Tobar 19051 Rainbow Orbit Ball, Mixed

Product Information

Main article: Newton's cannonball Newton's cannonball, an illustration of how objects can "fall" in a curve

The velocity relationship of two moving objects with mass can thus be considered in four practical classes, with subtypes: An animation showing a low eccentricity orbit (near-circle, in red), and a high eccentricity orbit (ellipse, in purple) At a specific horizontal firing speed called escape velocity, dependent on the mass of the planet and the distance of the object from the barycenter, an open orbit (E) is achieved that has a parabolic path. At even greater speeds the object will follow a range of hyperbolic trajectories. In a practical sense, both of these trajectory types mean the object is "breaking free" of the planet's gravity, and "going off into space" never to return.An open orbit will have a parabolic shape if it has the velocity of exactly the escape velocity at that point in its trajectory, and it will have the shape of a hyperbola when its velocity is greater than the escape velocity. When bodies with escape velocity or greater approach each other, they will briefly curve around each other at the time of their closest approach, and then separate, forever. From Newton's Second Law, the summation of the forces acting on m 2 related to that body's acceleration: As two objects orbit each other, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest. (More specific terms are used for specific bodies. For example, perigee and apogee are the lowest and highest parts of an orbit around Earth, while perihelion and aphelion are the closest and farthest points of an orbit around the Sun.) One form takes the pure elliptic motion as a basis and adds perturbation terms to account for the gravitational influence of multiple bodies. This is convenient for calculating the positions of astronomical bodies. The equations of motion of the moons, planets, and other bodies are known with great accuracy, and are used to generate tables for celestial navigation. Still, there are secular phenomena that have to be dealt with by post-Newtonian methods. The differential equation form is used for scientific or mission-planning purposes. According to Newton's laws, the sum of all the forces acting on a body will equal the mass of the body times its acceleration ( F = ma). Therefore accelerations can be expressed in terms of positions. The perturbation terms are much easier to describe in this form. Predicting subsequent positions and velocities from initial values of position and velocity corresponds to solving an initial value problem. Numerical methods calculate the positions and velocities of the objects a short time in the future, then repeat the calculation ad nauseam. However, tiny arithmetic errors from the limited accuracy of a computer's math are cumulative, which limits the accuracy of this approach. In the case of planets orbiting a star, the mass of the star and all its satellites are calculated to be at a single point called the barycenter. The paths of all the star's satellites are elliptical orbits about that barycenter. Each satellite in that system will have its own elliptical orbit with the barycenter at one focal point of that ellipse. At any point along its orbit, any satellite will have a certain value of kinetic and potential energy with respect to the barycenter, and the sum of those two energies is a constant value at every point along its orbit. As a result, as a planet approaches periapsis, the planet will increase in speed as its potential energy decreases; as a planet approaches apoapsis, its velocity will decrease as its potential energy increases.

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.For a given orbit, the ratio of the cube of its semi-major axis to the square of its period is constant. Within a planetary system, planets, dwarf planets, asteroids and other minor planets, comets, and space debris orbit the system's barycenter in 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 that 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.