Display vectors: Display values:
The initial position is generated randomly and uniformly over a circle of radius bmax orthogonal to the initial velocity. The animation displays the motion in the orbital plane.
The units in the animation are MKS (meters, kilograms, and seconds). Each grid space represents two meters. The mass of the object is 1 kg. Click on a point in the animation to display the x and y coordinates. In the vector displays, the vector components are blue arrows, while the resultant vector is displayed in red.
The scale of the 1/r2 force is an arbitrary value chosen for convenience. Newton's 2nd law is integrated numerically by a Runge-Kutta algorithm. In the numerical displays, the total-energy and angular momentum values are calculated from the instantaneous position and velocity, not from the initial conditions. Therefore, checking that they remain constant is a good crosscheck of the integration accuracy. Note that some initial conditions may give strange results if they result in the object passing too close to the force center. For example, a very small impact parameter with an attractive force (negative sign) will bring the object too close and result in a large unphysical jump across the screen.
By Robert Johnson, using the Physlet Animator and dataGraph classes from Wolfgang Christian and Mario Belloni.