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Re: [Phys-L] apparent weight



Thanks for the detailed reply and notes. Very helpful.

One more thing. I heard/read once somewhere that
because the Sun's force on the Moon is about 2x the
Earth's force on the Moon, the Moon orbits the Sun more
than it orbits the Earth. In other words, the Moon's true
orbital path is always concave around the Sun.

How would the Moon's orbit actually look? Similar
to the epicycle model to show planetary motion? Would the
Moon's orbital path ever cross itself? Trying to visualize this...
Is there an onlne simulation anywhere?


Phys-L@Phys-L.org writes:
On 12/13/2014 09:10 PM, Anthony Lapinski wrote:
I might not ask this question to my HS students!
Seems a bit advanced for them.

If left strictly to their own devices, they're not likely
to figure it out anytime soon. It took Isaac Newton a
good long while to figure it out ... using calculus.

OTOH we don't have to leave them to their own devices.
We can leave a trail of breadcrumbs for them to follow.

The basic idea can be understood using basic principles
of physics and a little bit of algebra. (It would be
a whole lot easier using calculus, but we can get by
without that.) Basically all you need is the equivalence
principle plus some simple scaling ideas. I wrote up
the details at
https://www.av8n.com/physics/tides.htm#sec-low-tech

The math is not rocket science. You need to convince
yourself that the difference between 1/60^2 and 1/61^2
is very nearly 2/60^3. That is to say, the tidal stress
scales like inverse distance /cubed/.

We do calculate the forces of the Sun and Moon on the Earth. The
Sun's force is 175x more, but the Moon's tidal force is 3x more.

Closer to 2.15x more, I would think.
https://www.av8n.com/physics/periods.m

More importantly: The force scales like distance squared,
but the tidal stress scales like distance cubed, so we would
expect them to be different.

Kids wonder about this.

As well they should. It's a good question, and deserves
a good answer. The answer is that in view of the equivalence
principle, the only thing that could possibly matter is the
/difference/ between the moon's field at the center of the
earth and the moon's field at the surface of the earth.
The field scales inversely like r squared, but the difference
scales inversely like r cubed.

The Sun's force is 2x more, yet the Moon "appears" to orbit the
Earth. It actually orbits the Sun more! Kids wonder about this, too.

That's basically the same question. The same answer applies,
mutatis mutandis.

That is, we invoke the equivalence principle again. If the
earth and the moon were freely falling toward the sun at
the same rate, there would be no observable consequences.
Therefore the only thing that could possibly matter is the
/difference/ between the sun's field at the two locations.
This scales like distance cubed. The pair/sun distance is
389 times the intra-pair distance, so we can pretty much
ignore the sun when analyzing the dynamics of the pair.

There is "some" tidal stress that messes with the orbital
dynamics, but it's really small.

======================

In this context, the best way to handle the centrifugal
force is to not mention it at all.

If somebody insists on bringing it up, the answer is:
Remember, the centrifugal field exists in the rotating
reference frame and not otherwise. It does not matter
at all whether the earth is rotating; the only thing
that matters is whether the reference frame is rotating.
Repeat as many times as necessary: The centrifugal field
exists in the rotating reference frame and not otherwise.
https://www.av8n.com/physics/rotating-frame.htm

For the tide question, choose an appropriate /non rotating/
reference frame and turn the crank.

======================

This is what I consider "conceptual physics". You take two
really basic concepts -- the equivalence principle plus scaling
laws -- and combine them using a bit of reasoning. It really
offends me when I see books and courses that use the term
"conceptual physics" as a euphemism for /bonehead physics/.
The concepts are useless if you don't know how to combine
them. If folks are going to teach the concepts without the
reasoning, they might as well not bother. The students will
(rightly) judge the disconnected concepts to be useless, and
will forget them as quickly as possible.

======================

BTW the tide question, if handled correctly, helps motivate
kids to sign up for calculus. Newton invented calculus for
a reason, so he could do physics.

The idea that the tidal stress scales like 1/r cubed was
not just some lucky guess. You can predict that with
zero effort if you know a little bit of calculus. I
plotted it out so I could show people, but I knew in
advance what the plot was going to look like.
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