Re: Kepler ,Newton and orbital geometry

Quadibloc <jsavard@xxxxxxxxx> wrote:

They know the Sun is part of a galaxy, and they know when the gravity
of other stars may be safely ignored, just as they know when the
effects given by Einstein's Special and General theories of relativity
may be safely ignored, for they know the sizes of these things.

Hi, everyone.

With this statement I would agree. It reminds me of when I was studying
a bit of calculus -- and I could use a refresher! -- and considering
free-fall problems. The two obvious considerations were the acceleration
of gravity near the Earth's surface, usually taken as a constant in these
problems, and also atmospheric drag or wind resistance.

However, if one wanted to be more precise, then it would also be necessary
to consider that according to Newton's equation, the acceleration of gravity
is _not_ a constant, but will slightly change as the distance between the
falling body and the Earth's center decreases!

Similarly, strictly speaking, all motion is "relativistic," and once I had
fun calculating how much time dilation I may have experienced during a
long walk from the frame of reference of an observer stationary with respect
to the Earth. The result was a fraction of a picosecond (10^-12 second), as
I recall. This result nicely illustrated why for most purposes, indeed,
a Newtonian approach is more than accurate enough.

Anyway, I don't see why we can't approach the idea of a heliocentric Solar
System and planetary motions in more than one way: either using modern
imaging to illustrate Kepler's explanation of apparent retrograde motion,
or using Newton's heliocentric reference frame (to me, a fine thought
experiment). We're hardly limited to one frame of reference, and I'd
consider it elegant to use two or more, rather like having alternative
proofs for a theorem of whatever.

Most appreciatively,

Margo Schulter
mschulter@xxxxxxxxxx
Lat. 38.566 Long. -121.430

.

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