plotting a joining line between points in simulation.

I am in the middle of a simulation of planetary orbits. I am using Euler integration for Newtons law of universal gravity and have inputted the numbers for Earth's and venus' orbit (simulating the two body problem). I am plotting the position of the planets as well as a trail behind them (the trail always consists of the last twenty points). However I would like to plot the orbit of Earth (and other planets) under the influence of the other planet against Earth's orbit only influenced by the Sun. The problem that I have is that in order to illustrate the difference in the two orbits I want to plot a line joining the two points. How do I do this?

Answer 1

[Star Strider]

I’m not sure I’m understanding ‘a line joining the two points’. If you want lines connecting corresponding points (for example with respect to time) between the two orbits, this will work:

t = linspace(0, 2*pi, 100);                                     % Time Parameter
Re = 1.5E8;                                                     % Mean Earth Orbit Radius (km)
eu_xy = [Re*cos(t); Re*sin(t)];                                 % Unperturbed Orbit (Created)
ep_xy = [1.1*Re*cos(t); 1.05*Re*sin(t)];                        % Perturbed Orbit (Created)

figure(1)
plot(eu_xy(1,:),  eu_xy(2,:))                                   % Plot Unperturbed Earth Orbit
hold on
plot(ep_xy(1,:),  ep_xy(2,:))                                   % Plot Perturbed Earth Orbit
plot([eu_xy(1,:); ep_xy(1,:)], [eu_xy(2,:); ep_xy(2,:)])        % Plot Lines Between Parametrically Similar Points
hold off

The formats of the orbit calculations ‘eu_xy’ and ‘ep_xy’ are straightforward. To plot the corresponding time points between the two orbits, plot the x-values of both in one matrix against the y-values of both in the other. The result is this plot:

I have no idea what your orbits actually look like so I just guessed. This approach should work, regardless. (I tested it with a few other aberrant orbits that crossed the unperturbed orbit and it worked also.) If you have problems getting it to work with your data, let me know and I will help you get the problem sorted.