Video: How to Weigh the Earth (4+ minutes)

How to Weigh the Earth (4+ minutes)
http://www.sciencedump.com/content/how-weigh-earth

Although precision satellite telemetry can be used to determine
the mass of the earth to about six places of accuracy, here's
an experiment you can you yourself.

This video demonstrates how to determine the mass of the earth using
some very simple equipment and a powerful mathematical expression. A
century wide collaboration between Newton and Cavendish makes this
possible. The video includes a discussion of Newton's universal law of
gravitation and Cavendish's famous experiment that led to the
determination of "G" the universal gravitational constant.

On 9/6/2011 5:19 PM, Sam Wormley wrote:
How to Weigh the Earth (4+ minutes)
http://www.sciencedump.com/content/how-weigh-earth

Although precision satellite telemetry can be used to determine
the mass of the earth to about six places of accuracy, here's
an experiment you can you yourself.

This video demonstrates how to determine the mass of the earth using
some very simple equipment and a powerful mathematical expression. A
century wide collaboration between Newton and Cavendish makes this
possible. The video includes a discussion of Newton's universal law of
gravitation and Cavendish's famous experiment that led to the
determination of "G" the universal gravitational constant.

That's a very good video that explains the concepts. But I feel there's
some "circular" reasoning going on in the use of the device used to
measure the mass of the Bocce ball. The Taylor scale does not actually
determine the mass of the Bocce ball but really measures the force the
ball exerts on its weighing platform. That's what a scale does: measure
force. That force would normally be displayed as pounds or ounces. In
fact, at 2:47 in the video you can see the choice of display under the
button on the right as g-lb-oz. The 2nd and 3rd options are forces,
which is *all* the scale is really capable of reading. But, as a
convenience for those of us that live on the surface of the earth, the
manufacturers of the force-measuring scale have used the formula
m1=(F*r^2) / (G*m2) to give us the "computed" mass of the object and,
thus, the 1st option of that button. The scale manufacturers know 'r',
'G', and 'm2' are constants for people on the surface of Earth. The
scale has measured the force 'F'. Plugging those 4 values into the
equation gives you m1, the Bocce ball's mass in grams, which it
"cleverly" displays. But if you used this scale on the surface of Mars,
even adjusting 'r' for Mars' smaller radius, you would not be able to
calculate the mass of Mars because you would get an incorrect
(significantly less) value for the mass of the Bocce ball. There needs
to be a device capable of measuring true mass without taking the
"short-cut" of simply measuring force in a known gravitational field.

On Sep 6, 5:18*pm, TR Oltrogge wrote:
But I feel there's
some "circular" reasoning going on in the use of the device used to
measure the mass of the Bocce ball.

You do need to measure the force the Earth's gravity exerts on the
Bocce ball, to compare that force to the force the Bocce ball exerts
on the test mass on the torsion balance.

Once you've done that, you have measured the mass of the Earth in
Bocce balls.

To determine the mass of the Bocce ball in kilograms, it wouldn't be
circular to take a 1 kg weight and put it on the same scale as was
used to weigh the Bocce ball. But that was already done when the scale
was marked in kilograms. So there's no real circularity.

Of course, a certain regular poster on these forums would say that
Newton's law of universal gravitation is just empirical nonsense,
attempting to destroy the beauty of astronomy as a creative and
interpretive endeavour by reducing the heavenly framework to ignoble
ballistics... but that's another issue.

John Savard

On 9/6/2011 7:57 PM, Quadibloc wrote:
On Sep 6, 5:18 pm, TR wrote:
But I feel there's
some "circular" reasoning going on in the use of the device used to
measure the mass of the Bocce ball.

You do need to measure the force the Earth's gravity exerts on the
Bocce ball, to compare that force to the force the Bocce ball exerts
on the test mass on the torsion balance.

That's correct, and that force between Earth and the Bocce ball gets
measured at 2:55 in the video with the Newton spring scale.

Once you've done that, you have measured the mass of the Earth in
Bocce balls.

Agreed. The question now is what is the mass of the Bocce ball?

To determine the mass of the Bocce ball in kilograms, it wouldn't be
circular to take a 1 kg weight and put it on the same scale as was
used to weigh the Bocce ball.

Agreed. And your introduction of a standard 1kg mass (notice I did not
call it "weight", which is force) allows the determination of the ratio
between the Bocce ball and the 1kg mass. That's because the force due to
gravity of the Earth is directly proportional to their masses. BTW,
either the Taylor scale (using any of its 3 measures: g,lb,oz) or the
Newton spring scale may be used to make the comparison since they both
measure these directly proportional forces. I guess the "circularity"
disappears for me once you introduce the 1kg standard.

But that was already done when the scale
was marked in kilograms. So there's no real circularity.

Well, we can be sure the manufacturer of the Taylor scale has calibrated
it so the *force* exerted by Earth on a standard 1kg mass *at the
Earth's surface* causes a reading of 1000 grams, even though grams is
mass, not force. In that sense you are correct that the Taylor scale
measures mass, but ONLY at the Earth's surface!

Of course, a certain regular poster on these forums would say that
Newton's law of universal gravitation is just empirical nonsense,
attempting to destroy the beauty of astronomy as a creative and
interpretive endeavour by reducing the heavenly framework to ignoble
ballistics... but that's another issue.

Entirely!

John Savard

On Sep 6, 11:19*pm, Sam Wormley wrote:
How to Weigh the Earth (4+ minutes)
* *http://www.sciencedump.com/content/how-weigh-earth

Although precision satellite telemetry can be used to determine
the mass of the earth to about six places of accuracy, here's
an experiment you can you yourself.


You get what you pay for,instead of discussing geodynamics of the
viscous interior as it applies to geomagnetism,crustal evolution/
motion and other issues you and your buddies traffic in wide sweeping
novelties which no longer have any real relevance.

How many places of accuracy do you say you can determine the rotation
of the Earth yet your empirical system is an entire rotation out each
annual cycle,to a reader unfamiliar with the arguments it would look
shocking that people paid to do this kind of thing ,billions upon
billions of dollars each year,yet cannot openly conclude that the
Earth turns at a rate of 15 degrees per hour and 365 1/4 times in a
year.If it doesn't draw such sort of disgust or a sense of dismay then
nothing will but that is not the end point,it is what comes when the
proper principles are adapted and all of it is good.


This video demonstrates how to determine the mass of the earth using
some very simple equipment and a powerful mathematical expression. A
century wide collaboration between Newton and Cavendish makes this
possible. The video includes a discussion of Newton's universal law of
gravitation and Cavendish's famous experiment that led to the
determination of "G" the universal gravitational constant.

No matter how you put it,what Newton did was try to use the Ra/Dec
system as a predictive bridge between the behavior of objects at a
human level and the behavior of planetary motion and while it is fine
for empiricists to believe you can squeeze the rotational and orbital
dynamics into the 365/366 day format of the calendar system,it is a
universal disaster for everyone else.The terrestrial sciences have
grown to such an extent that not even empiricists can afford an agenda
that uses a wide sweeping generalization based on a system which
predicts lunar and solar eclipses as days and dates within the
calendar system or the position of celestial objects in a framework of
stellar circumpolar motion.

I would imagine that there are mathematicians out there who have a
sense of adventure,not commentators of a fictional history and how
things came to be as they now are,but people with a sense that whole
areas are left unexplored because it does not suit those unwilling or
unable to make the journey into the world of astronomy and the
principles of planetary dynamics and solar system structure.