MAE 5595: Space Mission Analysis
Homework #2
Due: 01 Oct 2008, 1630 MDT
1. A spacecraft with a ballistic coefficient of 65 kg/m2 is being designed for a lowEarth orbit. At the proposed time of launch, the solar conditions were given by a
F10.7 = 225 sfu (solar flux units).
a. What orbital altitude is required for to meet the mission objective of a 1
year lifetime?
b. If the launch is delayed for several years and F10.7 is estimated to be
closer to 75 sfu, what would the lifetime be at the same orbital altitude you
found in part a?
c. What is the lifetime difference between the two F10.7 values discussed
above for an orbital altitude of 900 km? Explain.
2. What wavelength or wavelengths emitted from the sun are capable of dissociating
molecular nitrogen? (Hint: The dissociation energy for N2 is 9.8 eV)
3. What is the probability that a satellite will receive a proton dose in excess of 1010
protons/cm2 during a one year mission?
4. A satellite in a circular orbit at an altitude of 10,000 km and inclination of 63º has
experienced sporadic malfunctions in a computer subsystem. It is suspected that
the malfunctions are caused by energetic particles from the radiation belts
penetrating the processor. The malfunctions occur preferentially with the satellite
is at latitudes above 45º.
a. Are the malfunctions more likely to be caused by energetic electrons or
protons?
b. What are the peak electron and proton fluxes for this orbit and where do
they occur?
5. A satellite is designed to be launched into low-Earth parking orbit and
subsequently boosted into a circular polar orbit at an altitude of 1000 km. A
large, sensitive electronics package on the satellite must be shielded against the
anticipated radiation dose. An area of 1.2 x 105 cm2 is to be shielded with a
sufficient thickness of aluminum to reduce the radiation dose to less than 104
rads/year. What shielding thickness is required? What is the weight of the
shield?
6. The satellite program manager has made an announcement that the satellite (from
Problem #5) requirements have changed. To meet the changing requirements, the
satellite must have an orbital altitude of 2400 km (rather than the 1000 km
previously required).
a. How much shielding thickness would be required to keep the radiation
dose to less than 104 rads/year in the new orbit?
b. What is the weight of the required shield?
c. At $28,300 per kilogram to orbit for the launch vehicle (Pegasus),
calculate the addition cost or cost savings of this change.