1. Star with Newton's third law: dp/dt = ΣF where p is the momentum. In space,...

1. Star with Newton's third law: dp/dt = ΣF where p is the momentum. In space, the sum of the external forces ΣF = 0. For a rocket in space, the mass and velocity change with time as the rocket expends its fuel. Show from Newton's third law that ΔV = v ln(m/M) where m is the initial mass of the rocket, M is the final mass of the rocket after the fuel is expended, v is the rocket's exhaust velocity and ΔV is the change in the velocity for the rocket

2. Now, the rocket needs to get to escape velocity to get to the moon. Use conservation of energy to derive an expression for the escape velocity. If we start at 200km above the surface of earth, calculate the ΔV we need to escape from Earth and get to the moon.

3. Finally, use the earlier Rocket Equation calculate the fraction of the initial rocket's mass that is dedicated to fuel to make the journey from the Earth to the Moon. In this case, v is 4500 m/s.

Expert Solution

genius_generous answered 3 hours ago

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