(a) Suppose 10 astronauts are sent to Mars and then back to Earth. The average power usage of
each astronaut is 10,000,000 joules per day. What is the average power usage of each astronaut
in watts and horsepower?
(b) It will take approximately 2 years for the astronauts to make the round trip. The average astronaut
has a mass of 70.0 kg. Assume the astronauts are on a fat-free diet. Carbohydrates and proteins
on average produce approximately 17,300,000 joules of energy per kilogram. How much mass of
food do the astronauts need to take with them? Note that we are assuming that 100% of the
food calories that are eaten are absorbed and used by the body. This is actually not true. A
person’s metabolic efficiency” is the percentage of calories eaten that are actually used; the rest
are eliminated by the body. Metabolic efficiency varies considerably from person to person. This
means that the mass of food calculated is an underestimate of what would be needed.
(c) 1 food calorie (Cal) = 1 kilocalorie (kcal) = 1,000 calories (cal) = 4,184.5 joules of food requires
approxiamtely 0.000248 kg of oxygen for the body to metabolize the food. How many kilograms
of oxygen are required for the trip?
(d) Assume it costs $10,000,000 to send 1 kg to Mars. How much will it cost to send the astronauts,
their food and oxygen to Mars?
(e) Assume 15% of the energy goes into mechanical energy, how much mechanical work will the 10
astronauts do over the 2 years?