Thanks for this Tom. I had regenerated the ephemeris again yesterday using Starry Night Pro + and there was still no congruence with the data returned by Horizons. Now I can stop "scratching my head." Bob On Feb 12, 2013, at 11:21 AM, Tom Polakis wrote: > This is only sort of related to observing in Arizona, so delete if you're not > interested. > > People who use desktop and tablet planetarium software/apps have been > noticing that the predicted position of Friday's close-approaching asteroid > is many tens of degrees off. The error is due to most software neglecting > the perturbation of the orbit due to Earth's gravity. > > The authors of the SkySafari for iOS decided to do something about it. The > latest release of SkySafari nails the position within arcseconds. The > method, which includes some high math and understanding of orbital mechanics, > is explained below by co-author Tim Debenedictis. I copied and pasted his > message from the southern-stars mailing list. > > The mention of "4th order Runge-Kutta" made me flash back to my engineering > numerical methods class, in which the professor interrupted his lecture to > tell us that we'll never use this stuff. Thankfully, in my case, he was > right. > > Tom > > ========= > > Apple has just released SkySafari Plus/Pro 3.7.3 for iOS, and we've released > SkySafari 1.7.3 for Mac OS X and Android. > > About 2 weeks ago, we started to get these questions about 2012 DA14, and why > our apps fail to predict its position accurately. The problem was that > SkySafari - like basically all other mobile and desktop planetarium apps - > models the motion of comets and asteroids as having a simple Keplerian, > elliptical orbit around the Sun. We did not take pertubrations by Earth's > gravity into account. So any orbit that describes the asteroid's motion > before the flyby will completely fail to predict its position afterwards, and > vide-versa. After answering this question the 327th time, I finally decided > to do something better. > > The solution was to build an "orbit integrator" into SkySafari. Instead of > modelling the trajectory of the asteroid as a simple Keplerian ellipse, we > now model it using true N-body newtonian physics, taking the gravitational > perturbations of Earth (and the Moon, Venus, Mars, Jupiter, and Saturn) into > account, along with a decent numerical method (4th order Runge-Kutta). It > took a few tries to get this right. After reaching out to some professionals > in the field of solar system dynamics, we got some assistance JPL as well. > JPL has made clear that they cannot officially endorse any commercial > product, but I can confidently say they were impressed that we got this > working on a smartphone at all. > > We did take some shortcuts. Our model does not take relativity into account, > nor the oblateness of the Earth. We also don't include Mercury, Uranus, or > Neptune in the set of asteroid-perturbing masses. (Smartphones, whiie very > capable, are still not supercomputers. The code still has to run fast enough > to be useable.) Nevertheless, even with these shortcuts, our model predicts > the position of 2012 DA14 to within arcseconds of JPL's positions on the day > of the flyby and for many days before and after. We've even run our > integrator out 9 years into the past or future, for a selection of different > asteroids and comets, and in nearly all cases it does much better than a > simple Keplerian orbit. So we're very confident that we're doing the math > right. > > Anyhow, that's the theory. In practice, here's what you need to know. > > 1) Plus and Pro only. The integrator is not in the Basic version. > > 2) You still need to update your minor body orbit data, just like you did > before. The orbit integrator is useless if it doesn't have a decent orbit to > start from. > > 3) The integrator only gets "turned on" when you select a particular comet or > asteroid, and it's only used for the asteroid/comet you selected. > > 4) We run the integrator for one year in the past and future from the date of > the orbital elements, using a 1-hour timestep. All that math takes about 1.5 > seconds on my iPhone 4, which is the slowest device I own. (You'll feel a > brief pause when first selecting a new asteroid or comet). > > 5) Since we only run the integrator one year from the date of issue of the > orbital elements, don't try to use it to find out if asteroid Apophis will > hit Earth in 2036. It won't work. At least not in this release. Yet. > -- > See message header for info on list archives or unsubscribing, and please > send personal replies to the author, not the list. > -- See message header for info on list archives or unsubscribing, and please send personal replies to the author, not the list.