The orbit is designed to be a terminator orbit, so that the local time at the nadir point is always either approximately sunset or sunrise. Figure shows the variation in path length as a function of elevation when the spacecraft is above the local horizon. The path loss due to range is defined by the equation This can be derived through the following:

The orbit is designed to be a terminator orbit, so that the local time at the nadir point is always either approximately sunset or sunrise. Figure shows the variation in path length as a function of elevation when the spacecraft is above the local horizon. The path loss due to range is defined by the equation This can be derived through the following: The power density in watts per square meter of an isotropic radiator is given by where r is the radius in meters of the sphere surrounding the isotropic radiator and pt is the transmitter power.

All power emitted by that isotropic radiator will be distributed equally on the surface of the sphere. A receiving antenna located on the surface of that sphere intercepts total power equal to the power density multiplied by the surface area of the receiving antenna as follows: It can also be shown that a transmitting antenna of effective area At which concentrates its gain within a small solid angle has an on-axis gain of where l is the wavelength of the radiation.

The receiving antenna has a gain too. Multiplying we get and this reduces to The distance and frequency-dependent term in the previous equation is the free-space path loss.

Inverting it and taking the log generates the path loss equation on the previous page. The Doppler frequency shift due to the spacecraft - CGS relative motion is derived first by determining the included angle between the spacecraft velocity vector and the spacecraft - CGS orientation vector.

With this angle information, it is a simple thing to calculate the portion of that velocity vector that is parallel to the spacecraft - CGS vector and thus calculate the Doppler shift.

Due to geometry, these beams intersect the earth at approximate angles of Neglecting atmospheric losses, there is less than a 0. The primary classification of the regions of the atmosphere is according to the temperature gradient. Radio waves that travel from space to earth encounter four distinct regions.

The first region is outer space itself; the next lower is the ionosphere, next lower is the stratosphere, and finally, where we all live and where all weather exists, the troposphere. Each layer has characteristics that affect the propagation of radio waves. For our purposes, outer space provides lossless radio wave transmission.

The ionosphere exists from to km above the ground. Here the pressure is low enough that the ultraviolet radiation that impinges on the earth from the sun causes a thin plasma to form as it separates electrons from atoms and molecules.

These free electrons can affect a radio wave through effects such as Faraday rotation, reflection and absorption. The stratosphere resides between about 15 km and 60 km.

The atmosphere contained in this region is low density and very dry. However, the pressure is high enough that there is a very low content of charged particles. Due to these factors, radio wave propagation through the stratosphere is essentially lossless. In this system the lowest part of the atmosphere extended from the surface up to about 15 km is called the troposphere, and it is bounded by the tropopause.

This angle is neither grazing nor high-angle, but the radar signal must still pass through a substantial distance of atmosphere, not apparent from the vanishingly thin line that represents the top of the troposphere shown in Figure 3.

In Figurethe light blue region represents a 15 km atmospheric thickness approximately the top of the troposphere, or the tropopausewhile the dark blue zone underneath it represents the 4 km scale atmosphere used for modeling the effects due to oxygen.

Figure Path through the Atmosphere Other factors include pointing error due to refraction of the radar beam as it passes from space into the atmosphere. At the relatively high elevation angles that are used for this station, the difference in apparent observed angle and geometric angle is very small and so this effect can be ignored [2].

Path Loss Variation due to Atmospheric Water, Oxygen and Other Airborne Substances The atmosphere contains substances that can impact the transmission of radio signals passing through it. These materials include molecular oxygen, water, dust and other aerosols.

At 14GHz, the primary impact on the radar transmitter signal is due to molecular oxygen and water as vapor and liquid. Oxygen and Water Vapor There is a local maximum in the atmospheric attenuation due to water vapor at approximately 22 GHz.

For an earth-space link, total clear sky loss for a vertical path through the atmosphere is approximately 0. In general, the paths along which the CGS will view the spacecraft are slant paths. A correction factor approximately equal to the cosecant of the viewing angle above the horizon should be applied.

Rain and Snow Water as a liquid has dielectric and conductive properties that cause it to interact with electromagnetic radiation.

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Sample homework submission with title page and logo. APA or MLA manuscript preparation guidelines for Master’s theses and Doctoral dissertations. and page numbers in the body of the thesis. + The number of chapters and their titles may vary. The examples given here are common, but Thesis Formatting Guidelines.

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