force stops them, forces cause movement, and every action has an equal opposite reaction.

Imagine throwing a ball horizontally from a very high mountain. If you throw it slowly, it will drop and hit the ground. Throw it faster, and it will travel farther before hitting the ground. If you throw it fast enough, the Earth will curve away from the ball as it falls, and the ball will keep moving around the Earth without ever hitting it. This is an orbit! The ball is moving in a curved path because of Earth’s gravity, and 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 objects move in space when pulled by gravity. They tell us that the pull of 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 gravitational pull.

When objects orbit each other, like planets around the Sun, their paths are usually oval-shaped, called ellipses. There are special rules, known as Kepler's laws, that describe exactly how these orbits work. One rule says that the planet moves faster when it is closer to the Sun and slower when it is farther away. These laws help scientists predict 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 constantly pulled toward the center but also moves forward, creating a continuous loop.

Orbits follow predictable 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 orbit over time. These forces are usually small compared to the main force pulling the object, like gravity from a planet or star. Things that can cause perturbations include the shape of the planet not being a perfect sphere, the pull of other bodies, and even the drag 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 perpendicular to the path. These forces can change how stretched the orbit is 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 tilt the plane of the orbit. Even with these changes, the orbit will still follow a smooth path.

Strange orbits

Mathematicians have found that it is possible to have special paths in space where objects move in repeating 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, such as Newton’s laws, to understand and 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. Sometimes, more advanced theories are needed for very precise calculations, especially when objects are close to large gravitational forces like those from the Sun or big planets.

Earth orbits

Main article: List of orbits

There are several types of 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 (1,240 miles) above our planet. Medium Earth orbit (MEO) is a bit farther out, ranging from 2,000 to almost 36,000 kilometers (1,240 to 22,236 miles).

Two special types of 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 fixed 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 (22,240 miles) 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 stay similar. 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 understand how orbits work in different sizes of solar systems.