Binary Orbital Motion of Electrically Charged Spheres in Weightlessness

Abstract
Coulomb’s Law of Electrostatics suggests that two oppositely charged spheres should be able to orbit each other solely by means of the electrostatic force between them.  Although Coulomb’s Law is over 200 years old, a purely electrostatic orbit between two free spheres has never been demonstrated.  The goal of this project was to produce an electrostatic orbit between two 3 cm diameter, 1.6 gram graphite coated Styrofoam spheres charged to +/- 20 kV.  Because the electrostatic force between the spheres is much less than the weight of the spheres, the experiment was performed aboard a specialized NASA C-9B aircraft that simulates weightlessness by flying in a parabolic trajectory.  Flight time aboard the aircraft was awarded through NASA’s Reduced Gravity Student Flight Opportunities Program.  Funding for the project was supported in part by a Sigma Pi Sigma Undergraduate Research Award.  A team of six undergraduate physics majors from Rhodes College in Memphis, TN traveled to NASA facilities in Houston, TX to perform the experiment in July 2008.  We successfully achieved multiple electrostatic orbits.  This is the first experimental demonstration of an electrostatic orbit between two free spheres.  The student team was responsible for all aspects of the experiment including the initial proposal to NASA, design and fabrication of the experimental apparatus, development of the experimental procedure, ground based testing of the apparatus and procedure, interim and final reports to NASA, data collection aboard the aircraft, analysis of the data, and educational outreach associated with the project.  Our outreach activities involved interactions with over 400 students in local area K-12 schools. Analysis of the orbits has revealed that the electrostatic force can deviate significantly from the inverse square prediction of Coulomb’s Law.  This indicates that the spheres electrically polarize each other causing the charge distribution on each sphere to be non-uniform.  In addition, our experimental results support recent theoretical predictions for conditions necessary to achieve a stable electrostatic orbit when polarization effects are considered.

Abstract
An excess microwave emission from the region around the Galactic Center has been observed by the Wilkinson Microwave Anisotropy Probe (WMAP). It has been argued that this anomalous signal, known as the WMAP Haze, may be the synchrotron emission from relativistic electrons and positrons produced in dark matter annihilations. In particular, the angular distribution, spectrum, and intensity of the observed emission are consistent with the signal expected to result from a Weakly Interacting Massive Particle (WIMP) with an electroweak-scale mass and an annihilation cross section near the value predicted for a thermal relic. In this work we revisit this signal within the context of supersymmetry, and evaluate the parameter space of the Constrained Minimal Supersymmetric Standard Model (CMSSM). We find that, over much of the supersymmetric parameter space, the lightest neutralino is predicted to possess the properties required to generate the WMAP Haze. We pay particular attention to the features of the parameter space which provide the correct dark matter abundance: the focus point, the A-funnel, the bulk, and the stau-coannihilation region. The focus point, A-funnel, and bulk regions typically predict a neutralino with a mass, annihilation cross section, and dominant annihilation modes which are within the range required to produce the observed features of the WMAP Haze. The stau-coannihilation region, in contrast, is disfavored as an explanation for the origin of this signal. If the WMAP Haze is in fact generated by annihilating neutralinos, then the prospects for direct and indirect dark matter detection experiments are quite promising.