Fossil Fuel Carbon Footprints and Global Warming

  Fossil fuels are responsible for an increase in carbon dioxide in the atmosphere. Since CO₂ is a greenhouse gas its presence contributes to global warming. CO₂ is also a component of vocanic gases so we can't just blame fossil fuels for our problems. To help reduce our carbon footprint we can rank fossil fuels by how much CO₂ they release for each Joule of energy they produce. The results for carbon (coal), octane and ethanol (oil) and methane (natural gas) are shown in the table below (source).

  If we had to choose from among the fossil fuels natural gas is the best choice since it releases half the amount of carbon dioxide for each Joule of energy produced. Due to the laws of thermodynamics not all of this energy is available for use since some of it has to be wasted in our heat engines.

  If we treated the choice of fossil fuel as an economic problem with the CO₂ being a "cost" to the environment then to optimize the amount of energy produced while minimizing the release of CO₂ the "economic" choice is natural gas. Biofuels also release CO₂ into the atmosphere but we can't treat them the same way that we treat fossil fuels since they remove CO₂ from the atmosphere when they are produced.

  The alternative to the use of fossil fuels is energy from nuclear, solar, wind and wave sources. The last three require large areas for production since the energy density is low. Using them the cities would have to impose on the rural areas to get energy like they have done to get water in the past. Does eminent domain apply when city and state boundaries need to be crossed? National regulations are clearly needed here since nuclear energy has problems with its risks and waste.

  What else can we do to reduce the nation's carbon footprint? Global warming is a problem for the entire world. We can't reduce our nation's carbon footprint by moving the "costs" of production outside the country. Transferring jobs overseas can increase the nation's global carbon footprint while reducing the footprint within our borders if we rely on countries like China whose energy comes from coal power plants. So to reduce the nation's footprint we have to look at ways of reducing our global footprint which might involve changes in our trade policy. To regain control over our carbon footprint we may need to look at doing more for ourselves at home.

The Debate in Washington, DC over Carbon Emissions

  Yesterday President Obama gave an address at Georgetown University on Climate Change. Today the Speaker of the House, John Boehner, gave a Republican response to his proposals. We need to seek middle ground on climate change.

More on the Transmission Range SNR Limit

  There is a point that could be cleared up a little in the derivation of the Friis transmission formula. The power received is P_r=IΔΩ_r, where ΔΩ_r=A_r/r² is the solid angle formed by a receiving antenna with effective aperture A_r. P_t/4π is the intensity for an isotropic radiator which radiates uniformly in all directions. The derivation with the additional step is,

  The Nyquist noise is due to the random motion of the electrons in the resistor. It is similar to Brownian motion. The formula is only true if the frequency is not too large. See Kittel, Elementary Statistical Physics for more information on this.

Friis Transmission Formula and S/N Ratio Limit on Communication Range

  The signal power that can be transmitted between two points in space is dependent on the flux tube connecting two antennas. The transmitting antenna creates a beam of radiation for which the radiation intensity, I, or power per unit solid angle is a constant. The receiving antenna intercepts part of this beam and collects a fraction of the power in it. The received power and the transmitted power are related by the Friis transmission formula. A derivation of the relation between antenna aperture and gain can be found in Papas, Theory of Electromagnetic Wave Propagation (1965). The Friis transmission formula is derived as follows.

  If there is little or no noise in the transmitted signal then we only have to consider the receiver noise which is just Nyquist noise. Dividing the received signal power from the Friis transmission formula by this noise we get the S/N ratio.

  One sees that the inverse square degrades the signal to the point where the received signal is less that the noise level and this imposes a limit on the range of communications. There are a few tricks that one can use to boost the signal like summing over a period of time to let some of the random noise cancel itself out. If one sums over a number of cycles then this effectively increases the wavelength of the signal but lowers the channel capacity. A competing signal in the receiver's angular aperture will be mixed with the transmitted signal and also degrades the signal. This would be the case if the signal had to compete with the thermal noise from a star and would limit one's ability to detect a civilization on an alien planet since it would likely be near a star. To increase the range and speed of a channel one might consider a relay network connecting two points in space.

Changes in the ESTCube-1 Orbital Elements to Date

  ESTCube-1 has has been in orbit for a little over three weeks now. It has already downloaded a few images using the onboard camera. The orbit has decayed slightly since the cubesat was placed in orbit as can be seen from the plots of the orbital elements obtained from the Space-Track TLEs. The horizontal axis is the day of the year. The inclination and ascending node specify the plane of the satellites orbit. The eccentricity, e, and the argument of perigee give the shape and orientation of the orbit. And the period, T, and the semimajor axis, a, which are related specify the size of the orbital ellipse. There is still a trace amount of atmosphere left at the satellite's altitude which causes it to slowy decay. Torques caused by gravitation due to the shape of the Earth, the Moon and the Sun cause the satellite to slowly precess changing the ascending node, alters the eccentricity and shifts the argument of perigee.