OSP-based Programs for Advanced Physics:
Classical Orbit Demos

 

The curricular material is organized into six units:
 

Center-of-Mass Orbits show variations on a planet orbiting a much more massive central star in Cartesian and polar coordinates. The examples show one circular and two elliptical orbits that begin at the same position, yet have different initial velocities. It is the difference in initial velocity that accounts for the difference in orbital trajectory around the central star.

Two-body Orbits show a variety of two-body orbits where the masses of the two objects are comparable (unlike above). One set of examples varies one of the object's mass, while the other varies the initial position of one of the masses.

Three-body Orbits show four three-body orbits.  The Euler example shows a special solution determined by Euler in which all three masses always lie on a straight line.  The Lagrange example shows a special solution determined by Lagrange in which the objects maintain a geometric relationship to each other as vertices of a polygon.  In this case, the three objects are always at the vertices of an isosceles triangle (whose sides can change length).  The Montgomery example shows a stable orbit of three objects that orbit each other in a figure-eight pattern with all three objects tracing out the exact same orbital trajectory.  The Restricted Three-body example shows an example of this class of exactly-solvable problems.  Two objects with the same mass are in orbit around each other.  A third, much less massive, object also orbits, following one object around its orbit.

4- and 5-body Orbits show a variety of unstable orbits with four and five masses all with similar masses with all three objects tracing out the exact same orbital trajectory. The 4-body Clover example is one of Lagrange type where the four objects are always at the vertices of a square (whose sides can change length).

Gravitational Scattering shows a variety of examples of unbounded scattering of an object in the gravitational field of a more massive object. The impact parameter varies in each simulation.

Additional Orbits shows center-of-mass orbits of a wider variety than that of the Center-of-Mass Orbits unit.
 

 

© Mario Belloni and Wolfgang Christian (2006).