Roche potential

thingiverse

This describes the gravitational and centrifugal force field surrounding an accreting neutron star system. The system, called PSR J1023+0038, comprises a radio millisecond pulsar orbited by a star similar in mass to our Sun. In 2013, a change occurred, causing the companion star to dump material onto the pulsar. This model demonstrates how: the larger object represents the force field surrounding both objects. Gravity creates wells around each object, while centrifugal force pushes anything too far outwards. The five Lagrange points are the peaks and saddle points of this model. The companion is less massive than the pulsar, so it resides in the smaller well, but the wells are extremely small - this entire model would fit inside our Sun - that the companion nearly fills its well. In fact, when accretion began, the companion started overflowing its well and material began falling towards the pulsar. The smaller piece of this model represents the companion filling its well just enough for matter to reach the L1 point (between the stars) and fall into the pulsar, where it becomes so hot that it emits intense X-rays. The print settings used were as follows: printer - Kossel Mini; rafts - no; supports - no; resolution - 0.2 mm layer height; infill - 10%. This model is a very easy print; the main challenge encountered was that it tended to lift up from the bed. It is recommended to print the potential in black and the companion in orange or yellow, as these colors closely match the actual color of our Sun. The proportions used seem aesthetically pleasing. The Roche geometry is defined by a simple formula (whose derivative gives the combination of gravity and centrifugal force). The only input required is the ratio of the masses of the objects, which in this case is 7.2. Supplying other ratios would result in a differently shaped potential field. This value is fed into an ipython notebook (included), shifted and scaled vertically so that L1 is at zero and L4/L5 area at 1, and written out as a text matrix giving the values everywhere above a minimum. An OpenSCAD file is also created that defines certain key quantities. OpenSCAD can read this in and create an object; the companion is made by Boolean operations within OpenSCAD. The files are quite large due to the preference for smoothness.