On the choice of orbits for an altimetric satellite to study ocean circulation and tides

The choice of an orbit for satellite altimetric studies of the ocean's circulation and tides requires an understanding of the orbital characteristics that influence the accuracy of the satellite's measurements of sea level and the temporal and spatial distribution of the measurements. Three orbital parameters determine the temporal and spatial sampling characteristics of the satellite: the orbital altitude, the inclination of the orbit, and the repetition period. The eccentricity of the chosen orbit should be less than 0.001 to minimize altimeter errors caused by uncertainty in determining the time of each altimeter measurement and to maintain the rate of height variation over the oceans within the limits of the altimeter tracker. The choice of the satellite's orbital altitude is constrained by the influences of atmospheric drag and errors in models of the gravity field, which decrease with height, and the required complexity of the altimeter (e.g., the power and/or antenna size required) and the effect on satellite systems of radiation from Earth's radiation belts, which increase with height. The choice of inclination is constrained by a desire to measure sea level over all the ocean, by the requirement that the acute angle between intersections of the subsatellite track be as large as possible, and by the time phasing of the repeat of the satellite's ground track as a function of inclination, which determines the aliased frequencies of the measurements of the oceanic tides. The choice of repetition period is constrained by tradeoffs between temporal and spatial coverage and by the aliasing of tidal constituents. Combining the above constraints leads to a set of orbits in a narrow range of altitude and inclination, called here the “Topex/Poseidon window.” This window extends from 1100 to 1500 km altitude and 62° to 66° inclination for a 10-day repeat period and consists of three subwindows following lines of equal orbit plane precession. There are four choices of orbits within these subwindows that overfly the planned calibration sites at Bermuda and Dakar. These are at 64.80° and 1335 km, 62.01° and 1252 km, 65.84° and 1255 km, and 62.69° and 1173 km. These choices have a minimum separation between the aliased frequencies of the eight largest diurnal and semidiurnal tides of one cycle per 4.71 years, one cycle per 4.86 years, one cycle per 4.87 years, and one cycle per 4.27 years, respectively. Thus there will be less than one cycle separation over the nominal (3 years) mission. Of these four choices, the first at 64.8° and 1335 km is preferable, because it is less sensitive to error in estimating the upcoming solar cycle (which will be a maximum during the mission), and because it is more nearly centered in terms of inclination than the other choices. For other calibration sites, other choices would have to be made. Additional work, beyond the scope of this paper, will also be necessary to determine if the Topex/Poseidon mission requires a frozen orbit (i.e., an orbit for which there are no long-term variations in the eccentricity and argument of perigee of the orbit). If a frozen orbit is required, then the first and third choices listed above have frozen orbits with an eccentricity that is acceptable for Topex/Poseidon.