# Deriving Kepler's First Law

## and/or determining the path of an asteroid from angular and time data

The goal of this web page - figure out and show how Johannes Kepler "did his astronomical thing".
- - a secondary goal is to understand how astronomers express the paths of sun centered orbits.

Introduction:
 Many years ago, there was a impoverished, pathetic nut case called Johannes Kepler (1571 – 1630) who spent way too much time doing arithmetic and trigonometry on some tables of numbers (of positions of "planets") provided by a rich weird Danish nobleman called Tycho Brahe. Tycho collected and wrote those numbers down in the dark!! Really !! Starting with just the above tables of numbers, Kepler said that he could tell you that paths of a few wandering stars called "planets" - which you can sometimes see in the night sky if you have nothing else to do. Like who could possibly care ?!?! The score of some game played by neighborhood kids in much more important! He didn't even get a Nobel Peace Prize - which are being passed about as rewards for "interpreting" some weather "data" which has since been scrubbed from a hard drive in "East Anglia" to make room for ???? or to avoid closer examination. Maybe I can be awarded a "Me Too" Prize if I can figure how Kepler computed the path of the wandering "planet" Mars. Unfortunately, "planets" are so unimportant that a group of humans can ( late at night, like Tycho Brahe ) promote and/or demote them - such as the tragic case of Pluto which more people mourn than have seen.

The Challenge:
Derive from "first principles" and tables of numbers such as available from Tycho Brahe, Kepler's First and Second Law. Completed 1605, )published 1609 after finally getting permission to publish Brahe's data). (Kepler is credited with a third astronomical law (1618), but I haven't been able to get to step 1 ( Law I ) yet. :-((

These tables of numbers consisted of (in modern terms) I presume:
 - date ( Julian ) - right ascension ( angle east/west of vernal equinox ) - declination ( angle north/south from celestial equator )

Poor Tycho Brahe had interesting problems also. He had to build and use:
 Enormous (3 meter) protractors for accuracy - no telescopes - a later example Open sights - no cross hairs - Galileo and astronomical telescope (no cross hairs) years later Lamps to light the open sights and protractor scales, and screw up his night vision
in the cold dank Danish nights (no wonder Tycho drank a lot !! ;-)
And since he didn't have a proper clock, likely had to wait until the upper (or lower ;-)) culmination of the object. (Christiaan Huygens later utilized Galileo's pendulum for a proper clock. )

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PS - have you given any thought of how Kepler
could have figured that say Mars is in an ellipse?
From such angles and dates(times) as provided by Brahe ?
I originally thought that Brahe might have provided
angles from local horizontal and time - say:
-  angle from east horizon
-  angle from south horizon
-  date & time
But that has the problem that time has to be accurate
and the pendulum clock had not yet been invented :-((
So the data must have been given as
- east angle to some fixed star
- south angle to  "        "     "
- date and approximate hour
which makes horizon location and time less vital.

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"First Principles" seem very limited:
 - crude trig tables, you may have to interpolate - - ??? Kepler did not have "modern conveniences" such as: - calculators - or even tables of logarithms - Henry Briggs published in 1617 - Newton's "Law of Universal Gravity" - Newton published in 1686

some web sites I am studying
- Kepler’s "Vicarious Hypothesis" - including Kepler found that using the Mean Sun position is not good !!
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If you have comments or suggestions, Send e-mail to Ed Thelen

Updated May 6, 2012