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Tracking equation producing wrong acceleration value

Thread starter AirForceOne
Start date Sep 5, 2011
Tags

Multiple Tracking

2 replies · 2K views · last reply Sep 6, 2011

AirForceOne

Thread starter
Sep 5, 2011

#1

Homework Statement

Printed problem text describing two tracking stations observing a satellite S, with station B directly under the satellite and station A at 45 degrees from its path, giving values for B, B dot, r2, r2 dot and total acceleration, then parts a and b asking for second derivatives and r1, r1 dot, r1 double dot, theta dot and theta double dot.

Homework Equations

Typeset polar coordinate kinematics equations: position p2 = (r2) e_r2, velocity v2 = (r2 dot) e_r2 + (r2 theta dot) e_theta2, and acceleration a2 = (r2 double dot - r2 theta dot^2) e_r2 + (2 r2 dot theta dot + r2 theta double dot) e_theta2.

The Attempt at a Solution

Handwritten derivation of radial acceleration a2 = (r2'' - r2 theta2'^2) e_r2 + (2 r2' theta2') e_theta2, substituting r2'' = -30.7 and r2 = 100 with theta2' = -4.88e-2, giving r2'' - r2 theta2'^2 = -30.46 ft/s^2.

But the correct answer is 1227 ft/s^2.

Thanks.

Discussion

SteamKing

Staff Emeritus

Science Advisor

Homework Helper

Sep 5, 2011

#2

Check your units for r2.

AirForceOne

Sep 6, 2011

#3

Thank you. I was able to find part a) and r1. However, I was unable to find r^.. in part b). This is what I have so far:

Handwritten-style typeset derivation of polar-coordinate kinematics: position, velocity and acceleration of r2 with results r2 double dot = 1227 ft/s^2 and beta double dot = 0 rad/s^2, then p1 and r1 = 7.47x10^5 ft.

I don't know how to integrate the acceleration vector to velocity vector it seems.

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