# Examination Space Missions and Applications I (AE2103) Faculty of Aerospace Engineering Delft University of Technology SAMPLE EXAM

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1 Examination Space Missions and Applications I AE2103 Faculty of Aerospace Engineering Delft University of Technology SAMPLE EXAM Please read these instructions first: This are a series of multiple-choice questions that are similar to what you might expect for the actual exams. Note that the number of questions here is not necessarily representative of the number of questions on the actual exam there will likely be more questions given on the actual exam. You will record your answers on an answer that will be provided to you along with the exam questions. The exam is closed-book, meaning you are not allowed to have any books, hand-outs, or notes on your table during the exam. You should bring a pocket calculator with you to the exam; however, for programmable calculators, you must clear the memory beforehand and show this to the exam proctor if asked. Question 1: True/False, 2 pts. A geostationary orbit can be geosynchronous, but not all geosynchronous orbits are geostationary. Question 2: True/False, 2 pts. A repeat orbit is often defined in terms of the number of orbits within the repeat time frame. Is it possible to have a low Earth orbit LEO repeat track of 200/8, i.e. 200 orbits every 8 days? Assume a circular orbit with an angular velocity defined by w 0 = µ a 3 1/2 = 1.107e-3 rad/s. Question 3: True/False, 2 pts. An orbit can be both in a sun-synchronous orbit and in a repeat orbit at the same time. Question 4: True/False, 2 pts. Until the early 1920 s, a clock did not exist that was more accurate than that of the Earth s daily rotation about its axis. Question 5: True/False, 2 pts. The geoid is a mathematically perfect ellipsoid that is sized to coincide with the mean sea level. 1

2 Sample Examination AE2103 Page 2 of?? 2010 Question 6: The Global Positioning System GPS, 10 pts. We are able to determine our absolute position using the Global Positioning System GPS through signals transmitted by the various orbiting GPS satellites. These signals must propagate through the ionosphere and the rest of the atmosphere, whose high electron content can often cause distortions. This, in turn, can lead to errors in the estimated position at the ground level. The designers of the GPS satellite network were aware of this problem in advance, but used the fact that, when not in a vacuum, different frequencies travel at different velocities to their advantage to help eliminate these errors. The measured travel time delay t iono due to the ionosphere for a GPS signal of a given frequency, f, is described as: t iono s c vac + A f 2 Using this equation, which of the expressions below for s represents the range correction that can be computed when using the L1 and L2 frequencies of the GPS system. ] a s = c vac [ iono f 2 L1 f 2 L2 b s = c vac [ iono f 2 L2 c s = c vac [ iono + d s = fl1 f 2 L2 2 e s = f 2 L1 f 2 L2 f 2 L1 f 2 L2 f 2 L1 f 2 L2 f 2 L1 f 2 L2 fl2 2 f L1 2 fl1 2 f L2 2 ] ] Question 7: Gravity, 10 pts. A new satellite was launched last year by ESA called the Gravity field and steady-state Ocean Circulation Explorer GOCE mission. The goal of the GOCE mission is to measure the Earth s static i.e., non-variable gravity field using the technique of satellite gravity gradiometry SGG, which involves 3 pairs of very precise accelerometers taking direct measurements of the gravity gradient at satellite altitude. For GOCE, the accelerometer pairs are separated by roughly 0.5 meter, and each accelerometer has an accuracy i.e. σ, of 1.5e-12 m/s 2. Assuming the GOCE satellite is flying in an orbit with an altitude of 250km, what is the expected overall accuracy of the the on-board gradiometer, expressed in units of Eötvös 1 Eötvös = 1E = 1e-9 Gal/cm = 1e-9 1/s 2, and 1 Gal =.01 m/s 2? a 2.5e-4 me b 3e-3 me c 60 me d 6 me e 250 me Question 8: Gravity cont d, 10 pts. The accelerometers on GOCE are extremely sensitive because they must detect small variations in the gravity field, caused by mass elements located at or below the Earth s surface, from a distance of 250km away. The required sensitivity of the accelerometers would decrease if the gradiometer of GOCE could take measurements directly at the Earth s surface. Assuming this could be done, what level of sensitivity would the accelerometers need to have in order for the gradiometer to maintain the same level of accuracy as that described in the previous question? a 3.0e-6 m/s 2 b 1.62e-12 m/s 2 c 3.0e-12 m/s 2 d 1.39e-12 m/s 2 e 3.75e-7 m/s 2

3 Sample Examination AE2103 Page 3 of?? 2010 Question 9: EO Mission Design, 5 pts. Satellite altimetry missions often use a sun-synchronous, repeat track orbit design so that the solar panels can receive the highest degree of exposure. Assuming a spherical Earth, what would the rate of the longitude of the ascending node, Ω, need to be in order to maintain this orbit? a 1.16 rad/s b 7.27e-5 rad/s c 3.64e-5 rad/s d.0172 rad/s e 1.991e-7 rad/s Question 10: EO Mission Design cont d, 5 pts. The Topex/Poseidon altimetry satellite was a joint NASA/CNES mission launched in It flew for 13 years collecting valuable information about the surface of the Earth s oceans. It was placed into a sun-synchronous orbit at roughly 1300 km in altitude, with a repeat period of 10 days, meaning that the satellite would fly over the same location on the Earth once every ten days. What would the sampling density at the equator be for such a mission design? In other words, if you were to plot the ground track of the Topex/Poseidon mission, how far apart would the ascending tracks be along the equator? a 313 km b 127 km c 6695 km d km e 400 km Question 11: RADAR, 5 pts. A radar antenna with a length of 10 m, operating at a center frequency of 1.25 GHz, will have a beam width of a 140 degrees b 14 degrees c 1.4 degrees d 0.14 degrees e degrees Question 12: Optical remote sensing, 5 pts. Categorizing visible wavelengths from high to low frequencies, we find a red, yellow, blue b red, blue, yellow c blue, yellow, red d blue, red, yellow e yellow, red, blue Question 13: Optical remote sensing cont d, 5 pts. The spatial resolution of a VIR satellite sensor... a is limited by optics lenses etc. b is limited by the minimum integration time of the sensor c depends on the width of the spectral bands d all of the above may apply e none of the above applies

4 Sample Examination AE2103 Page 4 of?? 2010 Equation sheet AE2103, Space Missions and Applications I Physical constants c Speed of light in vacuo m s 1 defined as m s 1 h Planck constant J s e Charge on the proton C m e Mass of the electron kg u Atomic mass unit kg m 0 Permeability of free space H m 1 defined as 4π 10 7 H m 1 ε 0 Permittivity of free space F m 1 Z 0 Impedance of free space Ω G Gravitational constant N m 2 kg 2 R Gass constant J K 1 mol 1 N A Avogadro number mol 1 k Boltzmann constant J K 1 σ Stefan-Boltzmann constant W m 2 K 4 A Wien s displacement constant K m AU Astronomical unit m Units Properties of the Sun and Earth Sun s radius m Sun s mass kg Total radiated solar power W Sun s black-body temperature 5770 K Earth s equatorial radius m Semi-major axis of Earth s orbit around the Sun m Earth s mass M kg Standard gravitational parameter µ = GM m 3 s 2 Mean global albedo 0.35 Moon s radius m Average Earth-Moon distance m Law of cosines: c 2 = a 2 + b 2 2ab cos γ Surface area of a sphere: 4πr 2 4 Volume of a sphere: 3 πr3 Circumference of a circle: 2πr

5 Sample Examination AE2103 Page 5 of?? 2010 Planck: L λ = 2hc 2 λ 5 e hc/λkt 1 Rayleigh-Jeans: L f 2kT f 2 c 2 = 2kT λ 2 Stefan: M = σt 4 Wien: λ max = C 3 /T C 3 = 2898 µm K Kirchhoff: L λ = ελl λ,bb Wave equation: E = Ae jkr ωt+φ k = 2π ε r /λ λ = 2πc/ω ω = 2πf Miscellaneous: GSI = inter-detector spacing H inter-detector spacing f = m Θ = λ/d IF OV GIFOV = 2H tan 2 = w H f = w m db 10 log 10 P P r = AeGPt 4π 2 R σ 0 A 4 G = 4πAe λ 2 P n = k T sys B SNR = P r /P n Ω = 2π1 cosα/2 Keplerian orbits: r = a1 e e cosθ e = r a r p r a + r p T = 2π n n = µ a 3 Repeat orbits: j L 1 + L 2 = k2π L 1 = 2π T T E L 2 = 3πJ 2R 2 e cosi a 2 1 e 2 2 dω Node rate: dt = 3πJ 2 a1 e 2 2 cosi 1 Newton s 2nd Law: F = mā = µm r r 2 r R e 2π µ a 3

6 Sample Examination AE2103 Page 6 of?? 2010 Solutions: 1 a 2 b 3 a 4 a 5 b 6 b 7 d 8 b 9 e 10 a 11 c 12 c 13 d

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