Planetary Motion,Feynman Lectures

[@run]

Homework Statement

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.

Homework 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)

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.

 

[Nate810]

So it can be concluded that v(y) depend on initial x value. But how feynman computed the value 1.63 remain a mystery.

 

[kerimek]

I would first commend the student for their efforts in trying to understand the concept of planetary motion and the calculations involved. It is clear that they have put in a lot of thought and effort into their attempts.

To answer the question about why Feynman chose the specific value of 1.63 for v(y), it is important to understand that the initial conditions chosen by Feynman were not arbitrary. They were carefully selected in order to accurately model the motion of a planet around the sun.

In this case, the initial conditions were chosen to represent a planet with a specific eccentricity (e=0.1) and initial velocity in the y-direction (v(y)=1.63) at a specific position (x=0.5, y=0). These values were chosen based on the equations of motion for a planet, as shown in the homework statement. The value of v(y) was not randomly chosen, but rather calculated using the given equations and the known values of x and e.

Furthermore, as seen in the student's second attempt, changing the value of v(y) significantly affects the resulting motion of the planet. This is because the initial conditions have a direct impact on the trajectory of the planet. Therefore, Feynman's choice of 1.63 for v(y) was based on careful consideration and calculation, in order to accurately model the motion of a planet around the sun.

In conclusion, as a scientist, I would encourage the student to continue their efforts in understanding the concept of planetary motion and to keep exploring different approaches to solving the problem. It is important to keep in mind that the chosen initial conditions are not arbitrary, but rather based on careful calculations and considerations.