Why is my Earth orbit plot not elliptical in Maple?

incredibe1999 · Apr 5, 2018

Hey there! I was trying to plot a ODE solution, but am not getting what I should be. It is actually plotting the orbit of Earth with Sun at the origin.
My equations

Maple code defining the system ODEa: diff(x(t),t) = u(t), ODEb: diff(y(t),t) = v(t), ODEc: diff(u(t),t) = -(0.00011847) x(t) / (x(t)^2 + y(t)^2)^(3/2), ODEd: diff(v(t),t) = -(0.00011847) y(t) / (x(t)^2 + y(t)^2)^(3/2), and eqns as the list of the four equations.

The (-0.00011847) is GM.
The Initial Conditions:

Maple worksheet lines setting initial conditions: ICx := x(0) = -0.81449, ICy := y(0) = 1.41483, ICu := u(0) = -4.23729, ICv := v(0) = -2.11473.

The plot I get:

Maple plot of a straight red line running from the origin down to the lower right, with x axis from 0 to 10 and y axis from 0 to about -55.

Should not I be getting a elliptic/circular plot as the orbital positions of the Earth? Also, here the period is t=1. The position is supposed to be same at t=0 and t=1. Help, please!

scottdave · Apr 7, 2018

What is the code you used to generate this plot?

incredibe1999 · Apr 7, 2018

scottdave said:

What is the code you used to generate this plot?

I used the ODE Analyzer.

BvU · Apr 8, 2018

Well, that is not very helpful for us in finding out what goes wrong.

If I use your picture (please post something one can copy as text next time -- it avoids typos) but take different values, even good old Euler in Excel gets me a plot I expect:

Plot of a closed, slightly non-circular orbit in the x-y plane with axes from -1.5 to 1.5; the curve passes near (0, 1), (-1, 0) and (0, -1.1) and ends with a short gap near (1, -0.45).

values:

Code:

dt 0,01
x_0 1
y_0 0
vx_0 0
vy_0 1
GM 1

so the expressions look OK (provided I reproduced them correctly)

Now: what are the units for your values (and for time) ?

Why is my Earth orbit plot not elliptical in Maple?

Discussion

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