# The Naked Scientists Forum

### Author Topic: Difference of weight with altitude  (Read 7426 times)

#### fgt55

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##### Difference of weight with altitude
« on: 02/04/2012 14:32:29 »
Hi,

Gravity change with altitude, when 2 masses of 1kg are at h=0 m we have 2*g N like weight. Now, if we turn these 2 masses with radius of 1 m when we turn of 90°, one masse is at h=1m and another massis at h=-1m. Like the formula for gravity is like g = G*Mt/r², it's not possible to have the same weight when 2 masses was at h=0m. The weight is greater when we have turned, why ?

#### imatfaal

• Neilep Level Member
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##### Re: Difference of weight with altitude
« Reply #1 on: 03/04/2012 09:48:39 »
fgt - firstly the amounts we are talking about are so insignificant that in reality who cares?  secondly, at present we just cannot do the numerical calculation - newtons constant is accurate to about 1 part in 10000, whereas you are introducing a change that will manifest at around 1 part in a million million. and lastly, why would this be a problem - it is not as if the change (if there actually is one) in force occurs without effort being made to change the system.  why don't you, for the moment assume G is well known to huge accuracy and actually do the sums

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#### Nizzle

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##### Re: Difference of weight with altitude
« Reply #2 on: 03/04/2012 10:58:49 »
Shrunk
:o
I remember you telling me (and Aethelwulf and probably others too) not to be condescending imatfaal ;)

#### MikeS

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• Posts: 1044
##### Re: Difference of weight with altitude
« Reply #3 on: 05/04/2012 08:10:12 »
The lower mass is heavier by the same amount that the higher mass is lighter.  Together they both weigh the same as they did when horizontal.

And just for the record I care.

#### imatfaal

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##### Re: Difference of weight with altitude
« Reply #4 on: 05/04/2012 11:04:20 »
Mike - what is wrong with this calculation
1/5999999^2+1/6000001^2-2/6000000^2

or even more accurately ( ie setting fulcrum at 6*10^6 and modelling realistically)
1/5999999^2+1/6000001^2-2/sqrt(36000000000001)^2

#### MikeS

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##### Re: Difference of weight with altitude
« Reply #5 on: 05/04/2012 11:27:45 »
imatfaal

The figures may seem insignificant.  It's the theory that interests me and its implications in explaining time and gravity.  The figures may seem minute but the Universe takes them into account.  If it did not then gravity and time would not exist.

Or are you suggesting that my reply was wrong?

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#### Ęthelwulf

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##### Re: Difference of weight with altitude
« Reply #6 on: 05/04/2012 11:30:57 »
Shrunk
fgt - firstly the amounts we are talking about are so insignificant that in reality who cares?  secondly, at present we just cannot do the numerical calculation - newtons constant is accurate to about 1 part in 10000, whereas you are introducing a change that will manifest at around 1 part in a million million. and lastly, why would this be a problem - it is not as if the change (if there actually is one) in force occurs without effort being made to change the system.  why don't you, for the moment assume G is well known to huge accuracy and actually do the sums

Certainly the post that brought the sword to the heart!

#### imatfaal

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##### Re: Difference of weight with altitude
« Reply #7 on: 05/04/2012 12:01:32 »
Mike - Please click on those links to (simplified) sums that are important
If you don't see what they represent - here goes

let G and M_earth = 1  we can do that without loss of precision or meaning (it just means the units are no longer SI)

you then end up with

The OP is asking if is equal to   Now I might have got something wrong with my interpretation - but I see that as a fairly simple sum and a definite No.

#### MikeS

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##### Re: Difference of weight with altitude
« Reply #8 on: 05/04/2012 15:20:28 »
imatfaal

Point taken I was wrong and fgt55 was correct.

The question still has not been answered though.

I suspect that my answer should have been correct but relativistic effects have not been accounted for.  Does this make sense?

If not what does account for the difference?

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#### Ęthelwulf

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##### Re: Difference of weight with altitude
« Reply #9 on: 05/04/2012 16:14:46 »
Shrunk
Why has my post been censored, and why when I click it I cannot see it?

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#### imatfaal

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##### Re: Difference of weight with altitude
« Reply #10 on: 05/04/2012 17:09:19 »
Shrunk
Why has my post been censored, and why when I click it I cannot see it?
Cos it was completely off the point. We are having a problem with shrunk posts not unshrinking with the new forum software

#### imatfaal

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##### Re: Difference of weight with altitude
« Reply #11 on: 05/04/2012 17:15:12 »
imatfaal

Point taken I was wrong and fgt55 was correct.

The question still has not been answered though.

I suspect that my answer should have been correct but relativistic effects have not been accounted for.  Does this make sense?

If not what does account for the difference?

It is not really something I had thought a great deal about.  Relativistic effects? - possibly but which? if you got an idea I will number-crunch it.  Perhaps ask why it is assumed they should be the same, are there any consequences for them not being the same, are there positives for them not being the same.

This sort of the problem exemplifies why I always harp on about going back to the math

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#### Ęthelwulf

• Sr. Member
• Posts: 358
##### Re: Difference of weight with altitude
« Reply #12 on: 05/04/2012 17:40:17 »
Shrunk
Why has my post been censored, and why when I click it I cannot see it?
Cos it was completely off the point. We are having a problem with shrunk posts not unshrinking with the new forum software

I am sorry, but I think censoring posts is more of a time-waste unless there is a serious problem, afterall, how much bandwidth has it caused now?

Post by Ęthelwulf click to view.

#### Ęthelwulf

• Sr. Member
• Posts: 358
##### Re: Difference of weight with altitude
« Reply #13 on: 05/04/2012 18:57:25 »
Shrunk
Why has my post been censored, and why when I click it I cannot see it?
Cos it was completely off the point. We are having a problem with shrunk posts not unshrinking with the new forum software

I am sorry, but I think censoring posts is more of a time-waste unless there is a serious problem, afterall, how much bandwidth has it caused now?

All I am saying, as a moderator, you should not waste time for time.

Ironic yes? Considering I don't think time exists yes? :) But do not waste my time either. I will quickly leave this place if all it has in mind to censor my posts.

#### MikeS

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• Posts: 1044
##### Re: Difference of weight with altitude
« Reply #14 on: 07/04/2012 07:10:05 »
imatfaal

Point taken I was wrong and fgt55 was correct.

The question still has not been answered though.

I suspect that my answer should have been correct but relativistic effects have not been accounted for.  Does this make sense?

If not what does account for the difference?

It is not really something I had thought a great deal about. Relativistic effects? - possibly but which? if you got an idea I will number-crunch it.  Perhaps ask why it is assumed they should be the same, are there any consequences for them not being the same, are there positives for them not being the same.

This sort of the problem exemplifies why I always harp on about going back to the math

imatfaal
I wish I was a mathematician but I'm not and I'm too long in the tooth.

Gravitational time dilation
The gravitational constant is approximately
6.67300 × 10-11 m3 kg-1 s-2

What this does not seem to take into account is that a second at a lower altitude is longer than a second at a higher altitude so the formula can only be an approximation to reality.

It's a poor answer I know but it just seems logical.

Yes, it seems to show the inadequacies of using Newtonian gravity where relativistic effects are present.

The positives are, if I am correct, another confirmation of the correctness of GR.

#### fgt55

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##### Re: Difference of weight with altitude
« Reply #15 on: 08/04/2012 00:02:23 »
What do you think with a fixed column of water with a left fixed mass under it ? The pressure is different ? So the water move ?

#### MikeS

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##### Re: Difference of weight with altitude
« Reply #16 on: 08/04/2012 05:34:24 »
No, that would be perpetual motion.

Your reasoning is only taking into account a difference in weight due to gravity.  It is not allowing for the difference in gravitational time dilation which effectively cancels what may appear at first sight, to have been a gain.

It would be interesting if someone did the math using Newtonian gravity to see whether or not it would predict perpetual motion?
« Last Edit: 08/04/2012 08:10:56 by MikeS »

#### MikeS

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##### Re: Difference of weight with altitude
« Reply #17 on: 08/04/2012 08:05:36 »
imatfaal

Previously I assumed they would be the same as it seemed logical but could not offer any reasoning.

Here is the reasoning.
Going back to the original experiment.
It seems to me that if the gain in weight were real it could be used as the basis for a perpetual motion machine.
That's another reason for me thinking that relativistic effects need to be taken into consideration.

#### fgt55

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##### Re: Difference of weight with altitude
« Reply #18 on: 08/04/2012 10:51:11 »
Quote
It seems to me that if the gain in weight were real it could be used as the basis for a perpetual motion machine.
not at all because when you move down a reverse torque appears and you lost energy. The sum of energy is always 0 in this case like forever ;)

#### MikeS

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##### Re: Difference of weight with altitude
« Reply #19 on: 08/04/2012 12:05:51 »
You may well be right.  It obviously can't work but I can't seem to get my head around why.

#### fgt55

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##### Re: Difference of weight with altitude
« Reply #20 on: 08/04/2012 17:43:01 »
When a mass move down it lost energy because it never move up with the same gravity (it move down).

#### MikeS

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##### Re: Difference of weight with altitude
« Reply #21 on: 09/04/2012 10:48:41 »
No that's not it.  There are two masses about a fulcrum.  Assuming the fulcrum to remain an equidistant from the Earth.  The system weighs more when the weights are in vertical alignment than when they are in horizontal alignment.
When they rotate one mass moves down the other moves up so they balance and the energy of the system should remain constant.  In the vertical alignment the system weighs more which represents an increase in energy of the system.  The gravitational potential energy of the system remains the same.  As far as I understand it there should not be an increase of weight when the masses are vertically aligned.  The discrepancy, I believe is caused by not taking into account gravitational time dilation.

#### fgt55

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##### Re: Difference of weight with altitude
« Reply #22 on: 09/04/2012 12:52:28 »
Quote
When they rotate one mass moves down the other moves up so they balance and the energy of the system should remain constant.
why ?

Quote
In the vertical alignment the system weighs more which represents an increase in energy of the system.
it's normal for me, because one mass is lower and other upper. Don't forget there is a torque.

#### MikeS

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##### Re: Difference of weight with altitude
« Reply #23 on: 10/04/2012 07:43:47 »
Let me re-phrase the question to get rid of problems to do with torque and inertia.
Lets have your original system but two identical ones.  One vertical and one horizontal, both with the fulcrum the same height above the Earth.
Why is the vertical one heavier using Newtonian gravity?

#### fgt55

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• Posts: 42
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##### Re: Difference of weight with altitude
« Reply #24 on: 10/04/2012 10:31:11 »
I don't understand could you make drawings ? and explain step by step ?

#### The Naked Scientists Forum

##### Re: Difference of weight with altitude
« Reply #24 on: 10/04/2012 10:31:11 »