Why Shape the rth Circling the Sun's orbit elliptical?

Why Shape the rth Circling the Sun's orbit elliptical? | New
Question:Why form trajectory / orbit of the rth around the sun is elliptical ?

Answer:You have to distinguish between the gravitational vector field object trajectories in a gravitational field. In junior high schools were taught about uniformly accelerated motion and parabolic motion caused by the gravitational acceleration at the rth's surface that are considered large and constant direction (down / negative y). In the free fall motion, object trajectories are straight lines, but the pace changed uniformly with constant acceleration, in this case the same as the acceleration of gravity. While the parabolic motion, such as cannonball trajectory, a constant horizontal velocity component, while the vertical velocity component is always reduced by negative g. This does not mn that the parabolic gravitational field, because as mentioned rlier, g is assumed constant downward direction / negative y-axis.In the above subjects are usually taken several assumptions as follows:1. Surface soil / ground is considered straight and flat, loed on the x axis in the Cartesian coordinate.2. Positive y-axis is the upward direction, negative y-axis down, ignored the z axis.3. Magnitude and direction of the acceleration of gravity is constant at all points in the coordinate, with the downward direction.4. Force of air friction is negligible.The consequences of the above assumptions, the object will parabolic trajectory. At the turning point, object velocity component in the direction of the y-axis is equal to 0.In the case of planetary orbits, some of the above assumptions are not valid, especially the third assumption. Based on Newton's law of universal gravitation, the force of gravity acting on the two point masses is proportional to the mass of ch object and inversely proportional to the square of the distance. Direction of gravitational force acting on the object are both hded to the central point of the total system mass. In the case of the solar system, the mass of the Sun dominates the total mass of the solar system, so that the direction of the force of gravity acting on the planets tend towards the center of mass of the Sun. Can be concluded that the Sun's gravity field spherical / spherical the direction toward the center of mass of the solar system, the field strength is inversely proportional to the square of the distance from the center of mass of the solar system.If the trajectory of the planet's orbit is placed on the xy plane in Cartesian coordinates, the direction and magnitude of the acceleration experienced by the planet's gravity varies depending on its position relative to the Sun. With calculus can be shown that the gravitational field as it will produce a conic trajectory, which is usually elliptical or hyperbolic. http://en.wikipedia.org/wiki/Conic_section parabola and circle track is a special case.If you like computer animation program, you can crte a simulated planetary orbits with gravitational acceleration corresponding Newton equation. Just enter the initial position and velocity, you will get a diagram of its orbit trajectory. In practice, the analysis of object movement under the influence of gravity is very difficult to do if the of objects more than two at once. Therefore the solution is usually to use the brute force method, which calculates the gravitational pull is done by ch object to other objects, and then calculate the change of pace and change of position in ch timeframe, similar to that done by the animation program.