Re: Transformation from heliocentric to geocentric frame of reference

From: John C. Polasek (jpolasek_at_cfl.rr.com)
Date: 03/18/05 

Date: Fri, 18 Mar 2005 18:30:17 +0000 (UTC)

On Fri, 11 Mar 2005 08:28:36 +0000 (UTC), JF.Hofmann@t-online.de
wrote:

>Seen from the sun the planets have elliptic trajectories. I would be
>interested to find a reference where somebody has converted these
>trajectories into a frame of reference where earth is at rest. Can the
>trajectories be specified in closed form? If so, how do they relate to
>the Ptolemaic picture with earth as centre?

It's so simple. First write the orbit of the earth and all planets in
cartesian coordinates vs the Sun (after first doing them as polars),
as
        F(plan - Sun) = F0(plan - 0) taking Sun as 0,0,0.
Now the orbit seen from earth for a given planet use its
        F(planet vs earth) = F0(plan - 0) - F0(earth - 0)
Then, most likely, convert back to r(theta)
The cartesian circles turn into tangled spirals, but bear in mind that
they did not enjoy the privilege of floating above to see the 2d
patterns. They only get to observe and plot the angle theta in
r(theta). I have done this exercise.

John Polasek

Mr. Dual Space

If you have something to say, write an equation.
If you have nothing to say, write an essay

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