# The Naked Scientists Forum

### Author Topic: How much does the Earth weigh?  (Read 56658 times)

#### JP

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##### How much does the Earth weigh?
« Reply #50 on: 02/12/2010 08:05:29 »
Its just a definition thing

It's more fundamental than that. Mass is a property of matter. Weight is a measure of the interaction between matter.

It's still partly a definition thing.  There are two accepted definitions of weight:
1) the force required to keep you stationary against gravity in your particular reference frame, i.e. this is the one that a scale would measure if put under your feet
2) the force exerted on you by gravity (in a Galilean reference frame, I believe).

The big difference is that if I'm in a freely falling elevator, within my reference frame, a scale will read zero, but gravity is still pulling on me with a force of ~700 Newtons.  Both answers are correct, since there are two alternative definitions of weight.  They both agree, however, if I'm standing on the earth's surface.

This is precisely why weight isn't commonly used in physics, and certainly not used unless you make it clear under what circumstances you're using it.

So the answer to the earth's weight could be either zero, or some value obtained by computing the force that the sun exerts on the earth.  What the person who posed the question probably wanted to know was the mass, since I'm not sure what use it would be to know either definition of the weight...

-------------

Actually, the definitions might be even more muddled, since the earth isn't itself a Galilean reference frame due to its orbit and rotation, but I suppose it's close enough...

#### Foolosophy

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##### How much does the Earth weigh?
« Reply #51 on: 02/12/2010 08:13:36 »
Its just a definition thing

It's more fundamental than that. Mass is a property of matter. Weight is a measure of the interaction between matter.

So the answer to the earth's weight could be either zero, or some value obtained by computing the force that the sun exerts on the earth.  What the person who posed the question probably wanted to know was the mass, since I'm not sure what use it would be to know either definition of the weight...

-------------

Actually, the definitions might be even more muddled, since the earth isn't itself a Galilean reference frame due to its orbit and rotation, but I suppose it's close enough...

Is this some sort of quantum defintion of weight? Could be zero could be a positive value?

Would you question that a astronauts weight is equal to zero when in a space station that is in free fall motion around the earth?

Is the astronauts weight either zero or some computed force value?

The definition of weight is unambiguous

« Last Edit: 02/12/2010 08:18:25 by Foolosophy »

#### JP

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##### How much does the Earth weigh?
« Reply #52 on: 02/12/2010 08:20:12 »
Its just a definition thing

It's more fundamental than that. Mass is a property of matter. Weight is a measure of the interaction between matter.

So the answer to the earth's weight could be either zero, or some value obtained by computing the force that the sun exerts on the earth.  What the person who posed the question probably wanted to know was the mass, since I'm not sure what use it would be to know either definition of the weight...

-------------

Actually, the definitions might be even more muddled, since the earth isn't itself a Galilean reference frame due to its orbit and rotation, but I suppose it's close enough...

Is this some sort of quantum defintion of weight? Could be zero could be a positive value?

Would you question that a astronauts weight is equal to zero when in a scape station that is in free fall motion around the earth?

Is the astronauts weight either zero or some computed force value?

The definition of weight is unambiguous

Quantum has nothing to do with any of this.

These are the two textbook definitions of weight.  The definition is indeed ambiguous, as there are two possibilities.

If you asked me what an astronaut's weight was in the space station, I would ask you which definition you wanted to use, since they would give you two different answers.

Then I'd probably tell you that asking for the weight is confusing, and that it would be better to ask for force, measured in a particular reference frame, or mass.
« Last Edit: 02/12/2010 08:22:29 by JP »

#### Geezer

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##### How much does the Earth weigh?
« Reply #53 on: 02/12/2010 08:27:34 »
Its just a definition thing

It's more fundamental than that. Mass is a property of matter. Weight is a measure of the interaction between matter.

It's still partly a definition thing.  There are two accepted definitions of weight:
1) the force required to keep you stationary against gravity in your particular reference frame, i.e. this is the one that a scale would measure if put under your feet
2) the force exerted on you by gravity (in a Galilean reference frame, I believe).

The big difference is that if I'm in a freely falling elevator, within my reference frame, a scale will read zero, but gravity is still pulling on me with a force of ~700 Newtons.  Both answers are correct, since there are two alternative definitions of weight.  They both agree, however, if I'm standing on the earth's surface.

This is precisely why weight isn't commonly used in physics, and certainly not used unless you make it clear under what circumstances you're using it.

So the answer to the earth's weight could be either zero, or some value obtained by computing the force that the sun exerts on the earth.  What the person who posed the question probably wanted to know was the mass, since I'm not sure what use it would be to know either definition of the weight...

-------------

Actually, the definitions might be even more muddled, since the earth isn't itself a Galilean reference frame due to its orbit and rotation, but I suppose it's close enough...
[/quote]

Much as I hate to disagree with my learned colleague JP, that's bollocks

Weight is what you measure with a calibrated spring, or a comparitive reference on some sort of balance in a gravitational field. It is always a relative measurement. e.g. the Earth equals x Moons

On the other hand, mass can be quantified quite independently of any gravitational field.
« Last Edit: 02/12/2010 08:29:13 by Geezer »

#### Geezer

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##### How much does the Earth weigh?
« Reply #54 on: 02/12/2010 08:35:01 »
I'm not quite sure what happened there, but this is what I tried to post:

Much as I hate to disagree with my learned colleague JP, that's bollocks

Weight is what you measure with a calibrated spring, or a comparitive reference on some sort of balance in a gravitational field. It is always a relative measurement. e.g. the Earth equals x Moons

On the other hand, mass can be quantified quite independently of any gravitational field.

#### Foolosophy

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##### How much does the Earth weigh?
« Reply #55 on: 02/12/2010 08:54:18 »

On the other hand, mass can be quantified quite independently of any gravitational field.

This is true for "Newtonian non-relativistic mass"

relativistic mass varies with all sorts of variables and conditions - including gravitational fields

As it is now the weight of the earth is zero

You will find that if an examination question asked the student "What is the weight of the earth"? any answer other than zero will be wrong.

« Last Edit: 02/12/2010 08:56:17 by Foolosophy »

#### JP

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##### How much does the Earth weigh?
« Reply #56 on: 02/12/2010 08:57:42 »
It's hard to argue against "that isn't true," so here's some sources:

National Institute of Standards and Technology: Weight is mass in kg times g, which is the gravitational acceleration at the earth's surface~9.8 m/s2.  NIST would disagree with you and say that your weight is the same no matter where you are, with nothing relative about it.  In other words, NIST is saying that weight is equal to mass multiplied by a constant that only makes sense at the earth's surface.
(See: http://physics.nist.gov/Pubs/SP330/sp330.pdf, p. 52)

ISO (International Organization for Standardization) defines it in terms of the apparent gravitational acceleration in some reference frame.  I.e. in their case, you would weigh less on the surface of the moon, and be weightless in a falling elevator.  [I can't find their publication online, but it's in International Organization for Standardization, International Standard ISO 31-3. (1992). “Quantities and units. Part 3, Mechanics.” (Geneva, Switzerland)]

For the problems with weight definitions (and why weight is fairly useless as a technical term) see, for example: http://books.google.com/books?hl=en&lr=&id=CoB5w9Km0mUC&oi=fnd&pg=PA45#v=onepage&q&f=false

also: http://sites.huji.ac.il/science/stc/staff_h/Igal/Research%20Articles/Weight-AJP.pdf

If that doesn't make it clear that the definition ambiguous, I don't know what will.

#### Geezer

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##### How much does the Earth weigh?
« Reply #57 on: 02/12/2010 09:01:55 »
JP beat me to it!

On the other hand, mass can be quantified quite independently of any gravitational field.

This is true for "Newtonian non-relativistic mass"

relativistic mass varies with all sorts of variables and conditions - including gravitational fiels

As it is now the weight of the earth is zero

No it ain't.

Any differences between Newtonian and relativistic masses in these frames are extremely small. Relativity did not cancel out Newton's work, it just refined it in certain situations.

#### Foolosophy

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##### How much does the Earth weigh?
« Reply #58 on: 02/12/2010 09:07:50 »
It's hard to argue against "that isn't true," so here's some sources:

National Institute of Standards and Technology: Weight is mass in kg times g, which is the gravitational acceleration at the earth's surface~9.8 m/s2.  NIST would disagree with you and say that your weight is the same no matter where you are, with nothing relative about it.  In other words, NIST is saying that weight is equal to mass multiplied by a constant that only makes sense at the earth's surface.
(See: http://physics.nist.gov/Pubs/SP330/sp330.pdf, p. 52)

ISO (International Organization for Standardization) defines it in terms of the apparent gravitational acceleration in some reference frame.  I.e. in their case, you would weigh less on the surface of the moon, and be weightless in a falling elevator.  [I can't find their publication online, but it's in International Organization for Standardization, International Standard ISO 31-3. (1992). “Quantities and units. Part 3, Mechanics.” (Geneva, Switzerland)]

For the problems with weight definitions (and why weight is fairly useless as a technical term) see, for example: http://books.google.com/books?hl=en&lr=&id=CoB5w9Km0mUC&oi=fnd&pg=PA45#v=onepage&q&f=false

also: http://sites.huji.ac.il/science/stc/staff_h/Igal/Research%20Articles/Weight-AJP.pdf

If that doesn't make it clear that the definition ambiguous, I don't know what will.

But you just said that weight is the product of mass and "g" and your weight will be the same wherever you are???

g is a variable isnt it? what is the value of g at the centre of the earth? What is your weight at the centre of the earth?

When you see an astronaut floating in a space station are they experiencing weightlessness or masslessness?

#### JP

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##### How much does the Earth weigh?
« Reply #59 on: 02/12/2010 09:14:13 »
Here's the problem, which is expressed well by the NIST and ISO disagreement on standards.  Both say the equation for weight is

W=gm, where W is weight, m is mass and g is a number.

NIST says that g = 9.8 m/s2 no matter where you are and what you're doing.

ISO says that you need to tell me where you're defining weight in order to define g.  If you're in a freely falling elevator, g is zero.  If you're standing on the earth's surface, g=9.8, and if you're standing on the moon, g=9.8/6.

That's why there is ambiguity.

As for the astronaut, they have mass.  Whether they are weightless or not depends how you define weight.  NIST says they are never weightless, while ISO says they are weightless, in their own reference frame.  They might not be weightless in some other reference frame.

#### Geezer

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##### How much does the Earth weigh?
« Reply #60 on: 02/12/2010 09:27:52 »
They don't get it.

You "weigh" something by comparing the force it exerts in a gravitational field (which is virtually inescapable) with the force exerted by another "thing".

#### Geezer

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##### How much does the Earth weigh?
« Reply #61 on: 02/12/2010 10:12:56 »
BTW, the term "weightless", as frequently applied to objects that are orbiting the Earth at a particular speed, may be slightly suspect.

I am reasonably confident that if those objects were to stop in orbit they would immediately attain significant weight.

#### Foolosophy

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##### How much does the Earth weigh?
« Reply #62 on: 02/12/2010 12:12:24 »
BTW, the term "weightless", as frequently applied to objects that are orbiting the Earth at a particular speed, may be slightly suspect.

I am reasonably confident that if those objects were to stop in orbit they would immediately attain significant weight.

wow - you change the conditions and you get a different result.

Why not stop the earth and take the earth to a scale situated on Jupiter and weigh it?

The question is "How much does the earth weigh"?

In its current free falling orbit around the sun the earth's weight is equal to zero.

Look at the physical theory - not some ISO standards used to make weighing carrots or salmon more easier to understand. Their terms of reference dont include commerce on the planet Venus
« Last Edit: 02/12/2010 12:16:16 by Foolosophy »

#### JP

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##### How much does the Earth weigh?
« Reply #63 on: 02/12/2010 13:44:59 »
They don't get it.

You "weigh" something by comparing the force it exerts in a gravitational field (which is virtually inescapable) with the force exerted by another "thing".

If I had to pick a definition or be shot, I'd go with something like that.  My personal preference is to skip all the sillyness about defining weight and stick to forces and masses, which are far less ambiguous.  If the OP had asked what the mass of earth was, the question would have been much easier!

#### Foolosophy

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##### How much does the Earth weigh?
« Reply #64 on: 02/12/2010 14:01:45 »
They don't get it.

You "weigh" something by comparing the force it exerts in a gravitational field (which is virtually inescapable) with the force exerted by another "thing".

If the OP had asked what the mass of earth was, the question would have been much easier!

nothing wrong with a little bit of intellectual wrestling

the worst thing that can result is that something is learnt

#### peppercorn

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##### How much does the Earth weigh?
« Reply #65 on: 02/12/2010 15:55:35 »
nothing wrong with a little bit of intellectual wrestling

the worst thing that can result is that something is learnt

Yeah, sometimes you learn how obstinate some posters are!
...More like an intellectual 100-years-war with some...

#### Bored chemist

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##### How much does the Earth weigh?
« Reply #66 on: 02/12/2010 18:20:36 »
Actually, NIST says
"The kilogram is the unit of mass; it is equal to the mass of the international prototype
of the kilogram;
2. The word “weight” denotes a quantity of the same nature as a “force”: the weight of a
body is the product of its mass and the acceleration due to gravity; in particular, the
standard weight of a body is the product of its mass and the standard acceleration due
to gravity;
3. The value adopted in the International Service of Weights and Measures for the
standard acceleration due to gravity is 980.665 cm/s2, value already stated in the laws
of some countries."

So they talk about a "standard weight" that is 9.80665 times the mass (in KG) but the weight might be anything.

I note with amusement that a work titled "The international system of units" uses a non-SI unit for the standard value of g.

#### Geezer

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##### How much does the Earth weigh?
« Reply #67 on: 02/12/2010 19:45:11 »

In its current free falling orbit around the sun the earth's weight is equal to zero.

Er, if it's weightless, why is it falling?

#### CPT ArkAngel

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##### How much does the Earth weigh?
« Reply #68 on: 03/12/2010 03:47:17 »
g = G * M / R^2

where

G is he gravitational constant
M is the mass of the earth
R is the radius of the earth

Between an object on the surface of the earth and the earth,

m * g =  - (M * a)

where

m is the mass of the object
g is the acceleration constant due to gravity of the earth (not really a constant)
M is the mass of the earth
a is the acceleration due to the gravity of the object (constant only if the object is spherical and uniformly dense)
« Last Edit: 03/12/2010 04:57:15 by CPT ArkAngel »

#### Foolosophy

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##### How much does the Earth weigh?
« Reply #69 on: 03/12/2010 05:31:43 »

In its current free falling orbit around the sun the earth's weight is equal to zero.

Er, if it's weightless, why is it falling?

Do you know how satellites orbit another body?

(hint: look at their trajectory and project it through space - does it go past the earths horizon or intersect with the earths surface

#### Foolosophy

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##### How much does the Earth weigh?
« Reply #70 on: 03/12/2010 05:38:12 »
g = G * M / R^2

where

G is he gravitational constant
M is the mass of the earth
R is the radius of the earth

Between an object on the surface of the earth and the earth,

m * g =  - (M * a)

where

m is the mass of the object
g is the acceleration constant due to gravity of the earth (not really a constant)
M is the mass of the earth
a is the acceleration due to the gravity of the object (constant only if the object is spherical and uniformly dense)

so do you agree that the earth is in free fall motion around the sun and so its weight is equal to zero?

#### Geezer

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##### How much does the Earth weigh?
« Reply #71 on: 03/12/2010 05:55:40 »

In its current free falling orbit around the sun the earth's weight is equal to zero.

Er, if it's weightless, why is it falling?

Do you know how satellites orbit another body?

Yes I do, and I also know that you are ducking my question.

#### CPT ArkAngel

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##### How much does the Earth weigh?
« Reply #72 on: 03/12/2010 06:37:22 »
it is a question of definition...

#### Geezer

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##### How much does the Earth weigh?
« Reply #73 on: 03/12/2010 06:50:23 »
it is a question of definition...

No. I think it's a question of lack of definition.

#### Foolosophy

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##### How much does the Earth weigh?
« Reply #74 on: 03/12/2010 11:30:02 »

In its current free falling orbit around the sun the earth's weight is equal to zero.

Er, if it's weightless, why is it falling?

Do you know how satellites orbit another body?

Yes I do, and I also know that you are ducking my question.

You mean your question about why something is falling when its weightless??

The question itself reveals something about you

I am not sure whether you know what that is Geezer

#### The Naked Scientists Forum

##### How much does the Earth weigh?
« Reply #74 on: 03/12/2010 11:30:02 »