Timeline for How to discover Neptune from the Uranus orbit (by computer simulation)
Current License: CC BY-SA 3.0
10 events
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| Sep 25, 2020 at 2:57 | comment | added | user33354 |
@RodyOldenhuis I used the 3-step leapfrog integrator; the initial condition uses the velocity at half of the time-step, as shown at the top of page 4. Also, the initial position vector of each body was taken as the average distance (as opposed to exact position at a given datetime) perpendicular to velocity ((x,0,0) and (0,v,0)) or (0,x,0) and (v,0,0), such that each body initially lies on the x-axis or y-axis. Maybe this affects the orbits (esp on long time-scales).
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| Sep 24, 2020 at 23:48 | comment | added | Rody Oldenhuis |
@allthemikeysaretaken Also: what exactly do you call "the" leap-frog integrator in Python? Verlet integration, though symplectic, may suffer from other sources of error that a variable-order multistep Adams-Bashforth-Moulton scheme (ode113 in MATLAB) deals better with. It really depends on specifics whether one outperforms the other
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| Sep 24, 2020 at 23:47 | comment | added | Rody Oldenhuis | @allthemikeysaretaken no, there's no source other than my code (which could also be wrong of course; I don't remember doing many validation tests on this to be honest). Those "squigglies" are the result of the Earth's orbit, and they should therefore have a period of very close to 1 year. Eyeballing your first plot and my plot would indicate that your Earth is orbiting twice as slow as mine...Also, the picture you linked to uses different initial conditions (they put Uranus directly opposite Neptune), so we can't directly compare mine to theirs... | |
| Sep 23, 2020 at 4:02 | comment | added | user33354 | Viewing from the respective center-of-mass of the system (as opposed to viewing from the respective Earth frame) removes all the "squigglies" but the scale doesn't appear to change by doing this. | |
| Sep 23, 2020 at 3:58 | comment | added | user33354 | Is there a source to confirm the accuracy of the last figure (separation in arcseconds of Uranus with and without Neptune, as viewed from respective Earth)? I ask because I tried to recreate this plot using the leap-frog integrator in python (and a time-step of 0.1 days); I got a similar shape but the scale of the angle is off. It may be a problem with my code, but the scale for the first 100 years in my simulation is comparable to the one found here (third image from the bottom). | |
| Jan 4, 2017 at 19:32 | vote | accept | Sergio Piccione | ||
| Dec 30, 2016 at 16:41 | history | bounty ended | HDE 226868♦ | ||
| Dec 20, 2016 at 20:36 | comment | added | zephyr | Brilliant answer! | |
| Dec 20, 2016 at 18:57 | history | edited | Rody Oldenhuis | CC BY-SA 3.0 |
added 5 characters in body
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| Dec 20, 2016 at 16:14 | history | answered | Rody Oldenhuis | CC BY-SA 3.0 |
