Hi please all show work, thank you. The energy of the particle from Problem 2 is given by1E =+U =2a(2)2mr2Show that the motion of the particle r(t) is given by parametric equations:1t =- -esin ξ),r = a(1 – e cos {),(3)where w =[a/(ma*)]1/2 is the mean angular velocity of the orbital motion and & is a parameter(which ranges from 0 to 27 for one revolution). The first relation, which gives (t), is called theKepler equation. Substituting r(t) into the equation of path (1) gives o(t).Hint: Use equations (3) to calculatedr/d£dt/dgdrdtand then substitute r and r into equation (2).Find r/a and wt for twenty values of E between 0 and 47, for some value of ebetween 0 and 1 of your choice. Graph these pairs: r/a on the vertical axis and wt on the horizontalaxis. They form a curve which is a trochoid. Graph the same parametric function for e → 1. Thiscurve is a cycloid.

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The energy of the particle from Problem 2 is given by 1 E = M2 +U = (2) 2mr2 2a Show that the motion of the particle r(t) is given by parametric equations: 1 t = - -esin ξ), r = a(1 – e cos E), (3) where w = [a/(ma³)]/2 is the mean angular velocity of the orbital motion and & is a parameter

The energy of the particle from Problem 2 is given by 1 E = M2 +U = (2) 2mr2 2a Show that the motion of the particle r(t) is given by parametric equations: 1 t = - -esin ξ), r = a(1 – e cos E), (3) where w = [a/(ma³)]/2 is the mean angular velocity of the orbital motion and & is a parameter

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Hi please all show work, thank you.

The energy of the particle from Problem 2 is given by
1
E =
+U =
2a
(2)
2mr2
Show that the motion of the particle r(t) is given by parametric equations:
1
t =
- -esin ξ),
r = a(1 – e cos {),
(3)
where w =
[a/(ma*)]1/2 is the mean angular velocity of the orbital motion and & is a parameter
(which ranges from 0 to 27 for one revolution). The first relation, which gives (t), is called the
Kepler equation. Substituting r(t) into the equation of path (1) gives o(t).
Hint: Use equations (3) to calculate
dr/d£
dt/dg
dr
dt
and then substitute r and r into equation (2).
Find r/a and wt for twenty values of E between 0 and 47, for some value of e
between 0 and 1 of your choice. Graph these pairs: r/a on the vertical axis and wt on the horizontal
axis. They form a curve which is a trochoid. Graph the same parametric function for e → 1. This
curve is a cycloid.

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