A particle of mass m is moving in a central field along a spiral orbit given in polar coordinates by r= roekø where ro and k are positive constants
A particle of mass m is moving in a central field along a spiral orbit given in polar coordinates by r= roekø where ro and k are positive constants
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Hi please show all work and explanation. Thank you.

Transcribed Image Text:A particle of mass m is moving in a central field along a spiral orbit given in polar coordinates by
r = roeko, where ro and k are positive constants.
a) Use the Binet equation:
d²b
+ b =
do2
m
F(r),
6² M²´
where b = 1/r, to show that the force is inverse-cube in r (F is proportional to r-3).
b) Substitute r into the conserved angular momentum in polar coordinates M =
that o varies logarithmically with t.
mr²o to show
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