Part of a series on
Astrodynamics
Orbital mechanics
Orbital elements Apsis Argument of periapsis Eccentricity Inclination Mean anomaly Orbital nodes Semi-major axis True anomaly
Types oftwo-body orbits by eccentricity Circular orbit Elliptic orbit Transfer orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit Radial orbit Decaying orbit
Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period Orbital velocity Surface gravity Specific orbital energy Vis-viva equation
Celestial mechanics
Gravitational influences Barycenter Hill sphere Perturbations Sphere of influence
N-body orbits Lagrangian points (Halo orbits) Lissajous orbits Lyapunov orbits
Engineering and efficiency
Preflight engineering Mass ratio Payload fraction Propellant mass fraction Tsiolkovsky rocket equation
Efficiency measures Gravity assist Oberth effect
Propulsive maneuvers Orbital maneuver Orbit insertion
v t e

Orbital decay is a gradual decrease of thedistance between twoorbiting bodies at their closest approach (theperiapsis) over many orbital periods. These orbiting bodies can be aplanet and itssatellite, astar and any object orbiting it, or components of anybinary system. If left unchecked, the decay eventually results in termination of the orbit when the smaller objectstrikes the surface of the primary; or for objects where the primary has an atmosphere, the smaller objectburns, explodes, or otherwise breaks up in the larger object'satmosphere; or for objects where the primary is a star, ends with incineration by the star's radiation (such as forcomets).Collisions of stellar-mass objects are usually accompanied by effects such asgamma-ray bursts and detectablegravitational waves.

Orbital decay is caused by one or more mechanisms which absorb energy from the orbital motion, such asfluid friction,gravitational anomalies, orelectromagnetic effects. For bodies inlow Earth orbit, the most significant effect isatmospheric drag.

Due to atmospheric drag, the lowest altitude above theEarth at which an object in a circular orbit can complete at least one full revolution without propulsion is approximately 150 km (93 mi) while the lowestperigee of an elliptical revolution is approximately 90 km (56 mi).

A simplified decay model for a near-circular two-body orbit about a central body (or planet) with an atmosphere, in terms of the rate of change of the orbital altitude, is given below.^[2]

${\displaystyle \frac{dR}{dt}=\frac{{\alpha }_o(R)\cdot T(R)}{\pi }}$

WhereR is the distance of the spacecraft from the planet's origin,α_o is the sum of all accelerations projected on the along-track direction of the spacecraft (or parallel to the spacecraft velocity vector), andT is the Keplerian period. Note thatα_o is often a function ofR due to variations in atmospheric density in the altitude, andT is a function ofR by virtue ofKepler's laws of planetary motion.

If only atmospheric drag is considered, one can approximate drag decelerationα_o as a function of orbit radiusR using thedrag equation below:

${\displaystyle {\alpha }_o=\frac{1}{2}\rho (R)v^2{c}_{\mathrm{d}}\frac{A}{m}}$

${\displaystyle \rho (R)}$ is themass density of the atmosphere which is a function of the radius R from the origin,

${\displaystyle v}$ is theorbital velocity,

${\displaystyle A}$ is the drag referencearea,

${\displaystyle m}$ is themass of the satellite, and

${\displaystyle c_{\mathrm{d}}}$ is thedimensionlessdrag coefficient related to the satellite geometry, and accounting forskin friction andform drag (~2.2 for cube satellites).

The orbit decay model has been tested against ~1 year of actual GPS measurements ofVELOX-C1, where the mean decay measured via GPS was 2.566 km across Dec 2015 to Nov 2016, and the orbit decay model predicted a decay of 2.444 km, which amounted to a 5% deviation.

An open-sourcePython based software,ORBITM (ORBIT Maintenance and Propulsion Sizing), is available freely on GitHub for Python users using the above model.

By theconservation of mechanical energy, the energy of the orbit is simply the sum of kinetic and gravitational potential energies, in an unperturbedtwo-body orbit. By substituting thevis-viva equation into the kinetic energy component, the orbital energy of a circular orbit is given by:

${\displaystyle U=KE+GPE=-\frac{G{M}_{E}m}{2R}}$

WhereG is the gravitational constant,M_E is the mass of the central body andm is the mass of the orbiting satellite. We take the derivative of the orbital energy with respect to the radius.

${\displaystyle \frac{dU}{dR}=\frac{G{M}_{E}m}{2R^2}}$

The total decelerating force, which is usually atmospheric drag for low Earth orbits, exerted on a satellite of constant massm is given by some forceF. The rate of loss of orbital energy is simply the rate at the external force does negative work on the satellite as the satellite traverses an infinitesimal circular arc-lengthds, spanned by some infinitesimal angledθ and angular rateω.

${\displaystyle \frac{dU}{dt}=\frac{F\cdot ds}{dt}=\frac{F\cdot R\cdot d\theta }{dt}=F\cdot R\cdot \omega }$

The angular rateω is also known as theMean motion, where for a two-body circular orbit of radiusR, it is expressed as:

${\displaystyle \omega =\frac{2\pi }{T}=\sqrt{\frac{G{M}_E}{R^3}}=\frac{F\cdot R\cdot d\theta }{dt}=F\cdot R\cdot \omega }$

and...

${\displaystyle F=m\cdot {\alpha }_o}$

Substitutingω into the rate of change of orbital energy above, and expressing the external drag or decay force in terms of the decelerationα_o, the orbital energy rate of change with respect to time can be expressed as:

${\displaystyle \frac{dU}{dt}=m\cdot {\alpha }_o\cdot \sqrt{\frac{G{M}_E}{R}}}$

Having an equation for the rate of change of orbital energy with respect to both radial distance and time allows us to find the rate of change of the radial distance with respect to time as per below.

${\displaystyle \frac{dR}{dt}=\left({\left(\frac{dU}{dR}\right)}^{-1}\cdot \frac{dU}{dt}\right)}$

${\displaystyle =2{\alpha }_o\cdot \sqrt{\frac{R^3}{G{M}_E}}}$

${\displaystyle =\frac{{\alpha }_o\cdot T}{\pi }}$

The assumptions used in this derivation above are that the orbit stays very nearly circular throughout the decay process, so that the equations for orbital energy are more or less that of a circular orbit's case. This is often true for orbits that begin as circular, as drag forces are considered "re-circularizing", since drag magnitudes at theperiapsis (lower altitude) is expectedly greater than that of theapoapsis, which has the effect of reducing the mean eccentricity.

Atmospheric drag at orbital altitude is caused by frequent collisions of gasmolecules with the satellite.It is the major cause of orbital decay for satellites inlow Earth orbit. It results in the reduction in thealtitude of a satellite's orbit. For the case of Earth, atmospheric drag resulting in satellite re-entry can be described by the following sequence:

lower altitude → denser atmosphere → increased drag → increased heat → usually burns on re-entry

Orbital decay thus involves apositive feedback effect, where the more the orbit decays, the lower its altitude drops, and the lower the altitude, the faster the decay. Decay is also particularly sensitive to external factors of the space environment such as solar activity, which are not very predictable. Duringsolar maxima the Earth's atmosphere causes significant drag up to altitudes much higher than duringsolar minima.^[3]

Atmospheric drag exerts a significant effect at the altitudes ofspace stations,Space Shuttles and other crewed Earth-orbit spacecraft, and satellites with relatively high "low Earth orbits" such as theHubble Space Telescope. Space stations typically require a regular altitude boost to counteract orbital decay (see alsoorbital station-keeping). Uncontrolled orbital decay brought down theSkylab space station,^[4] and (relatively) controlled orbital decay was used to de-orbit theMir space station.^[5]

Reboosts for the Hubble Space Telescope are less frequent due to its much higher altitude. However, orbital decay is also a limiting factor to the length of time the Hubble can go without a maintenance rendezvous, the most recent having been performed successfully bySTS-125, with Space ShuttleAtlantis in 2009. Newerspace telescopes are in much higher orbits, or in some cases in solar orbit, so orbital boosting may not be needed.^[6]

An orbit can also decay by negativetidal acceleration when the orbiting body is large enough to raise a significanttidal bulge on the body it is orbiting and is either in aretrograde orbit or is below thesynchronous orbit. This saps angular momentum from the orbiting body and transfers it to the primary's rotation, lowering the orbit's altitude.

Examples of satellites undergoing tidal orbital decay are Mars' moonPhobos, Neptune's moonTriton, and the extrasolar planetTrES-3b.

Small objects in theSolar System also experience an orbital decay due to the forces applied by asymmetric radiation pressure. Ideally, energy absorbed would equalblackbody energy emitted at any given point, resulting in no net force. However, theYarkovsky effect is the phenomenon that, because absorption and radiation of heat are not instantaneous, objects which are nottidally locked absorb sunlight energy on surfaces exposed to the Sun, but those surfaces do not re-emit much of that energy until after the object has rotated, so that the emission is parallel to the object's orbit. This results in a very small acceleration parallel to the orbital path, yet one which can be significant for small objects over millions of years. The Poynting-Robertson effect is a force opposing the object's velocity caused by asymmetric incidence of light, i.e.,aberration of light. For an object with prograde rotation, these two effects will apply opposing, but generally unequal, forces.

Gravitational radiation is another mechanism of orbital decay. It is negligible for orbits of planets and planetary satellites (when considering their orbital motion on time scales of centuries, decades, and less), but is noticeable for systems ofcompact objects, as seen in observations of neutron star orbits. All orbiting bodies radiate gravitational energy, hence no orbit is infinitely stable.

Satellites using anelectrodynamic tether, moving through the Earth's magnetic field, create drag force that could eventually deorbit the satellite.

A stellar collision is the coming together of twobinary stars when they lose energy and approach each other. Several things can cause the loss of energy includingtidal forces,mass transfer, andgravitational radiation. The stars describe the path of aspiral as they approach each other. This sometimes results in a merger of the two stars or the creation of ablack hole. In the latter case, the last several revolutions of the stars around each other take only a few seconds.^[7]

While not a direct cause of orbital decay, uneven mass distributions (known asmascons) of the body being orbited can perturb orbits over time, and extreme distributions can cause orbits to be highly unstable. The resulting unstable orbit can mutate into an orbit where one of the direct causes of orbital decay can take place.

• Effects of gravity
• Orbits
• Black holes

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