Download question 2 - School of Aerospace, Mechanical and Mechatronic

THE UNIVERSITY OF SYDNEY
School of Aerospace, Mechanical and Mechatronic Engineering
AERO 2705: Space Engineering 1
Final Examination 2015
READ THESE INSTRUCTIONS CAREFULLY!
Answer at least 4 (four) of the following 6 questions.
If you answer more than 4 questions in total, your final result will be averaged over all
questions attempted. All questions are worth equal marks.
Explanation of assumptions and accuracy of results will form a major component of the
assessment of each question.
Question 1.
A chemical rocket is to be used to launch a 1000Kg satellite to a geostationary earth orbit (altitude
37,800Km). It is proposed to use currently available engines with Kerosene fuel and O2 oxidizer with
a specific impulse of approximately 260sec. The rocket will be designed to operate in 3 separate
stages, each using the same motor system. Stage 1 weights 348,000 Kg, structural efficiency 9%,
stage 2 is 88,000 Kg, structural efficiency 9% and attached to the upper stage is a stage 3 GTO
transfer/GEO synchronization motor and the payload. The rocket is launched from the Earth's surface
(Earth's radius = 6370 Km), from the Cape Canaveral Space center in Florida , USA (Latitude 28.5 o)
The structural efficiency of the third stage can be estimated to be around 10%.
a) Calculate the required final velocity of the satellite in GEO.
b) Calculate required changes in velocity during each stage of the launch and transfer to final orbit.
c) Calculate the required mass of fuel for the GTO transfer motor
Question 2.
Your university team is planning to construct and launch a single unit cubesat. It is proposed that the
launch will be done using the UCLA Ppod system along with a set of other satellites on a Falcon 9
vehicle from Vandenberg Air Base in California.
Give details of all licensing that will need to be obtained before launch.
Give details of any manufacturing requirements or testing requirements that would need to be
completed before launch.
Question 3.
A small satellite uses 2 extended solar panels total area 2 m2. Each panel is made up of a sequence of
solar cells that are 28% efficient. The cells are connected in series and parallel in order to suit the
requirements of the power conditioning unit that they are connected to. Each cell produces 5V and has
an area of approximately 0.11m2
These solar panels are used to charge a battery system through a 98% efficient power conditioning
unit. The conditioning unit has a maximum limit of 5 Amps for any of the power bus lines that are
connected to it and has a maximum of 12 regulated power connections. These can be programmed for
independent voltages in the range 5V to 50 V. The battery pack operates at 30V and has a nominal
12.5AmpereHour capacity. It has a 5000 cycle recharge life.
The main power consuming unit on the satellite power bus is a 100 Watt X-band transmitter
(connected on a 28 Volt bus line). The transmitter is designed to run continuously in order to supply
the required data to relay satellites and ground stations. The remaining power consumption of all other
satellite components can be be assumed to be on average 10 Watts
a) sketch a connection layout for the solar cells on the panels that would be compatible with the power
conditioning unit specifications.
b) what is the expected life of the power system.
c) verify that power is available for the transmitter under all conditions encountered in a low earth
orbit.
Note : solar radiation in LEO is 1366 Watts/m2
Question 4.
Assuming a vehicle and attached boost motor are currently in an equatorial low earth orbit at 700km
altitude. The vehicle, not including boost motor weighs 102,000Kg.
Estimate the fuel and structural mass required for the boost motor (ISP 320) if the satellite is to be
delivered to a solar orbit that would reach the orbit of Mars. Entry to Mars will be done by
atmospheric braking.
As human passengers are to be on board, the time for the transfer should be no longer than 8 months
Comment on the sort of transfer orbit that could be used.
Question 5.
A small scientific satellite has been positioned as shown for a sling-shot boost to its orbit. The satellite
will sling-shot around Venus. The velocity of the satellite relative to the sun is 7.07km/s radially
toward the sun and tangentially 27.93km/s. Assume that the satellite is positioned so that its closest
approach to Venus will be at 1000 km altitude.
Sketch the satellite's predicted path around Venus.
Estimate the change in magnitude of the satellite's velocity from before to after this encounter with
Venus.
Question 6.
The circuit shown in the diagram
contains a measurement element
Rx which is used to measure
temperature. The device is a
peizo-resistive material whose
resistance changes in proportion to
temperature. 10 Ohms for 15o C,
10.5 Ohms for -30o, 9.5 Ohms for
60oC.
Predict the variation in output
voltage (Vo) for the range of
temperatures -20o to +50o.
If the output voltage is to be sent
to an Analogue to Digital
converter (12 bit accuracy, input
range +-1 V, sample rate 100 Hz), specify any additional analogue components that would be required
to ensure a good sample is received by the attached computer.
What is the average current drawn from the battery by this circuit?
OTHER RELEVENT INFORMATION.
Gravitational acceleration at any distance from earth can be calculated as,
g=
GM
r2
Where G is the gravitational constant 6.672 X 10-11 Nm2/kg2,
M is the mass of the earth 5.98 X 1024 kg and
r is the radial distance from satellite to the center of the planet.
For an ideal rocket motor : Δ V =Isp . g 0 . ln (
M initial
)
M final
Velocity in an Earth orbit is,
Circular :
V=
Properties of Elliptical Orbits,
V periapsis=
√
√
GM
r
2
Elliptical : V =2 g 0 R
2
( 1r − 21a )
√
2 GM Rapoapsis
2 GM R periapsis
, V apoapsis =
R periapsis ( R apoapsis + R periapsis )
Rapoapsis ( R apoapsis + R periapsis )
Rapoapsis =
R periapsis
(
)
2GM
−1
R perispsis V 2periapsis
,
R periapsis =
Rapoapsis
(
)
2 GM
−1
R apoapsis V 2apoapsis
Average planetary data..
Distance from Mecury to Sun = 57,900,000,000m. Mass relative to Earth = 0.0553 Radius = 2440Km
Distance from Venus to Sun = 108,500,000,000m. Mass relative to Earth = 0.815 Radius = 6000 Km
Distance from Earth to Sun = 149,597,892,000m.
Distance from Mars to Sun = 249,200,000,000m. Mass relative to Earth = 0.107 Radius = 3390 Km
Distance from Jupiter to Sun = 779,000,000,000m. Mass relative to Earth = 317 Radius = 69,900 Km
Distance from Saturn to Sun = 1,433,000,000,000m. Mass relative to Earth =95 Radius = 58,200Km
Period of Earth Orbit = 31557600 sec
Earth's velocity in orbit around Sun = 29,785 m/s
Mar's velocity in orbit around Sun = 23,077 m/s
Density of Earth atmosphere is approximately
ρ=10
(−7. altitude(km)/150)
kg/m3