EXPONENTIAL AND LOGARITHMIC FUNCTIONS

PROBLEM 11.

Using the equation derived in Problem 9, show that the launch vehicle constructed in Problem 8 can indeed orbit its payload.

Solution: Given

R1 x R2 = (3.4) (3.4) = 11.56

v = 2.7 log[base e] 11.56

= 3.7 (2.45)

= 9.06 km/s

The launch vehicle will impart sufficient velocity to overcome drag losses and insert the payload into a 160-km Earth orbit. Note that dividing the launch vehicle into stages increases the overall mass ratio to 11.56.

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