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Re: Measuring acceleration of Earth



Savinainen Antti wrote:

how can the acceleration of Earth with respect to Sun be measured? Of
course, it is quite easy to *calculate* an estimate using high school
physics but I wonder what methods might exist for a "direct"
measurement of the acceleration? By "direct" I mean how to measure it
if we didn't know that Earth revolves around Sun :-).

I don't understand the point of the question.
-- There is almost nothing in physics that depends on
calculation without measurement ... otherwise it would
be called math, not physics.
-- There is almost nothing in physics that depends on
measurement without calculation. In this case in
particular, Einstein's principle of equivalence tells
us that at any particular point, an acceleration of
the reference frame is indistinguishable from a
gravitational field. Therefore in principle, any
measurement of *any* acceleration must involve
multiple points and/or multiple times, and therefore
must involve *some* amount of calculation, i.e. at
least one subtraction.

*) For a direct-as-possible measurement, you could look
at the stars. In an hour or so you can convincingly
demonstrate the spin of the earth, and in a couple of
weeks you can equally well demonstrate the orbital motion
of the earth ... all without instruments. (You can do it
much faster using a telescope.)
*) There's also the "aberration of starlight". The
observed shape of the constellations changes with the
seasons by a nonzero amount, because the earth's orbital
velocity is a nonzero fraction of the speed of light.
http://www-istp.gsfc.nasa.gov/stargaze/Lframes1.htm
*) What about the very existence of seasons? In my
experience, in Finland this time of year, you don't need
to be a rocket scientist to notice that seasons exist.
This uses the earth itself as a gyroscopically-stabilized
reference frame for measuring the orbital motion.
*) Note that a Foucault pedulum is sufficient to answer
this question *and* the one below, since it indicates
sidereal time (with complications due to latitude).
*) A non-Foucault gyroscope could be use to (a) find
the orientation of the Earth's axis and then (b) observe
sidereal time ... all without needing to look outside.

Also, how can we measure "directly" the acceleration due to rotation
of Earth around its axis, say, on the equator. For instance,
Foucalt's pendulum and the coriolis effects can be used for this
purpose but there must be other ways as well?

See above. Locally, any acceleration is equivalent to
any other (spin, orbital, gravitational).

We don't "feel" directly either of the above accelerations whereas in
a merry-go-around acceleration (or more properly: the effects of
non-inertial reference frame) can be "felt".

Because we lump it in with gravity, via Einstein's principle
of equivalence.