The University of Queensland, School of Mechanical and Mining Engineering MECH2210 Dynamics and Orbital Mechanics Section B1- Tutorial Problems 2022 Assignment B1, Submit: 0.3 & 17 due Mon wk 11 Online

Dynamics Revision Quiz The following problems cover orbital mechanics material - please attempt all: Module/Question - 1/7, 2/12, 2/21, 3/5-12, 4/5, 6/3. (Answers online) F ᏛᎾ . B m Problem 1 Explorer No.1 launched in January 1958 had perigee and apogee heights above the Earth's surface of 360 km and 2550 km and an inclination of 33.2°. Calculate the: a) orbit period, b) its eccentricity, c) the total energy (per unit mass of the orbit) d) the angular momentum (per unit mass of the orbit), e) the maximum and minimum speeds and orbit positions f) the minimum impulse to change the inclination to 0° assuming the satellite passes the equator at its perigee, g) the minimum impulse Av required to escape Earth. (Answers: 1.92hr,0.14, -25.4 MJ/kg, 5.53x1010 m²/s, 8.2p & 6.2a km/s, 3.54 km/s, 2.67 km/s) Problem 2 An earth satellite is tracked from ground stations and is observed to have an altitude of 2200 km, a velocity magnitude 7 km/s and a radial velocity of 2.7 km/s. Determine: a) the total orbital energy per unit mass b) the orbital eccentricity e c) the minimum altitude and the maximum speed and d) the true anomalies at the observed position and at the point of maximum speed. e) Identify any potential difficulties with the orbit. (Answers: -22 MJ/kg, 0.389, -835km & 10 km/s, 105.3deg & 0 deg, crash into Earth) Problem 3 An early warning defence system detects an UFO travelling at 800km above earth's surface with a horizontal (perpendicular) speed of 8 km/s and a vertical (radial) speed of 1.3 km/s. Determine: a) the total energy (per unit mass of the orbit) b) the angular momentum (per unit mass of the orbit), c) the eccentricity of the orbit e d) the minimum and maximum radii of the orbit e) the true anomaly 9 at the point of observation. f) whether the UFO is possibly a missile, Earth satellite or comet and explain your answer. g) the minimum measured speed v of the UFO for it to be a comet and explain why. (Tot. 21 mks = 3 x 7) Problem 4