# Homework Help: Planetary Motion,Feynman Lectures

1. Dec 25, 2009

### @run

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

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.

Last edited: Dec 26, 2009