453 HW_2 - a eccentricity vector b true anomaly at this...

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MAE 453: Introduction to Space Flight Spring 2010 Department of Mechanical and Aerospace Engineering North Carolina State University Homework 2: Gravitational forces and the orbit equation DUE DATE: 2/10/10 1. Three particles of identical mass m are acted on only by their natural gravitational attraction. They are located at the vertices of an equilateral triangle with sides of length d . Consider the motion of any one of the particles about the system center of mass G and, using G as the origin of the inertial frame, determine: a) the distance r of each mass from the center of mass G b) the acceleration of each particle relative to an inertial frame located at G c) the angular velocity required for d to remain constant using Newton’s second law 2. Relative to a non-rotating, earth-centered Cartesian coordinate system, the position and velocity vectors of a spacecraft are k j i r ˆ 5210 ˆ 1690 ˆ 8900 (km) and k j i v ˆ 5 . 1 ˆ 5 . 4 ˆ 6 (km/s). Calculate the orbit’s:
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Unformatted text preview: a) eccentricity vector b) true anomaly at this instant 3. Relative to a non-rotating, earth-centered Cartesian coordinate system, the velocity of a spacecraft is k j i v ˆ 3 . 1 ˆ 9 ˆ 2 . 8 (km/s) and the unit vector in the direction of the radius is k j i u r ˆ 87 . ˆ 09667 . ˆ 4835 . ˆ . Calculate: a) the radial component of velocity v r b) the azimuth component of velocity v c) the flight path angle 4. Relative to a non-rotating, Cartesian coordinate frame with origin at the center of the earth, a spacecraft has the position and velocity vectors k j i r ˆ 15000 ˆ 5000 ˆ 10000 (km) and k j i v ˆ 5 . 7 ˆ 5 . 2 ˆ 5 (km/s). Calculate: a) the angular momentum. What statement can be made about the type of motion? b) the unit normal in the radial direction c) the position vector when the speed is 7 km/s (hint: use the energy equation)...
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