The inverse square law,and life on Earth

Thinking about the inverse square law a lot lately. I came to realize if
gravity worked by simple proportions our attraction to the Sun would be
stronger than our attraction to the center of Earth. Than we have again
the EM energies of the sun,and they also obey the inverse square law.
Of all of natures laws I like the inverse square law the best. Bert

"G=EMC^2 Glazier" wrote in message
...
Thinking about the inverse square law a lot lately. I came to realize if
gravity worked by simple proportions our attraction to the Sun would be
stronger than our attraction to the center of Earth. Than we have again
the EM energies of the sun,and they also obey the inverse square law.
Of all of natures laws I like the inverse square law the best. Bert

On this topic, here is a great link describing the Inverse Square Law, for
those of us (myself included) that need a little equation reminder from time
to time, http://hyperphysics.phy-astr.gsu.edu...orces/isq.html.

Bert, it would probably be a bit of fun to calculate how we are getting
tugged by the earth, moon and the sun...

--
BV.
www.iheartmypond.com

On Thu, 25 Mar 2004 10:11:31 -0500, BenignVanilla wrote:

"G=EMC^2 Glazier" wrote in message
...
Thinking about the inverse square law a lot lately. I came to realize if
gravity worked by simple proportions our attraction to the Sun would be
stronger than our attraction to the center of Earth. Than we have again
the EM energies of the sun,and they also obey the inverse square law.
Of all of natures laws I like the inverse square law the best. Bert

On this topic, here is a great link describing the Inverse Square Law, for
those of us (myself included) that need a little equation reminder from time
to time, http://hyperphysics.phy-astr.gsu.edu...orces/isq.html.

Bert, it would probably be a bit of fun to calculate how we are getting
tugged by the earth, moon and the sun...

Step on a scale to determine the pull of the earth.

According to my quick and dirty calculations, a person with a mass of 80kg
weighs roughly 0.2 pounds more at solar midnight than solar midday (the
sun pulls such a person with a force of about 0.1 pounds, adding to weight
at night, subtracting from weight at day).

The force from the moon amounts to something like 6 x 10^-4, and is
therefore quite negligible.


--
- Mike

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Mike The moon's gravity force is greater than the sun. So why is it
more negligible? I always found it interesting the diameter of a
conducting wire obeys the inverse square law Bert

On Fri, 26 Mar 2004 17:34:15 -0500 (EST), G=EMC^2 Glazier wrote:

Mike The moon's gravity force is greater than the sun. So why is it
more negligible? I always found it interesting the diameter of a
conducting wire obeys the inverse square law Bert

Where do you get that idea?

Newton's theory of gravitational force is this equation:

F = (G*M*m)/R^2

G is the gravitational constant (6.67x10^-11).

M and m are the two masses, and R is the distance between centers of mass.

The ratio of two forces would be this:

((G*M1*m1)/R1^2)/((G*M2*m2)/R2^2)

In this case, m1 and m2 are the same value, representing the person (whose
mass in a ratio calculation is irrelevant) on earth. Cancelling
variables, we're left with this for the ratio of forces:

(M1/R1^2)/(M2/R2^2)

Mass of the sun = 1.989 x 10^30 kg
Mass of the moon = 7.349 x 10^22 kg

Distance to the sun = 1.496 x 10^8 km
Distance to the moon = 3.844 x 10^5 km

Plug in the values, and you get (1.989E30/1.496E8^2)/(7.349E22/3.844E5^2)
= ~179

The gravitational force from the sun on a person is something like 179
times greater than the gravitational force of the moon on the same person.

A bit of simple algebra will show that for an object the mass of the moon
to match the gravitational influence of the sun, it would have to be
roughly 29,000 kilometers away, against the sun's distance of 150 million
kilometers. There's something to be said for having 27 million times the
mass of the body you're gravitationally competing with.

Your confusion probably stems from the fact that the tidal forces of the
moon on the earth are greater than the tidal forces of the sun on the
earth. This is not due to higher gravitational force, but due to a larger
gradient in gravitational force across the entire body of earth. The
inverse square nature of the force means that as distance increases, the
significance of subsequent changes in distance grows progressively
smaller.

To put it somewhat differently...

The mean distance of the sun is actually around 149,600,000 kilometers.
The diameter of the earth is about 12,756 kilometers. The difference in
gravitational force between the sun at 149,600,000 km and the sun at
149,612,756 kilometers is something like 0.02%. The difference between
the moon at 384,400 km and the moon at 397,156 km, however, is around
6.7%. That's why tidal forces from the moon are more important than tidal
forces from the sun. It's the difference in pull that counts, not the
overall force of the pull (which is, as calculated, around 179 times
greater from the sun than from the moon, both for a person on the earth,
and the earth itself).


--
- Mike

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On Fri, 26 Mar 2004 17:34:15 -0500 (EST), G=EMC^2 Glazier wrote:

Mike The moon's gravity force is greater than the sun. So why is it
more negligible? I always found it interesting the diameter of a
conducting wire obeys the inverse square law Bert

I neglected to address your second sentence. I assume that you're
referring to the relationship between a conductors resistance and its
diameter.

The area of a circle is proportional to the square of its radius. Double
the radius of a wire, and the number of atoms on the surface of a cross
section goes up by a factor of four. It's no surprise that the ease with
which electrons can travel also goes up by roughly a factor of four.


--
- Mike

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Mike:

Mike Ruskai wrote:

[snip]
The area of a circle is proportional to the square of its radius. Double
the radius of a wire, and the number of atoms on the surface of a cross
section goes up by a factor of four. It's no surprise that the ease with
which electrons can travel also goes up by roughly a factor of four.

[snip]

Wrong deduction.

Where you say, "The area of a circle is proportional to the square of
its radius", should you have said instead, "The area of a circle is
proportional to the square of its radius AND THE PRODUCT TIMES PI", as
in (A=PR^2). The radius value is the input, and the area the output.

Geometers, Pythagoras, Eudoxus, and Euclid, may be credited in the
reasons and the footnotes.

Recalculate the recipe as appropriate.

Ralph Hertle

Barry:

Barry Schwarz wrote:

On Sat, 27 Mar 2004 23:03:10 GMT, Ralph Hertle
wrote:


Mike:

Mike Ruskai wrote:

[snip]

The area of a circle is proportional to the square of its radius. Double
the radius of a wire, and the number of atoms on the surface of a cross
section goes up by a factor of four. It's no surprise that the ease with
which electrons can travel also goes up by roughly a factor of four.


[snip]

Wrong deduction.

Where you say, "The area of a circle is proportional to the square of
its radius", should you have said instead, "The area of a circle is
proportional to the square of its radius AND THE PRODUCT TIMES PI", as
in (A=PR^2). The radius value is the input, and the area the output.

Geometers, Pythagoras, Eudoxus, and Euclid, may be credited in the
reasons and the footnotes.

Recalculate the recipe as appropriate.


Read it again. He didn't say equal to, he said proportional to. In
fact, the constant of proportionality just happens to be pi.

snip


Check your mathematical operational principles. The constant in the form
you represented would have to be added, or multiplied, by each side of
the equation, i.e., equals added to equals are equal (Euclid).

Mathematicians, feel free to make the necessary observations. Thank you.

Ralph Hertle

Ralph Hertle wrote:

Barry Schwarz wrote:

Mike Ruskai wrote:

The area of a circle is proportional to the square of its radius. Double
the radius of a wire, and the number of atoms on the surface of a cross
section goes up by a factor of four. It's no surprise that the ease with
which electrons can travel also goes up by roughly a factor of four.

[snip]

Read it again. He didn't say equal to, he said proportional to. In
fact, the constant of proportionality just happens to be pi.

[snip]

Check your mathematical operational principles. The constant in the form
you represented would have to be added, or multiplied, by each side of
the equation, i.e., equals added to equals are equal (Euclid).


Of course! That's what "is proportional to" means in mathematics: one
side is always greater or less than the other in a constant ratio or
"proportion". Where the constant is explicitly given one says "is
equal to" instead. In general some such constants (like _pi_) are
dimensionless and others (like G) carry dimensions with them, so
there needn't be any problem with incommensurate quantities. In the
case of the relation between a circle's area and the square of its
radius, both have dimensions of area (distance squared) so Euclid has
nothing to complain of, with or without the _pi_.

What "operational principles" do you think Barry needs to check?

Mathematicians, feel free to make the necessary observations. Thank you.


One doesn't need to be a mathematician to comprehend the difference
between "is proportional to" and "is equal to". Anyone who's done any
mathematics can appreciate the value of simplifying the terms of a
problem; by discussing proportion rather than equality Mike was able
to omit mention of _pi_, the value of which is quite irrelevant to
his point -- as long as one understands it to be constant.

--
Odysseus

Hi Odysseus Thinking of round(circular) how about a conducting copper
wire. The "diameter" of this wire shows us it obeys the inverse square
law. We see this just by seeing the wires that are used coming off a 12
volt car battery. To the starting motor nice and thick. To the radio a
lot thinner. I can see the inverse square law in action when I stop
light an inch and a half from its source. Always like the simple math.
that shows a light bulb is 9 times dimmer when seen three feet away.
Here in Florida Odysseus I can appreciate the light from the sun obeying
the inverse square law in July. Bert