4262: Rockets and Mission Analysis
November 15, 2012
Name: _______________________
Exam #2
Question 1 (20 Points):
Consider the Boeing X-37B Orbital Test Vehicle shown in the picture below. In this picture the
vehicle is circumnavigating the Earth at a Low Earth Orbit 200 km above the Earth’s surface.
Because of a change in the mission profile, the X-37B needs to raise its orbit by 50 km (to a new
orbit of 250 km above the surface of the Earth) and the engines on the vehicle are sufficient to
accomplish this task.
The following information is provided:
 Radius of the Earth=6,378 km
 G=6.670x10-11 N m2/kg2
 Mass of the Earth = 5.975x1024 kg
 Mass of the Sun = 332,488 times the mass of the earth
 Mass of the X-37B = 10,000 kg
1. Determine the mission velocity increments that are needed from the X-37B’s engine
burns for an orbital transfer of the vehicle with the least fuel consumption.
2. How long does it take to accomplish this orbital maneuver?
3. The purpose of this top secret orbital transfer is to rendezvous with a satellite that is
already located in the higher orbit. Where must the satellite be with respect to the X-37B
at the instant the X-37B begins its orbital transfer maneuver?
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Question 2 (20 Points):
An electrostatic thruster produces 0.5 N of constant thrust over a 3 hour duration and consumes a
total of 0.5 kg of propellant while using 4 kW of power.
1. What is the specific impulse of the thruster?
2. What is the efficiency of the propulsive jet?
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Question 3 (20 Points):
A krypton ion rocket is being developed with the goal of producing a 5 N thrust with a specific
impulse of 5,000 seconds. Technological advancements have allowed for a minimum electrode
spacing of 2.0 mm and a maximum allowable gradient between the electrodes of 100 V/cm.
Assuming the acceleration region to behave as a simple space-charge-limited plane diode, what
beam area is required?
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Question 4 (20 Points):
A resistojet has a throat diameter of 0.3 mm and is to be operated with helium at a pressure of
1,000 psi. The exhaust nozzle exit diameter is 3.0 mm. The maximum allowable temperature is
1,000 K and the specific heat ratio of helium can be taken as a constant value of 5/3. Determine
the following parameters:
1. The mass flow rate.
2. The specific impulse.
3. The thrust level assuming an isentropic expansion in deep space with zero back pressure.
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Question 5 (20 Points):
A spacecraft with a solar electric powerplant has a specific mass of 15 kg/kW and will be used
on a deep space mission that will last 5 months.
1. What is the optimum specific impulse to carry out this mission?
2. Assume that the efficiency of the propulsive jet is 50%. Determine the maximum thrust
that can be developed if the solar array power delivered to the engine is 25 kW.
3. Find the total impulse delivered over the entire mission.
4. Calculate the mass of the powerplant.
5. Calculate the mass of the propellant required for this mission.
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Question 6 (20 Points):
An new ion engine has a specific impulse of 10,000 seconds and will be used to accelerate a
spacecraft through a velocity increment of V = 5,000 m/s. The thrust-to-weight ratio of the
vehicle is 10-4.
1. Calculate the operating time required.
2. Calculate the propellant mass fraction that is required.
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Extra Page
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