## celestia-developers

 RE: [Celestia-developers] Re: Apollo 11 Orbit From: - 2003-09-29 13:05:38 ```Thanks, Grant=2E Your value of eccentricity works just fine=2E I was using e =3D sqrt(1 - (b*b)/(a*a)), where a and b are the semimajor a= nd semiminor axis of the ellipse, respectively=2E I used the moon's volumetri= c mean radius to come up with these values: a =3D 186 + 1737=2E1 =3D 1917=2E1 b =3D 183 + 1737=2E1 =3D 1914=2E1 then e =3D 0=2E05592 Obviously, this is not at all correct=2E But why isn't it? Where's the fau= lt in my math? Have I been dillusional for half of my life? Thanks=2E Original Message: ----------------- From: Grant Hutchison granthutchison@...=2Eco=2Euk Date: Sun, 28 Sep 2003 22:22:18 +0100 To: cweisbrod@...=2Eca, celestia-developers@...=2Esourceforge=2Enet Subject: [Celestia-developers] Re: Apollo 11 Orbit Clint: The problem is with your calculated eccentricity=2E The eccentricity is eq= ual to (1 - perihelion/semimajor axis): for the orbit you describe, and using the moon's equatorial radius in Celestia, that's (1 - 1920=2E5/1922) =3D 0=2E00078=2E So the following definition produces good apo- and peri-cynthions: =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D "Apollo 11" "Sol/Earth/Moon" { Class "spacecraft" Mesh "apollo=2E3ds" Radius 0=2E010 EllipticalOrbit { Period 0=2E0873 SemiMajorAxis 1922 Eccentricity 0=2E00078 Inclination 5 } Albedo 0=2E10 } =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D (The apparent shift in orbital centre you found using your eccentricity is= just a property of the geometry of ellipses - for a given semimajor axis, pericentre and apocentre will alter by the *same amount* when you alter th= e eccentricity=2E) Grant ------------------------------------------------------- This sf=2Enet email is sponsored by:ThinkGeek Welcome to geek heaven=2E http://thinkgeek=2Ecom/sf _______________________________________________ Celestia-developers mailing list Celestia-developers@...=2Esourceforge=2Enet https://lists=2Esourceforge=2Enet/lists/listinfo/celestia-developers -------------------------------------------------------------------- mail2web - Check your email from the web at http://mail2web=2Ecom/ =2E ```
 Re: [Celestia-developers] Apollo 11 Orbit From: Grant Hutchison - 2003-09-29 16:20:35 ```> Obviously, this is not at all correct. But why isn't it? Where's the fault > in my math? Have I been dillusional for half of my life? Your formula is correct, but your difficulty is with the numbers you're using for semimajor axis and semiminor axis. The semimajor axis is half the long axis of the ellipse, and the semiminor axis is half the short axis - so these two measurements are at right angles to each other, each taken from the geometrical centre of the ellipse. But the two numbers you've used are actually the pericentre and apocentre radii - the distances from one focus of the ellipse to the two ends of the long axis. If you average these two you'll get the semimajor axis, but then you pretty much need to work out the eccentricity in order to calculate the semiminor axis, which isn't really any use for orbital calculations anyway. Grant ```