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Newtonian Gravity

The Galactic Disk Orbit Simulator

The stars in the galactic plane have velocities that increase with distance from the center until a characteristic radius is reached, after which the velocity becomes nearly independent of radius. The simulator on this page simulates the motion of stars in the galactic plane for a model gravitational field that roughly reproduces the motion observed in spiral galaxies.

The simulator's model gravitational field, which is simpler than that found in nature, preserves the essential orbital behavior observed in the disks of spiral galaxies. In the simulation, the region inside of 3 kpc is modeled as a uniform density region of an isotropic mass distribution; this region is shaded gray on the simulator. Outside of 3 kpc, the gravitational field is set to give an orbital velocity that is independent of distance from the galactic center for orbits that are circular.

This simulator illustrates several features of orbits in the galactic plane of a spiral galaxy. Orbits that are fully inside the 3 kpc boundary are closed ovals with identical orbital periods; the points of minimum and maximum distance from the from the galactic center are separated in angle by 90°. Orbits that cross the 3 kpc boundary are open, with the maximum distance from the center separated from the minimum distance by an angle between 90° and 180°;. All orbits that are fully outside of the 3 kpc boundary have approximately the same angle—approximately 250°—between the maximum and minimum distances from the galactic center, with this angle slightly smaller for the more eccentric orbits; if a subset of these orbits have the same average value of maximum and minimum distance from the galactic center, then they have approximately the same orbital period, with the more eccentric orbits having slightly longer periods.

Use of the Simulator

The simulator is a Java applet; to run this applet, the browser must be Java enabled. The control of this and all other applets on this web site is described in the Applet Control Guide. Once the applet has the keyboard focus, which it is given when the reader clicks anywhere on the applet with the mouse, it accepts commands from the keyboard. The Start and Stop buttons start and stop the simulator without resetting the starting point. Only one of these buttons is active, and it can be selected with the Return or Enter key. The Reset button places the stars back to their starting points for the current variables in the parameter table. The four radio buttons define specific parameters for the stars in the simulation.

The parameters of the individual stars used in the simulator can be modified by the reader by first stopping the simulator and then double-clicking on the table cell that needs modification. The values in the table are the minimum (rmin) and maximum (rmax) distances from the galactic center and the position in angle of rmin. The position angle is measured counterclockwise from directly below the galactic center.

If you encounter problems with the simulator, I would be grateful if you would inform me of the problem. Please send bug reports and suggestions to the editor of the website.

The Mathematics of the Simulation

In the simulator, at a distance from the galactic center of r < 3 kpc, the magnitude of the gravitational force is proportional to r. This is the force produced by a uniform mass distribution surrounded by an isotropic mass distribution. Outside of 3 kpc, the force is set proportional to the inverse of r, which gives a velocity for circular orbits that is independent of r.

Set Min/Max

The radio button marked Set Min/Max gives the stars the same value of rmin/rmax. The two orbits inside of the 3 kpc boundary exhibit the closed oval shape and fixed period of the orbit. The stars that fall either fully or in part outside of the 3 kpc boundary move on open paths.

Set Max

This set of initial conditions give all stars the same maximum distance from the galactic center, but different minimum distances. This simulation clearly shows that orbits fully outside of the 3kpc boundary have maxima and minima distances from the galactic center that fall at approximately the same angles.

Average

The stars in this simulation have the same average value of the maximum and minimum distance from the galactic center. All orbits are outside of the 3 kpc boundary. This simulation shows that these orbits have nearly the same period and nearly the same angle between the points of maximum and minimum distance from the galactic center. the slightly longer period and the slightly shorter angle between rmin and rmax of the more eccentric orbits is apparent in this simulation.

Circles

The stars are in circular orbits. The orbits inside and on the 3kpc boundary have the same orbital period, while the two orbits at larger distances from the galactic center have periods that are proportional to the distance.

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