Consider the ion rocket described in Problem. Let’s compare it to a chemical rocket whose exhaust velocity is 3 km/s. In the case of the ion rocket, 1 kg of fuel accelerates 1 kg of payload to a final velocity vf. What fuel mass is required to accelerate the same payload to the same final velocity with the chemical rocket? (In each case, ignore the mass of the rocket.)
Alpha Centauri is the nearest star system, about 4 light years from Earth. Assume that an ion rocket has been built to travel to Alpha Centauri. Suppose the exhaust velocity of the ions is one-tenth the speed of light. Let the initial mass of the fuel be twice that of the payload (ignore the mass of the rocket, itself). Also, assume that it takes about 100 hours to exhaust all the fuel of the rocket. How long does it take the rocket to reach Alpha Centauri? (The speeds are small enough that you can neglect the effects of special relativity.)
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