May 25, 2022

In physics, an orbit is the curved path followed by an object around a body in space due to the gravitation exerted by it, for example the orbit of a planet around the center of a star system, such as the solar system. The orbits of the planets are normally elliptical. The current understanding of the mechanics of orbital motion is based on Albert Einstein's theory of general relativity, which explains how gravity is due to the curvature of space-time, with orbits following geodesics. For ease of calculation, relativity is usually approximated with the law of universal gravitation, based on Kepler's laws relating to the motion of the planets.


Historically, the apparent motions of the planets were first explained geometrically (without reference to gravity) in terms of epicycles, i.e. the summation of numerous circular motions. This theory predicted the path of planets fairly accurately, until John Kepler proved that the motion of the planets was actually elliptical. In the geocentric model of the solar system, celestial spheres were used to explain the apparent motion of planets in the sky in terms of perfect spheres or rings. After the motion of the planets was measured more accurately, theoretical mechanisms such as deferents and epicycles had to be added. Even though the model was able to accurately predict the position of planets in the sky, over time it needed more and more epicycles, which made it more and more cumbersome. The basis for the modern understanding of orbits was first formulated by Kepler, whose results are summarized in the three laws of planetary motion. First, he discovered that the orbits of the planets in our solar system are elliptical, not circular (or epicycloidal) as previously believed, and that the Sun is not in the center of the orbits, but in one of the two foci. Second, he found that the orbital speed of each planet is not constant, but depends on its distance from the Sun. Third, Kepler found a common relationship between the orbital properties of all planets orbiting the Sun. For planets , the cubes of their distances from the Sun are proportional to the squares of their orbital periods. Jupiter and Venus, for example, are approximately 5.2 and 0.723 ua away from the Sun respectively, their orbital periods are approximately 11.86 and 0.615 years. The proportionality is given by the fact that the ratio of Jupiter, 5.2³ / 11.86², is practically equal to that of Venus, 0.723³ / 0.615², in accordance with the relationship. Isaac Newton showed that Kepler's laws are derivable from his theory of universal gravitation and that, in general, the orbits of bodies subject to the force of gravity, assuming an instantaneous propagation of the latter, are conic sections. Newton also showed that for a pair of bodies the size of the orbits are inversely proportional to their masses, and that the bodies revolve around their common center of mass. When one body is much more massive than the other, it is convenient to approximate by considering the center of mass coinciding with the center of the more massive body. Albert Einstein was able to demonstrate that gravity is due to the curvature of space-time, making the hypothesis of an instantaneously propagating gravity no longer necessary. In the theory of relativity, orbits follow geodetic trajectories that come very close to Newton's calculations. However, there are differences that can be used to determine which theory describes reality most accurately. Basically all the experimental tests that allow to distinguish between the theories agree with the theory of relativity, but the differences with Newtonian mechanics are usually very small (except for gravitational fields m