A recovery vehicle from a mission to Mars is designed to have its retrorockets fi re as it lands on Earth at an altitude of 1000 m based on measurements of a barometric altimeter. Assume the scale height is 8.5 km. (a) If the ambient surface pressure changes by 500 Pa from the standard atmospheric pressure of 101325 Pa, determine the altitude error that would be made. (b) If the surface temperature _T changed by 5C from the nominal value of 290 K, determine the error in altitude that would be made. (c) Determine the total error in the estimate of altitude if the errors

A recovery vehicle from a mission to Mars is designed to have its retrorockets fi re as it lands on Earth at an altitude of 1000 m based on measurements of a barometric altimeter. Assume the scale height is 8.5 km. (a) If the ambient surface pressure changes by 500 Pa from the standard atmospheric pressure of 101325 Pa, determine the altitude error that would be made. (b) If the surface temperature _T changed by 5C from the nominal value of 290 K, determine the error in altitude that would be made. (c) Determine the total error in the estimate of altitude if the errors are uncorrelated. For parts (a) and (b), you will need to differentiate the expression for pressure as a function of altitude, assuming no errors in the measurement of _p. For part (c), recall that if the errors are uncorrelated, the total error is given by their root sum square.

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