Orbits
Below are diagrams of the planets, asteroids, and comets showing the inner solar system (out to the orbit of Jupiter), the outer solar system (just beyond Pluto), and the distant solar system. There are two diagrams for each region: one showing the view looking down (or obliquely) onto the ecliptic plane and one showing the view from the edge of the ecliptic plane. All diagrams represent the positions of the bodies on 2018 January 1. These diagrams were created by Paul W. Chodas (NASA/JPL).
Alternate views of the solar system are available (currently without asteroids and comets) at JPL's Solar System Simulator site. Plots of the solar system can be created for any specified time. Here are examples of the inner and outer solar system on 2018 January 1. (Note that these alternate views are oriented with the vernal equinox to the top instead of the right and therefore appear rotated 90 degrees counterclockwise compared to our plots.)
In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a nonrepeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the central mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inversesquare law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to the curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.
The basis for the modern understanding of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. First, he found that the orbits of the planets in our Solar System are elliptical, not circular (or epicyclic), as had previously been believed, and that the Sun is not located at the centre of the orbits, but rather at one focus. Second, he found that the orbital speed of each planet is not constant, as had previously been thought, but rather that the speed depends on the planet's distance from the Sun. Third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter, 5.23/11.862, is practically equal to that for Venus, 0.7233/0.6152, in accord with the relationship. Idealised orbits meeting these rules are known as Kepler orbits.
Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation and that, in general, the orbits of bodies subject to gravity were conic sections (this assumes that the force of gravity propagates instantaneously). Newton showed that, for a pair of bodies, the orbits' sizes are in inverse proportion to their masses, and that those bodies orbit their common centre of mass. Where one body is much more massive than the other (as is the case of an artificial satellite orbiting a planet), it is a convenient approximation to take the centre of mass as coinciding with the centre of the more massive body.
Advances in Newtonian mechanics were then used to explore variations from the simple assumptions behind Kepler orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies. Lagrange (1736–1813) developed a new approach to Newtonian mechanics emphasizing energy more than force, and made progress on the threebody problem, discovering the Lagrangian points. In a dramatic vindication of classical mechanics, in 1846 Urbain Le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus.
Albert Einstein (18791955) in his 1916 paper The Foundation of the General Theory of Relativity explained that gravity was due to the curvature of spacetime and removed Newton's assumption that changes propagate instantaneously. This led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits. In relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions (except where there are very strong gravity fields and very high speeds) but the differences are measurable. Essentially all the experimental evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy. The original vindication of general relativity is that it was able to account for the remaining unexplained amount in the precession of Mercury's perihelion first noted by Le Verrier. However, Newton's solution is still used for most short term purposes since it is significantly easier to use and sufficiently accurate.
Within a planetary system, planets, dwarf planets, asteroids and other minor planets, comets, and space debris orbit the system's barycenter elliptical orbits. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about a barycenter near or within that planet.
There are a few common ways of understanding orbits:

A force, such as gravity, pulls an object into a curved path as it attempts to fly off in a straight line.

As the object is pulled toward the massive body, it falls toward that body. However, if it has enough tangential velocity it will not fall into the body but will instead continue to follow the curved trajectory caused by that body indefinitely. The object is then said to be orbiting the body.
As an illustration of an orbit around a planet, Newton's cannonball model may prove useful (see image below). This is a 'thought experiment', in which a cannon on top of a tall mountain is able to fire a cannonball horizontally at any chosen muzzle speed. The effects of air friction on the cannonball are ignored (or perhaps the mountain is high enough that the cannon is above the Earth's atmosphere, which is the same thing).