Hot- and Cold-Case Orbits for Robust Thermal Control

Abstract

Realizing cheaper, more flexible alternatives to traditional satellites requires robust design approaches. Robust satellite subsystems are designed to meet a broad range of mission requirements; consequently, they drastically reduce nonrecurring engineering costs and greatly diminish design, development, assembly, integration, and test schedules. Robust thermal control subsystems must be capable of handling a broad range of thermal environments, thus reducing design and development costs but can be susceptible to overdesign. Therefore, improved design methodologies are needed to maintain their advantages while minimizing excessive design. As a first step, design hotand cold-case orbits should be examined. The primary goal of the study described in this paper was to identify single hot-and cold-case design orbits that work well in the design of robust thermal control subsystems over a wide range of satellite surface properties and likely operating environments. A general approach was developed to identify worst-case orbits that employ a combination of statistical and historical data such that statistically insignificant orbits are disregarded. Using this method, individual hot-and cold-case design orbits were found at beta angle/ inclination combinations of 72 deg =52 deg and 0 deg =28 deg, respectively. The use of these design orbits works well for a wide range of different satellite surface properties. Nomenclature a = semimajor axis, km c = albedo correction term, dimensionless c = average albedo correction term, dimensionless cos = cosine solar zenith angle, dimensionless D = current day, day d = days from J2000.0, days E 00 = Earth-emitted irradiation, W=m 2 F s E = view factor from spherical satellite to spherical Earth, dimensionless f = eclipse fraction, dimensionless g = mean anomaly, deg h = low-Earth-orbit altitude, km i = inclination of orbit, deg JD = Julian Day, day K = orbital-averaged albedo flux correction factor, dimensionless L = mean longitude of the Sun, deg M = current month, month P = orbital period, min q 00 = orbital-averaged extreme external environmental heat load, W=m 2 q 00 alb = orbital-averaged albedo flux, W=m 2 q 00 OLR = orbital-averaged outgoing longwave radiation flux, W=m 2 q 00 sol = orbital-averaged direct solar flux, W=m 2 R E = Earth's radius, 6378 km r = spherical satellite radius, m S 00 = direct solar irradiation, W=m 2 t = time, day Y = current year, year = surface solar absorptivity, dimensionless = beta angle, deg = cutoff beta angle used to determine eclipse fraction, deg = reference direction in mean equinox of date system = declination of the sun, deg " = obliquity of ecliptic, deg " = surface longwave emissivity, dimensionless = solar zenith angle, deg = ecliptic longitude, deg = true anomaly, deg alb = albedo fraction, dimensionless alb = average albedo, dimensionless alb 0 deg = albedo fraction at solar zenith angle of 0 deg, dimensionless alb = solar zenith angle dependent albedo, dimensionless ' = angular orbital position measured at zero at the most-nearly su...

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