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Celestial Mechanics formulas? (Read 13829 times)
Brent
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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.
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Tony
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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
 

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Tony
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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
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« Last Edit: 04/20/06 at 17:21:38 by Tony »  
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Tony
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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
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Tony
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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.
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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)
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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.
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Tony
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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?
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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.
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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 ?  
 
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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.
 
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frankuitaalst
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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
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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.
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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 . ...
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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
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