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 Celestial Mechanics formulas? (Read 19917 times)
 Brent Guest Celestial Mechanics formulas? 03/22/05 at 23:27:14   There are some formulas that would be useful for using Gravity Simulator.  Do you know the formulas for velocity for circluar orbit, and for escape velocity?  I'd especially like to know escape since the program seems to compute circular for you. Back to top IP Logged
 Tony YaBB Administrator Posts: 1059 Gender: Re: Celestial Mechanics formulas? Reply #1 - 03/23/05 at 10:55:36   For circular and escape: G=6.673*10-11 M = Mass of the object being orbited d=distance from the center of mass M Back to top IP Logged
 Tony YaBB Administrator Posts: 1059 Gender: Re: Celestial Mechanics formulas? Reply #2 - 04/12/06 at 00:40:39   Here's a calculator for computing orbital period: http://orbitsimulator.com/gravity/articles/PeriodCalculator.html   And the same formula re-written to solve for semi-major axis: http://orbitsimulator.com/gravity/articles/smaCalculator.html   Use this calculator to solve for orbital altitude: http://orbitsimulator.com/gravity/articles/AltitudeCalculator.html Back to top « Last Edit: 04/20/06 at 17:21:38 by Tony »     IP Logged
 Tony YaBB Administrator Posts: 1059 Gender: Re: Celestial Mechanics formulas? Reply #3 - 11/13/06 at 22:28:47   A little off topic since it's not much use for Gravity Simulator, but here's a formula/calculator for computing the maximum velocity you can achieve from a solar sail.   http://orbitsimulator.com/astrobiology/solarpressure2.html Back to top IP Logged
 Tony YaBB Administrator Posts: 1059 Gender: Re: Celestial Mechanics formulas? Reply #4 - 11/22/06 at 00:13:01   Compute a star's visual magnitude from a its absolute magnitude and distance:   http://www.orbitsimulator.com/gravity/articles/vmag.html   Try entering 4.8 for the Sun's absolute magnitude, then switch the distance to different planetary distances (use AU) to see how the Sun's compares in brightness between planets. Back to top IP Logged
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Celestial Mechanics formulas? Reply #5 - 11/22/06 at 08:11:51   Quote from Tony   on 11/22/06 at 00:13:01:Compute a star's visual magnitude from a its absolute magnitude and distance: http://www.orbitsimulator.com/gravity/articles/vmag.html Try entering 4.8 for the Sun's absolute magnitude, then switch the distance to different planetary distances (use AU) to see how the Sun's compares in brightness between planets.   Erm, I'm not seeing a "Calculate" button, I can enter the AbsMag and the distance, but no number appears on the other side of the equals sign. I'm using Firefox 1.5 if that makes a difference. (I tried entering 1 PC and AbsMag 4.82) Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1059 Gender: Re: Celestial Mechanics formulas? Reply #6 - 11/22/06 at 10:43:57   Quote from Mal   on 11/22/06 at 08:11:51: Erm, I'm not seeing a "Calculate" button, I can enter the AbsMag and the distance, but no number appears on the other side of the equals sign. I'm using Firefox 1.5 if that makes a difference. (I tried entering 1 PC and AbsMag 4.82) I just tried it in Firefox and you're right.  It works fine in IE.  Firefox also gets the colors wrong.  The answer box should be dark red, and the 2 input boxes should be black.  I'll look into it.  I suspect that IE is more forgiving in javascript syntax errors. Back to top IP Logged
 Tony YaBB Administrator Posts: 1059 Gender: Re: Celestial Mechanics formulas? Reply #7 - 11/22/06 at 13:01:05   Try it now.  Appearently, IE is not that picky about bad syntax, and Firefox is.  I've cleaned it up so it works in both browsers now.  I'll have to do the same for all the other calculators in this post.   Thanks for pointing this out!   Can anyone tell me if this works in Opera or Netscape, or IE 7? Back to top IP Logged
 abyssoft YaBB Administrator I love YaBB 1G - SP1! Posts: 302 Re: Celestial Mechanics formulas? Reply #8 - 11/27/06 at 14:48:17   Does any one know the formula for determining the minimum distance of two ellipses in 3d space?   That would help me with the graphs to help show some more info. Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1510 Gender: Re: Celestial Mechanics formulas? Reply #9 - 11/29/06 at 12:52:24   hallo ,   can you explain your question some more ?   what coordinates are you using ?     x/a^2+y/b^2+z/c^2 = 1 ore something else ?     I suppose you have two ellipses of this form and want the determine the distance ? Back to top IP Logged
 abyssoft YaBB Administrator I love YaBB 1G - SP1! Posts: 302 Re: Celestial Mechanics formulas? Reply #10 - 11/29/06 at 18:25:29   I'm actully not sure.. I am defining the ellipse in astrometric terms a=semimajor Axis e=eccentricity i=inclination angle O=Longitude of the ascending node   The formula for this in standard algebraic notation is also baffleing me any help would be most appreciated. Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1510 Gender: Re: Celestial Mechanics formulas? Reply #11 - 11/29/06 at 22:46:02   hallo ,   i suppose that the two ellipses share 1 commom focus point .   Is this correct ? This might simplify things Back to top IP Logged
 abyssoft YaBB Administrator I love YaBB 1G - SP1! Posts: 302 Re: Celestial Mechanics formulas? Reply #12 - 11/30/06 at 05:17:51   Yes both share a common Focus point C which is by astrometric definition located at (0,0,0) in a cartesian system and (0, Sigma=0 deg, Theta=0 deg) in a 3d polar system. Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1510 Gender: Re: Celestial Mechanics formulas? Reply #13 - 12/01/06 at 14:05:38   I'm afraid there is no straightforward formula for this . Ellipses are very hard to deal with . At the first glance it seems one needs to solve a sixth order non linear equation . ... Back to top IP Logged
 abyssoft YaBB Administrator I love YaBB 1G - SP1! Posts: 302 Re: Celestial Mechanics formulas? Reply #14 - 12/01/06 at 16:42:51   Ty Vm for trying I was going to use the information to track potential approaches of Uranus, Neptune, and Pluto Back to top IP Logged
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