You observe a near-Earth satellite with theinertial position and velocity vectors:=(-4069.503,2861.786,4483.608) km=(-5.114,-5.691,-1.000) km/swhere the vector components are takenwith respect to an inertial frame.a) Using the energy equation, determinewhat type of orbit this is.b) Compute the eccentricity of this orbitusing the eccentricity vector expression.c) Determine the periapsis radius. Will thesatellite his the Earth (ignoring atmosphericeffects)?Question 9.11 from Fourth Edition ofAnalytical Mechanics of Space Systems byHanspeter Schaub and John Junkins

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You observe a near-Earth satellite with the inertial position and velocity vectors: =(-4069.503,2861.786,4483.608) km

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

You observe a near-Earth satellite with the
inertial position and velocity vectors:
=(-4069.503,2861.786,4483.608) km
=(-5.114,-5.691,-1.000) km/s
where the vector components are taken
with respect to an inertial frame.
a) Using the energy equation, determine
what type of orbit this is.
b) Compute the eccentricity of this orbit
using the eccentricity vector expression.
c) Determine the periapsis radius. Will the
satellite his the Earth (ignoring atmospheric
effects)?
Question 9.11 from Fourth Edition of
Analytical Mechanics of Space Systems by
Hanspeter Schaub and John Junkins

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