Minimum fuel control of a pitch motion of a satellite in circular orbit

Time function analysis for optimal control of satellite attitude and control jet fuel consumption in circular orbit

Importance of an Astrophysical Perspective for Textbook Relativity

The importance of a teaching a clear definition of the ``observer'' in special relativity is highlighted using a simple astrophysical example from the exciting current research area of ``Gamma-Ray Burst'' astrophysics. The example shows that a source moving relativistically toward a single observer at rest exhibits a time ``contraction'' rather than a ``dilation'' because the light travel time between the source and observer decreases with time. Astrophysical applications of special relativity complement idealized examples with real applications and very effectively exemplify the role of a finite light travel time.Comment: 5 pages TeX, European Journal of Physics, in pres

The cutaneous 'rabbit' illusion affects human primary sensory cortex somatopically

We used functional magnetic resonance imaging (fMRI) to study neural correlates of a robust somatosensory illusion that can dissociate tactile perception from physical stimulation. Repeated rapid stimulation at the wrist, then near the elbow, can create the illusion of touches at intervening locations along the arm, as if a rabbit hopped along it. We examined brain activity in humans using fMRI, with improved spatial resolution, during this version of the classic cutaneous rabbit illusion. As compared with control stimulation at the same skin sites (but in a different order that did not induce the illusion), illusory sequences activated contralateral primary somatosensory cortex, at a somatotopic location corresponding to the filled-in illusory perception on the forearm. Moreover, the amplitude of this somatosensory activation was comparable to that for veridical stimulation including the intervening position on the arm. The illusion additionally activated areas of premotor and prefrontal cortex. These results provide direct evidence that illusory somatosensory percepts can affect primary somatosensory cortex in a manner that corresponds somatotopically to the illusory percept

TeV Gamma Rays from Geminga and the Origin of the GeV Positron Excess

The Geminga pulsar has long been one of the most intriguing MeV-GeV gamma-ray point sources. We examine the implications of the recent Milagro detection of extended, multi-TeV gamma-ray emission from Geminga, finding that this reveals the existence of an ancient, powerful cosmic-ray accelerator that can plausibly account for the multi-GeV positron excess that has evaded explanation. We explore a number of testable predictions for gamma-ray and electron/positron experiments (up to ~100 TeV) that can confirm the first "direct" detection of a cosmic-ray source.Comment: 4 pages and 3 figures; Minor revisions, accepted for publication in Physical Review Letter

Physical parameters of GRB 970508 and GRB 971214 from their afterglow synchrotron emission

We have calculated synchrotron spectra of relativistic blast waves, and find predicted characteristic frequencies that are more than an order of magnitude different from previous calculations. For the case of an adiabatically expanding blast wave, which is applicable to observed gamma-ray burst (GRB) afterglows at late times, we give expressions to infer the physical properties of the afterglow from the measured spectral features. We show that enough data exist for GRB970508 to compute unambiguously the ambient density, n=0.03/cm**3, and the blast wave energy per unit solid angle, E=3E52 erg/4pi sr. We also compute the energy density in electrons and magnetic field. We find that they are 12% and 9%, respectively, of the nucleon energy density and thus confirm for the first time that both are close to but below equipartition. For GRB971214, we discuss the break found in its spectrum by Ramaprakash et al. (1998). It can be interpreted either as the peak frequency or as the cooling frequency; both interpretations have some problems, but on balance the break is more likely to be the cooling frequency. Even when we assume this, our ignorance of the self-absorption frequency and presence or absence of beaming make it impossible to constrain the physical parameters of GRB971214 very well.Comment: very strongly revised analysis of GRB971214 and discussion, submitted to ApJ, 11 pages LaTeX, 4 figures, uses emulateapj.sty (included

The Evolution of Cas A at Low Radio Frequencies

We have used archival 74 MHz VLA data spanning the last 15 years in combination with new data from the Long Wavelength Demonstrator Array (LWDA) and data from the literature covering the last 50 years to explore the evolution of Cas A at low radio frequencies. We find that the secular decrease of the flux density of Cas A at ~80 MHz is rather stable over five decades of time, decreasing at a rate of 0.7-0.8% yr^-1. This is entirely consistent with previous estimates at frequencies as low as 38 MHz, indicating that the secular decrease is roughly the same at low frequencies, at least between 38 and 80 MHz. We also find strong evidence for as many as four modes of flux density oscillation about the slower secular decrease with periods of 3.10+/-0.02$ yr, 5.1+/-0.3 yr, 9.0+/-0.2 yr, and 24+/-2 yr. These are also consistent with fluctuations seen previously to occur on scales of a few years. These results provide compelling motivation for a thorough low frequency monitoring campaign of Cas A to constrain the nature and physical origins of these fluctuations, and to be able to better predict the flux density of Cas A at any given epoch so that it may be used as a reliable low frequency calibrator.Comment: accepted for publication in A

HeII Recombination Lines From the First Luminous Objects

The hardness of the ionizing continuum from the first sources of UV radiation plays a crucial role in the reionization of the intergalactic medium (IGM). While usual stellar populations have soft spectra, mini-quasars or metal-free stars with high effective temperatures may emit hard photons, capable of doubly ionizing helium and increasing the IGM temperature. Absorption within the source and in the intervening IGM will render the ionizing continuum of high-redshift sources inaccessible to direct observation. Here we show that HeII recombination lines from the first luminous objects are potentially detectable by the Next Generation Space Telescope. Together with measurements of the hydrogen Balmer alpha emission line, this detection can be used to infer the ratio of HeII to HI ionizing photons. A measurement of this ratio would shed light on the nature and emission mechanism of the first luminous sources, with important astrophysical consequences for the reheating and reionization of the IGM.Comment: ApJ published version. Due to an error in one of the references, the strength of the 1640 A line was underestimated in a previous version; this line is now brighter by a factor of 1