J 2

Six identical objects are released 'om the International Space Station over a period of 24 hours. These objects do not carry any fuel onboard. They are passive objects that gradually lose altitude. Eventually, they will deorbit and burn up as they reenter the Earth's atmosphere. A ground-based tracking network monitors the altitude of these objects over a period of 10 months. The altitude observations are recorded in Table l, where the index, i, corresponds to the time since the object was released, for each object. The unit of the time interval is 28 days. i Altitude (km) Db'lect-l Obiect-z Obiect-B Union-4 Obiect-S Obiect-G 0 410 403 405 408 409 410 1 408 40? 408 408 406 410 2 406 405 406 405 406 409 3 401 400 403 402 404 407 4 396 380 400 401 403 407 5 3?5 368 399 399 401 406 6 36? 360 395 39? 400 405 7 355 348 390 396 399 404 8 340 335 380 392 396 403 9 285 275 378 390 396 403 10 170 160 365 381 386 402 Table 1 Time series of altitude observations of 6 objects released oor the International Space Station. A) Use the data provided to compute the ensemble average time series, where the ensemble should include all six objects. For each point in the ensemble average time series, compute the upper and lower values of the 95% condence interval. State your assumptions. Discuss your interpretation of the result and the limitations of the underlying model(s). [12 marks] B) Is it reasonable to model the orbital decay of objects released from the International Space Station as a stationary random process? Use the data provided andfor your results from Part A, along with any other statistics or gures you deem appropriate to justify your answer. [8 marks]