# Spacecraft landing on an alien planet

1. Feb 22, 2010

### squarky

1. The problem statement, all variables and given/known data

A spacecraft of mass m0 is descending with velocity v0 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 = m0 - 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. Feb 22, 2010

### squarky

starting with
v - v0 = vexln(m0/m)

where,
v= final velocity
v0 = initial velocity
vex= exhaust speed relative to spacecraft
m0= 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 = m0(e-v/vex -1)/ke-v0/vex