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Spacecraft landing on an alien planetby squarky
Tags: rocket 
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#1
Feb2210, 11:09 AM

P: 3

1. The problem statement, all variables and given/known data
A spacecraft of mass m_{0} is descending with velocity v_{0} to land on an alien plant where the value of g is 1/6 of g on the earth. In order to land safely (meaning the final velocity upon landing is zero), fuel has to be burnt at a constant rate dm/dt=k, where k is a constant. How far above the surface of the planet should one begin firing the spacecraft (assume constant deceleration) 2. Relevant equations m = m_{0}  kt 3. The attempt at a solution I am trying to use my knowledge of rocket motion. But i am having a hard time picturing the problem. Any comment/help will be great. 


#2
Feb2210, 11:37 AM

P: 3

starting with
v  v_{0} = v_{ex}ln(m_{0}/m) where, v= final velocity v_{0} = initial velocity v_{ex}= exhaust speed relative to spacecraft m_{0}= initial mass m = final mass because final velocity has to be zero and assuming constant exhaust speed, i simplified the above expression to get t. t = m_{0}(e^{v/vex} 1)/ke^{v0/vex} 


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