Orbital decay is a slow decrease in the distance between two objects that are orbiting each other at their closest point (called the periapsis) over many orbits. These objects can include a planet and its moon, a star and any object orbiting it, or parts of a binary system. If orbital decay continues without stopping, the orbit eventually ends. This can happen in several ways: the smaller object may crash into the surface of the larger object, burn up or break apart in the larger object’s atmosphere if it has one, or be destroyed by the star’s intense radiation, such as comets being burned by a star’s light. Collisions between large objects, like stars, often create effects such as gamma-ray bursts and gravitational waves that can be detected.

Orbital decay happens when energy is taken from the orbit through processes like fluid friction, gravitational irregularities, or electromagnetic forces. For objects in low Earth orbit, the most important cause is atmospheric drag, which is the resistance caused by Earth’s atmosphere.

Because of atmospheric drag, the lowest height above Earth where an object in a circular orbit can complete one full loop without propulsion is about 150 km (93 miles). For an elliptical orbit, the lowest point (called the perigee) can be around 90 km (56 miles).

Modeling

A simplified model for how the altitude of a spacecraft changes over time in a nearly circular orbit around a planet with an atmosphere is described below. In this model, R represents the distance between the spacecraft and the center of the planet. αo is the total acceleration acting on the spacecraft in the direction of its movement, and T is the time it takes to complete one full orbit, known as the Keplerian period. αo often depends on R because atmospheric density changes with altitude, and T depends on R based on Kepler's laws of planetary motion.

If only atmospheric drag is considered, the drag force acting on the spacecraft can be estimated using the drag equation. This equation relates the deceleration αo to the orbit radius R. The model was tested using one year of GPS data from the satellite VELOX-C1. During this time, the actual orbital decay measured by GPS was 2.566 kilometers, while the model predicted a decay of 2.444 kilometers, showing a 5% difference between the measured and predicted values.

A free, open-source Python program called ORBITM (ORBIT Maintenance and Propulsion Sizing) is available on GitHub. This software uses the model described above to help users analyze orbital decay.

According to the law of conservation of mechanical energy, the total energy of an orbit is the sum of kinetic energy (energy of motion) and gravitational potential energy (energy due to position in a gravitational field) in a two-body system without external forces. Using the vis-viva equation, which relates the speed of an object in orbit to its distance from the central body, the energy of a circular orbit can be calculated as:

Where G is the gravitational constant, M_E is the mass of the central body, and m is the mass of the orbiting object. The rate of change of orbital energy with respect to the radius R is calculated by taking the derivative of this equation.

The total force slowing down the spacecraft, usually atmospheric drag for low Earth orbits, is represented by F. The rate at which orbital energy decreases is equal to the rate at which this force does negative work on the spacecraft as it moves through a small arc of its orbit. This arc is defined by an infinitesimal angle dθ and the angular speed ω.

The angular speed ω, also called the mean motion, for a circular orbit of radius R is given by:

By substituting ω into the equation for the rate of change of orbital energy and expressing the drag force in terms of αo, the rate of change of orbital energy with respect to time can be written as:

This equation allows us to calculate how the orbital radius changes over time. The assumptions used in this derivation are that the orbit remains nearly circular throughout the decay process. This is often true because drag forces act more strongly at the lowest point of the orbit (periapsis) than at the highest point (apoapsis), which reduces the orbit's eccentricity over time.

Sources of decay

Atmospheric drag at orbital altitude happens when gas molecules frequently collide with a satellite. This is the main reason for orbital decay in satellites orbiting low Earth. Orbital decay causes a satellite's orbit to gradually move closer to Earth. For Earth, the process of atmospheric drag leading to satellite re-entry follows this pattern:

Orbital decay creates a cycle where the lower the orbit becomes, the faster it decays. This process is also influenced by unpredictable factors in space, such as solar activity. During periods of high solar activity, Earth's atmosphere causes significant drag at higher altitudes than during periods of low solar activity.

Atmospheric drag strongly affects space stations, Space Shuttles, and other crewed spacecraft, as well as satellites in high low Earth orbits, like the Hubble Space Telescope. Space stations often need regular altitude adjustments to counteract orbital decay. Uncontrolled orbital decay caused the Skylab space station to fall to Earth, while controlled decay was used to safely de-orbit the Mir space station.

The Hubble Space Telescope requires fewer altitude adjustments because it orbits much higher than most satellites. However, orbital decay still limits how long the Hubble can operate without maintenance. The most recent maintenance mission was conducted by the Space Shuttle Atlantis in 2009. Newer space telescopes are placed in higher orbits or sometimes in solar orbit, reducing the need for altitude adjustments.

Orbits can also decay due to negative tidal acceleration when an object orbits below the synchronous orbit. This process removes angular momentum from the orbiting object and transfers it to the rotation of the primary body, lowering the orbit's altitude.

Examples of objects experiencing tidal orbital decay include Mars' moon Phobos, Neptune's moon Triton, and possibly the exoplanet TrES-3b.

Small objects in the Solar System also experience orbital decay due to uneven radiation pressure. Normally, energy absorbed by an object would balance the energy it emits, creating no net force. However, the Yarkovsky effect occurs because absorbed sunlight is not immediately re-emitted. Instead, heat is released after the object rotates, creating a small force that pushes the object along its orbit. Over millions of years, this can significantly affect small objects. The Poynting-Robertson effect is another force caused by light bending, which opposes an object's motion. These two effects work in opposite directions for objects with prograde rotation.

Gravitational radiation is another cause of orbital decay. It has little effect on planets and their moons over short time periods but is noticeable in systems with compact objects, such as neutron stars. All orbiting bodies emit gravitational energy, meaning no orbit lasts forever.

Satellites using an electrodynamic tether, which moves through Earth's magnetic field, create drag that can eventually bring the satellite back to Earth.

Stellar collision

A stellar collision happens when two binary stars come together after losing energy. This energy loss can be caused by tidal forces, mass transfer, or gravitational radiation. As the stars lose energy, they move in a spiral path toward each other. This process may lead to the stars merging into one or the formation of a black hole. When a black hole is created, the final orbits of the stars around each other last only a few seconds.

Mass concentration

Uneven areas of mass (called mascons) on the object being orbited can change the path of orbits over time, even though they are not the main reason for orbital decay. If these mass areas are extremely uneven, the orbit can become very unstable. This unstable orbit may then change into a form where one of the direct causes of orbital decay can occur.