How to solve for multiple 'objects' in single ode function

Hi,

So I am trying to model the solar system by using ODE45 however I have run into an issue. Due to later concerns I'm trying to make the whole system dynamic and make it so that the planets interact with each other. I have a set of initial coordinates I have calculated for each of the planets, and I have calculated the distance between the planets and the sun for each of the planets I have. The next part I wanted to calculate was the acceleration for each of the planets however I have run into a problem I am not entirely clear on how to solve. The ODE wants the output value to be a column vector however this seems like a massive issue as having 4 parameters (at least if not more) on a single column for 8 planets would make the list very long. Currently it creates a matrix but this will only run the ODE once and it fails with an error.

I have not included the importing of the initial values as they are in spreadsheets I imported and don't believe it is relevant

Thanks

%% Planet motion
G = 6.67e-11; %Gravitational Constant
u = G*planetStart(1,6); %Gravitational Constant multiplied by sun mass 

res = 1; %The resolution the code should run at in days
last = 365; %The number of days the code should run for (from 1/1/19)

tSpan = 0:res:last;
[t,x] = ode45(@(t,x) pos(planetsXY,planetsVel,planetsMass,u),tSpan,planetsXY); 

planetsX = x(:,1); %Planets x coordinates
planetsY = x(:,2); %Planets y coordinates
planetsRad = x(:,3); %Distance between planets and sun
planetsAcc = x(:,4); %Acceleration of each planet

function ode45 = pos(planetsXY,planetsVel,planetsMass,u)
ode45 = [0 0 0 0]'; %Transposed matrix of initial values 

for i = 1:9
    ode45(i,3) = abs(norm(planetsXY(i,:)));
    ode45(i,4) = u/ode45(i,3)^2
end    

end

Answer 1

[Walter Roberson]

You can reshape the boundary values into a matrix to work with them and you can create your results in a matras long as you reshape to a vector just before you return.

[Robin Szabo]

So the issue with this is that it will create a very long column of numbers (upwards of at least 20 until more items are added, then even more) is there no way around this?

If not what is a good method to merge a matrix into a column then organise that into different values after?