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# Th1 - 36th International Physics Olympiad Salamanca(Espaa...

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36 th International Physics Olympiad. Salamanca (España) 2005 Th 1 Page 1 of 3 R.S.E.F. v 0 v 0 r F-1 m Th 1 AN ILL FATED SATELLITE The most frequent orbital manoeuvres performed by spacecraft consist of velocity variations along the direction of flight, namely accelerations to reach higher orbits or brakings done to initiate re-entering in the atmosphere. In this problem we will study the orbital variations when the engine thrust is applied in a radial direction. To obtain numerical values use: Earth radius m 10 37 6 6 = . R T , Earth surface gravity 2 m/s 81 9 . g = , and take the length of the sidereal day to be h 0 24 0 . T = . We consider a geosynchronous 1 communications satellite of mass m placed in an equatorial circular orbit of radius 0 r . These satellites have an “apogee engine” which provides the tangential thrusts needed to reach the final orbit. Marks are indicated at the beginning of each subquestion, in parenthesis. Question 1 1.1 (0.3) Compute the numerical value of 0 r . 1.2 (0.3+0.1) Give the analytical expression of the velocity 0 v of the satellite as a function of g , T R , and 0 r , and calculate its numerical value.

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