question: Why are the orbits of planets and moons elliptical? I don’t understand how they don’t either spiral inwards and collide with their planets/star or sort of sling shot out of orbit.
comment: When you orbit something, what you're really doing is falling towards it, but also moving sideways fast enough to not actually fall inward. Imagine you're going around a circle in a car. You have two 'forces' acting on you, the fictitious centrifugal force and the force of the car pushing you inward (the centrifugal force isn't real because the feeling of being pushed outward is just the wall of the car keeping you in). If the car speeds up, you feel like you're being pushed outward harder. To balance that out, you can drive in a bigger circle. The same thing happens with orbits. If you're orbiting something and you speed up, you move outward until the forces equal out again. Move slower, you get closer in. If you speed up or slow down enough, you can break orbit -Which small things do all the time, but the planets are so massive that it's incredibly difficult to just knock them out of orbit. Now, the reason the orbits are elliptical is because when you move farther out, you lose some of your energy (it turns into potential energy, just like when you lift something up), and so you move slower. You then fall, accelerating as you do so, and then get fast enough to go back up again. Most of the planets' orbits are almost perfectly circular, but while the ellipse is slight, it's still there. *EDIT: Changed "centripetal" to "centrifugal."*
passages: Most planetary orbits are nearly circular, and careful observation and calculation are required in order to establish that they are not perfectly circular. Calculations of the orbit of Mars indicated an elliptical orbit. From this, Johannes Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits.
  
  Kepler's work (published between 1609 and 1619) improved the heliocentric theory of Nicolaus Copernicus, explaining how the planets' speeds varied, and using elliptical orbits rather than circular orbits with epicycles.
   In the Solar System, planets, asteroids, most comets and some pieces of space debris have approximately elliptical orbits around the Sun. Strictly speaking, both bodies revolve around the same focus of the ellipse, the one closer to the more massive body, but when one body is significantly more massive, such as the sun in relation to the earth, the focus may be contained within the larger massing body, and thus the smaller is said to revolve around it. The following chart of the perihelion and aphelion of the planets, dwarf planets and Halley's Comet demonstrates the variation of the eccentricity of their elliptical orbits. For similar distances from the sun, wider bars denote greater eccentricity. Note the almost-zero eccentricity of Earth and Venus compared to the enormous eccentricity of Halley's Comet and Eris.
   The epicyclic Solar System of Ptolemy (c. 100 – 170 AD) – still 300 years in the future from the apparent date of the mechanism – carried forward with more epicycles, and was more accurate predicting the positions of planets than the view of Copernicus (1473 – 1543 AD), until Kepler (1571 – 1630 AD) introduced the possibility that orbits are ellipses.
   If an orbit is about a planetary body with significant atmosphere, its orbit can decay because of drag. Particularly at each periapsis, the object experiences atmospheric drag, losing energy. Each time, the orbit grows less eccentric (more circular) because the object loses kinetic energy precisely when that energy is at its maximum. This is similar to the effect of slowing a pendulum at its lowest point; the highest point of the pendulum's swing becomes lower. With each successive slowing more of the orbit's path is affected by the atmosphere and the effect becomes more pronounced. Eventually, the effect becomes so great that the maximum kinetic energy is not enough to return the orbit above the limits of the atmospheric drag effect. When this happens the body will rapidly spiral down and intersect the central body.
   List of orbits
  
  The following is a list of types of orbits:
  
  Section::::Centric classifications.
  
  BULLET::::- Galactocentric orbit : An orbit about the center of a galaxy. The Sun follows this type of orbit about the galactic center of the Milky Way.
  
  BULLET::::- Heliocentric orbit: An orbit around the Sun. In the Solar System, all planets, comets, and asteroids are in such orbits, as are many artificial satellites and pieces of space debris. Moons by contrast are not in a heliocentric orbit but rather orbit their parent object.
   Every planetary probe was placed into its escape trajectory by a multistage rocket, the last stage of which ends up on nearly the same trajectory as the probe it launched. Because these stages cannot be actively guided, their trajectories are now different from the probes they launched (the probes were guided with small thrusters that allow course changes). However, in cases where the spacecraft acquired escape velocity because of a gravity assist, the stages may not have a similar course and there is the remote possibility that they collided with something. Some objects in heliocentric orbit have been reidentified with a telescope, and so their trajectories can be confirmed. The stages on an escape trajectory are:
   The planets' orbits are chaotic over longer timescales, in such a way that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years. In all cases this means that the position of a planet along its orbit ultimately becomes impossible to predict with any certainty (so, for example, the timing of winter and summer become uncertain), but in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical.
   Planets close to their stars on circular orbits will tend to despin and become tidally locked. As the planet's rotation slows down the radius of a synchronous orbit of the planet moves outwards from the planet. For planets tidally locked to their stars, the distance from the planet at which the moon will be in a synchronous orbit around the planet is outside the Hill sphere of the planet. The Hill sphere of the planet is the region where its gravity dominates that of the star so it can hold on to its moons. Moons inside the synchronous orbit radius of a planet will spiral into the planet. Therefore, if the synchronous orbit is outside the Hill sphere, then all moons will spiral into the planet. If the synchronous orbit is not three-body stable then moons outside this radius will escape orbit before they reach the synchronous orbit.
   The outer planets' orbits are chaotic over longer timescales, with a Lyapunov time in the range of 2–230 million years.
  
  In all cases this means that the position of a planet along its orbit ultimately becomes impossible to predict with any certainty (so, for example, the timing of winter and summer become uncertain), but in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical.
   Careful timing of eclipsing binaries has shown that systems showing orbital period modulations on the order of ∆P/P ∼ 10 over a period of decades are quite common. A striking example of such a system is Algol, for which the detailed observational record extends back over two centuries. Over this span of time, a graph of the time dependence of the difference between the observed times of eclipses "versus" the predicted times shows a feature (termed the "great inequality") with a full amplitude of 0.3 days and a recurrent time scale of centuries. Superimposed on this feature is a secondary modulation with a full amplitude of 0.06 days and a recurrent time scale of about 30 years. Orbital period modulations of similar amplitude are seen in other Algol binaries as well.
   Section::::Small body orbiting a central body.
  
  According to Kepler's Third Law, the orbital period "T" (in seconds) of two point masses orbiting each other in a circular or elliptic orbit is:
  
  where:
  
  BULLET::::- "a" is the orbit's semi-major axis
  
  BULLET::::- "μ" = "GM" is the standard gravitational parameter
  
  BULLET::::- "G" is the gravitational constant,
  
  BULLET::::- "M" is the mass of the more massive body.
  
  For all ellipses with a given semi-major axis the orbital period is the same, regardless of eccentricity.
  
  Inversely, for calculating the distance where a body has to orbit in order to have a given orbital period:
   The eccentricities of the orbits of those planets known to Copernicus and Kepler are small, so the foregoing rules give fair approximations of planetary motion, but Kepler's laws fit the observations better than does the model proposed by Copernicus.
  
  Kepler's corrections are not at all obvious:
  
  BULLET::::1. The planetary orbit is "not" a circle, but an "ellipse".
  
  BULLET::::2. The Sun is "not" at the center but at a "focal point" of the elliptical orbit.
   The Lidov-Kozai mechanism causes the argument of pericenter (ω) to librate about either 90° or 270°, which is to say that its periapse occurs when the body is farthest from the equatorial plane. This effect is part of the reason that Pluto is dynamically protected from close encounters with Neptune.
  
  The Lidov-Kozai mechanism places restrictions on the orbits possible within a system, for example
   With the publication of his "Principia" roughly eighty years later (1687), Isaac Newton provided a physical theory that accounted for all three of Kepler's laws, a theory based on Newton's laws of motion and his law of universal gravitation. In particular, Newton proposed that the gravitational force between any two bodies was a central force "F"("r") that varied as the inverse square of the distance "r" between them. Arguing from his laws of motion, Newton showed that the orbit of any particle acted upon by one such force is always a conic section, specifically an ellipse if it does not go to infinity. However, this conclusion holds only when two bodies are present (the two-body problem); the motion of three bodies or more acting under their mutual gravitation (the "n"-body problem) remained unsolved for centuries after Newton, although solutions to a few special cases were discovered. Newton proposed that the orbits of planets about the Sun are largely elliptical because the Sun's gravitation is dominant; to first approximation, the presence of the other planets can be ignored. By analogy, the elliptical orbit of the Moon about the Earth was dominated by the Earth's gravity; to first approximation, the Sun's gravity and those of other bodies of the Solar System can be neglected. However, Newton stated that the gradual apsidal precession of the planetary and lunar orbits was due to the effects of these neglected interactions; in particular, he stated that the precession of the Moon's orbit was due to the perturbing effects of gravitational interactions with the Sun.
   BULLET::::- For a given semi-major axis the orbital period does not depend on the eccentricity (See also: Kepler's third law).
  
  Section::::Energy.
  
  Under standard assumptions, specific orbital energy (formula_12) of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form:
  
  where:
  
  BULLET::::- formula_1 is the orbital speed of the orbiting body,
  
  BULLET::::- formula_4 is the distance of the orbiting body from the central body,
  
  BULLET::::- formula_16 is the length of the semi-major axis,
  
  BULLET::::- formula_3 is the standard gravitational parameter.
  
  Conclusions:
   The most obvious approach to the problem of predicting the motions of the heavenly bodies was simply to map their positions against the star field and then to fit mathematical functions to the changing positions.
   Streaming instabilities, first described by Andrew Youdin and Jeremy Goodman, are driven by differences in the motions of the gas and solid particles in the protoplanetary disk. The gas is hotter and denser closer to the star, creating a pressure gradient that partially offsets gravity from the star. The partial support of the pressure gradient allows the gas to orbit at roughly 50 m/s below the Keplerian velocity at its distance. The solid particles, however, are not supported by the pressure gradient and would orbit at Keplerian velocities in the absence of the gas. The difference in velocities results in a headwind that causes the solid particles to spiral toward the central star as they lose momentum to aerodynamic drag. The drag also produces a back reaction on the gas, increasing its velocity. When solid particles cluster in the gas, the reaction reduces the headwind locally, allowing the cluster to orbit faster and undergo less inward drift. The slower drifting clusters are overtaken and joined by isolated particles, increasing the local density and further reducing radial drift, fueling an exponential growth of the initial clusters. In simulations the clusters form massive filaments that can grow or dissipate, and that can collide and merge or split into multiple filaments. The separation of filaments averages 0.2 gas scale heights, roughly 0.02 AU at the distance of the asteroid belt. The densities of the filaments can exceed a thousand times the gas density, sufficient to trigger the gravitational collapse and fragmentation of the filaments into bound clusters.
   Total apsidal precession for isolated very hot Jupiters is, considering only lowest order effects, and broadly in order of importance
  
  with planetary tidal bulge being the dominant term, exceeding the effects of general relativity and the stellar quadrupole by more than an order of magnitude. The good resulting approximation of the tidal bulge is useful for understanding the interiors of such planets. For the shortest-period planets, the planetary interior induces precession of a few degrees per year. It is up to 19.9° per year for WASP-12b.
  
  Section::::Newton's theorem of revolving orbits.
   However, it is suggested that this planetary system evolved in the following manner: Planetesimals at the disk's inner edge occasionally pass through gravitational encounters with the outermost giant planet, which change the planetesimals' orbits. The planets scatter the majority of the small icy bodies that they encounter inward, exchanging angular momentum with the scattered objects so that the planets move outwards in response, preserving the angular momentum of the system. These planetesimals then similarly scatter off the next planet they encounter, successively moving the orbits of Uranus, Neptune, and Saturn outwards. Despite the minute movement each exchange of momentum can produce, cumulatively these planetesimal encounters shift (migrate) the orbits of the planets by significant amounts. This process continues until the planetesimals interact with the innermost and most massive giant planet, Jupiter, whose immense gravity sends them into highly elliptical orbits or even ejects them outright from the Solar System. This, in contrast, causes Jupiter to move slightly inward.
   Orbital decay can occur due to tidal forces for objects below the synchronous orbit for the body they're orbiting. The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it. The gravity of the bulges is slightly off of the primary-satellite axis and thus has a component along the satellite's motion. The near bulge slows the object more than the far bulge speeds it up, and as a result the orbit decays. Conversely, the gravity of the satellite on the bulges applies torque on the primary and speeds up its rotation. Artificial satellites are too small to have an appreciable tidal effect on the planets they orbit, but several moons in the Solar System are undergoing orbital decay by this mechanism. Mars' innermost moon Phobos is a prime example, and is expected to either impact Mars' surface or break up into a ring within 50 million years.
   Although recurrent, these period modulations do not follow a strictly regular cycle. Irregular recurrence rules out attempts to explain these period modulations as being due to apsidal precession or the presence of distant, unseen companions. Apsidal precession explanations also have the problem that they require an eccentric orbit, but the systems in which these modulations are observed often show orbits of little eccentricity. Furthermore, third body explanations have the issue that in many cases, a third body massive enough to produce the observed modulation should not have managed to escape optical detection, unless the third body were quite exotic.
   Extreme mass ratio inspirals created in this way tend to have very large eccentricities ("e"  0.9999). The initial, high eccentricity orbits may also be a source of gravitational waves, emitting a short burst as the compact object passes through periapsis. These gravitational wave signals are known as extreme mass ratio bursts. As the orbit shrinks due the emission of gravitational waves, it becomes more circular. When it has shrunk enough for the gravitational waves to become strong and frequent enough to be continuously detectable by LISA, the eccentricity will typically be around 0.7. Since the distribution of objects in the nucleus is expected to be approximately spherically symmetric, there is expected to be no correlation between the initial plane of the inspiral and the spin of the central supermassive black holes.
   BULLET::::- Galactocentric orbit: An orbit around the centre of a galaxy. The Sun follows this type of orbit about the galactic centre of the Milky Way.
  
  BULLET::::- Geocentric orbit: An orbit around the planet Earth, such as the Moon or artificial satellites. Currently there are approximately 1,886 artificial satellites orbiting the Earth.
  
  BULLET::::- Heliocentric orbit: An orbit around the Sun. In our Solar System, all planets, comets, and asteroids are in such orbits, as are many artificial satellites and pieces of space debris. Moons by contrast are not in a heliocentric orbit but rather orbit their parent planet.
   for an elliptical orbit with semi-major axis "a", of a small body around a spherical body with radius "r" and average density "ρ", where "T" is the orbital period. See also Kepler's Third Law.
  
  Section::::Patents.
  
  The application of certain orbits or orbital maneuvers to specific useful purposes have been the subject of patents.
  
  Section::::Tidal locking.
  
  Some bodies are tidally locked with other bodies, meaning that one side of the celestial body is permanently facing its host object. This is the case for Earth-Moon and Pluto-Charon system.
  
  Section::::See also.
   Johannes Kepler's (1571–1630) cosmology eliminated the celestial spheres, but he held that the planets were moved both by an external motive power, which he located in the Sun, and a motive soul associated with each planet. In an early manuscript discussing the motion of Mars, Kepler considered the Sun to cause the circular motion of the planet. He then attributed the inward and outward motion of the planet, which transforms its overall motion from circular to oval, to a moving soul in the planet since the motion is "not a natural motion, but more of an animate one". In various writings, Kepler often attributed a kind of intelligence to the inborn motive faculties associated with the stars.
  
presuppositions: Planets and moons should spiral inwards based on their elliptical orbit.
corrections: When planets and moons orbit, they are moving sideways fast enough to not fall inward.
raw_presuppositions: Planets and moons should spiral inwards based on their elliptical orbit. Planets and moons should spiral inwards based on their elliptical orbit.
raw_corrections: When planets and moons orbit, they are moving sideways fast enough to not fall inward. When planets and moons orbit, they are moving sideways fast enough to not fall inward.