The movement of the body around the mass problem!

[jkowalski]

hi

I found a book in the movement of the planets around the masses. Rewrote all of the books but does not want to work. I would also like to make this move planets with animate to.

[ptc-286210 · Accepted solution]

Please, find Odesolve command in your sheet. You wrote vector as x,y,x, but it must be x,y,z.

[Werner_E]

See attached.

Changed parameter in Create Space and type of graph from surface to scatter.

Look what happens if you change the interval in odesolve (from 1 to3 or greater)

Thanks to rosenm for finding the typo.

[jkowalski]

How animate movments?

[Werner_E]

A description, esp. the meaning of your vars and functions wouls have been helpful.

Is F(t) a vector describung the position of moving a fifth planet (with mass 0???)

Does the attched help?

BTW, Freemake Video Converter did the job well. THnaks again.

[jkowalski]

If he was still visible lane 5 planet that would be great. The fifth planet has a mass very much less (close to zero) from 4 others.

[Werner_E]

Jan Kowalski schrieb:

If he was still visible lane 5 planet that would be great.

So why don't you add the path of the fifth planet?

I am not sure if that animations reflects real situation. What happens at 00:27/00:28 ? Bouncing back from the yellow planet or are we going round that planet so quickly that the animation did not catch it?

[jkowalski]

The odesolve is the previous value was inaccurate. You have to increase the number of step intervals. Or something like that.

Werner ,rosenm Thanks for your replay.

[Werner_E]

What happens here? It looks like the red "planet" is rejected by the yellow one.

Shown is the path between t=260 and t=276.

[jkowalski]

Try to enter the values ​​shown by arrows(file.gif).Odesolve solves the equation in an approximate manner. The higher the number (intvls) the more accurate solution.

Odesolve([vector], x, b, [intvls])

• b is the real terminal point of the integration interval. b can be greater than or less than the initial value, which is inferred from the initial conditions in the solve block.
• intvls (optional) is the integer number of discretization intervals used to interpolate the solution function. The number of solution points is the number of intvls + 1. The default value of intvls is 1000. More is more accurately eg: 50000

in our case it b=500,intvls=20000.

[Werner_E]

I left b at 400 but the change of the intervals of odesolve does significantly affect the path of that planet. Decent accuracy is achieved by intervals>10^5. But then, solving an DE from 0 to 400 (!!) numerically is quite a task.

Attached the change of the path (t=260 to t=276) when changing the intervals of odesolve from 10^3 to 10^6.

At least it shows the the red planet goes around the yellow one as it should be.

[jkowalski]

See the example of how the function changes it, odesolve accuracy by changing the step parameter.

see file attached.

[Werner_E]

Significant, indeed. An the interval we are calculating the solution for is only from 0 to pi, not from 0 to some hundreds as we did with the planets.

[jkowalski]

WOW unbelievable result!!!!!!!!!!!

[Werner_E]

Jan Kowalski schrieb:

WOW unbelievable result!!!!!!!!!!!

You are using a numerical approximation and you divide the solve range, which is about 1500 wide, into 100 intervals only. That has to become quite random.