Relativistic Positioning Systems: The Emission Coordinates

This paper introduces some general properties of the gravitational metric and the natural basis of vectors and covectors in 4-dimensional emission coordinates. Emission coordinates are a class of space-time coordinates defined and generated by 4 emitters (satellites) broadcasting their proper time by means of electromagnetic signals. They are a constitutive ingredient of the simplest conceivable relativistic positioning systems. Their study is aimed to develop a theory of these positioning systems, based on the framework and concepts of general relativity, as opposed to introducing `relativistic effects' in a classical framework. In particular, we characterize the causal character of the coordinate vectors, covectors and 2-planes, which are of an unusual type. We obtain the inequality conditions for the contravariant metric to be Lorentzian, and the non-trivial and unexpected identities satisfied by the angles formed by each pair of natural vectors. We also prove that the metric can be naturally split in such a way that there appear 2 parameters (scalar functions) dependent exclusively on the trajectory of the emitters, hence independent of the time broadcast, and 4 parameters, one for each emitter, scaling linearly with the time broadcast by the corresponding satellite, hence independent of the others.Comment: 13 pages, 3 figures. Only format changed for a new submission. Submitted to Class. Quantum Gra

A Case Study of the Impact of Bioenergy Development Upon Crop Production, Livestock Feeding, and Water Resource Usage in Kansas

The development of grain-based ethanol production in Kansas has had a marked impact upon the feedgrain and livestock industries of the state. The increased focus on feedgrain production stemming from ethanol development impacts the use and sustainability of Kansas water resources, and has changed the proportional mix of crops grown in the state. The need to handle increased amounts of feedgrains and to transport them to ethanol plants has affected the functional role of local grain elevators as well as the directional flow of grain within the state. The grain trucking industry has been dramatically affected by the increase in demand for moving both feedstock inputs and co-product outputs to and from ethanol plants in the state.Crop Production/Industries, Livestock Production/Industries, Resource /Energy Economics and Policy,