problem 1 explorer no 1 launched in january 1958 had perigee and apoge

Question

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)
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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