Billy T
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Thanks - very interesting - pretty pictures. I wrote simple three-body finite-time-step code in a spread sheet and could not follow full orbit year beyond a few Earth years, but Earths orbit closed very well when code was tested with DV's mass set to zero - graph overlapped so well I could not see the starting point or final points and numerical data fit ellipse well. (Total run time was limited - not enough lines "copied down" in spread sheet and time step was limited to about 4 days max, even though each step was computed twice in same line of code - forces acting at first results for end of time step position were averaged with the forces at the start of time step to get "effective average force" acting during the time step. - I know there are much better ways to increase time step size, but I wanted to keep every thing very simple so my target reader could follow it all. I also wanted to use the spread sheet's automatic graphing capacity.)tony873004 said:...A simulation where the dark visitor approaches from above yields similar results. In this case, Saturn, Uranus, Neptune & Pluto were ejected, Jupiter was forced into an elliptical orbit with a high inclination. Mercury, Venus, Earth and Mars were virtually unchanged...
My graphs and data for Pluto were thus limited to the begin of its fall towards the sun. I fit ellipse thru two computed points to get Pluto's apogee and perigee -not a very good method, in view of your statements as they don't even exist! I did not actually compute anything for any planets except Pluto and Earth. The entire code, step by step explained, prints in less than three pages of the book' appendix 2 - ridiculous by your standards!
Please keep in mind that I never give the initial conditions used exactly and am not trying to do anything but interest a person not currently interested in science to be come so. I wanted to give a flavor of the method of science, not do any. I set the miss distance to 12AU so I could go into details about gravity gradient ripping Saturn apart, if the timing was such that they got close.
I am glad you confirm that the change in Earth's orbit is very slight. Can you easily extract the new eccentricity? How does it compare to my 0.0836? I can't be sure, because of the perspective in your figures, but looks like from the curvature of the purple dark visitor line that your 2.2 mass is going significantly slower than mine, so I expect that even though you don't see much effect on Earth, your computed change in eccentricity is greater. My dark visitor is initially taking approximately 10 days to close on the sun by 1AU. What speed did you assume (before solar acceleration is significant)? I am nearly at a speed where the "impulse approach" is meaningful. For reasons I will not go into here, but will tell in private msg, I can't give its absolute speed relative to "fixed stars" or sun's initial position.
Again thanks - BTW I have read (and repeated here) that even the solar system is chaotic. How far into the future does one need to go to see an object in it signficantly change its orbit, or does that never happen unless a few of the larger asteroids (orbit crossing bodies) are included?
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