(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This question is a part of independent study.

The problem is based on Feynman lectures volume 1,chapter 9,Newton's laws of dynamics,section 9-7 planetary motion. To compute numerically path of motion of a planet around sun using Newtons laws of kinematics and gravitation Feynman took initial conditions as x=0.5,y=0,v(x)=0,v(y)=1.63 & e=0.1.I understand that v(x)=0 and v(y) should have some value initially,but cannot understand why he take the value 1.63 for v(y) and how he computed 1.63.

2. Relevant equations

F = -G*M*m/r^2

r=sqrt(x^2+y^2)

x=x(0) + e* v(x) , v(x) = v(0) + e*a(x) , a(x) = -x/(r^3)

y=y(0) + e* v(y) , v(y) = v(0) + e*a(y) , a(y) = -x/(r^3)

3. The attempt at a solution

Two attempts are made

1

.x = a cos $, y = b sin $ -------(1)

v(x) = -a(d$/dt) sin $ -------(2),

v(y) = -b(d$/dt) cos $ = -(bx/a)(d$/dt)--------(3)

y = 0 means $ = 0, x=a.

so, v(y) = -b(d$/dt) = -bw

now there is a relation connecting the parameters a,b and e of an ellipse

b*b = a*a(1-e*e).

taking e = 0.8(a guss) value of b is calculated.

If I can calculate w in some way, i can get v(y). Some attempts made using the w*r^2 is conserved.

But couldn't calculate w.

2.

This attempt is made first for understanding that v(y) = 1.63 have any importance.

A simple program in c++ is made and plotted x-y graph.This analysis revealed that 1.63 have importance,then only perfect ellipse will be formed. If v(y) is taken as 0.8 planet will not revolve

around sun,the same thing happens when a value greater than 1.63 is taken ,for example 2.2

Analyis also says that the value of v(y) depend on x.When i take x=1 ,v(y) should have a value

near 1.4.This can be expect naturally because when x value changes from 0.5 to 1 the

gravitational force decreased,so less v(y) required.

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# Homework Help: Planetary Motion,Feynman Lectures

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