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ORBITAL MECHANICS (L.S. 1st year) February 7, 2011 1. From a same location on Earth, the difference between the visibility periods of the Alfa Centauri and the Altair stars is 10 h40m 18.48 s. The declinations of those stars are 60° 50' 08.8" S and 8° 52' 05.2" N respectively; the Alfa Centauri right Ascension is 14h 39m 37.24s. Evaluate: • The geographical coordinates of the observer and the date of the maximum height occurrence for Alfa Centauri; that stars reaches its maximum height at the GCT 6h 40m 48s a.m. of the 19th of May. • The Local Civil Time when the maximum height of Altair occurs; when Altair rises above the horizon, Alfa Centauri has a height of 57° 8’ 13.52”, and its still didn’t reach its maximum height. If more than an observer is identified, keep that one who presents the larger maximum height for Centauri star. • The ecliptic coordinate of Altair α~, 19/05=3h 44m E 19/05=3m 31s ST’ 19/05=15h 48m 0.78s α~, 20/05=3h 48m E 20/05=3m 28s ST’ 20/05=15h 51m 57.33s 2. The ratio between the total mass of the second and the fi rst stage, in a two stage launcher, is 0.1361; the ratio between the total mass and the dry mass of the sec ond stage is 3.62; at the first stage the needed fuel mass is 7.7032 times the fuel mass needed at the second stage. The specific impulses of the two stages are different and the ratio between them at the first and the second stage is 1.1829. The second stage total mass is 16327.24 kg, and the burn-out velocity for the launcher is 10196.8353 m/s; the ratio of the structural ratios “s”, between the first and the second stage is 0.5980. Evaluate: • The payload mass that can be placed in orbit; the cost function; the specific impulses of each stage. • The specific impulse, identical for the two stages, if an optimum design…