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Discussion Overview

The discussion revolves around the application of Newton's law of gravitation, particularly in hypothetical scenarios involving masses of varying sizes and configurations. Participants explore the implications of gravitational forces between large masses, such as Earth-sized objects, and question the validity of gravitational equations under specific conditions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions the validity of the gravitational force equation F=GM^2/d^2 when considering two Earth-sized masses, arguing that the gravitational forces cancel each other out.
  • Another participant asserts that equal and opposite forces do not cancel out in the context of gravitational interactions, using the example of a baseball being thrown to illustrate this point.
  • There is a suggestion that the gravitational equation must be adjusted when dealing with non-point masses, referencing Newton's gravity theory and the shell theorem.
  • Participants discuss the implications of having masses with equal size but different gravitational effects, particularly in relation to the center of mass.
  • One participant expresses confusion regarding the application of gravitational equations to non-point masses and the relevance of density in this context.
  • Another participant emphasizes that the force experienced by one mass is only from the other mass, highlighting the attractive nature of gravitational forces between them.

Areas of Agreement / Disagreement

Participants express differing views on the application of gravitational equations in hypothetical scenarios, with no consensus reached on the validity of the arguments presented. Some participants challenge the interpretations and assumptions made by others, indicating ongoing debate.

Contextual Notes

Participants note the importance of considering density and the nature of point masses when applying gravitational equations. There are unresolved questions regarding the implications of gravitational forces when masses are not treated as point-like.

Who May Find This Useful

This discussion may be of interest to those exploring gravitational theory, the nuances of Newton's laws, and the implications of mass and distance on gravitational interactions.

zarmewa
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QUESTION ONE

Newton derived F=GMm/R^2 by puting one kg of sphere on the surface of earth. Now consider if the same sphere is bigger and bigger till it reach the size of earth. OR simply put imaginary Earth on Earth

Now apply F= GMm/R2 where g = GM/d2. M= m= mass of Earth = mass of imaginary earth, centre to centre distance between two masses = diameter of earth.
According to universal law of gravitation; there is force of F=GM^2/d^2 between aforementioned masses.

As gravities of both Earth's cancel out and both masses exert a force which is equal but opposit in direction on each other therefore it is wrong to say that there is force of F=GM^2/d^2 between aforementioned masses.

This means that weight of mass of 1 kg of sphere is start decreasing by increasing its size on the surface of ground.

________________________________-

Suppose there are two sphere of masses m1 = m2 = 1 kg, diameter of m1 = m2 = 0.5 m. Both masses are in space and the centre to center distance between them is 1 metre = r , then
F= Gm1m2/r2 = G = 6.67*10-11 Newton.

But technically, both masses exert a force which is equal but opposit in direction on each other (gravaties of both masses g= Gm2/r2= Gm1/r2) and hence cancel out.

if not, how come F= Gm1m2/r2 = G = 6.67*10-11 Newton exist and how both are gravitating and falling masses at the same time.

QUESTION TWO

Let “P” is a point or an origin of two circles of radius r1=1 meter and r2= 2 meter. Consider these two circle are spheres (empty from inside) or two bangles in space. OR a spherical boiled egg with removed shell such that the center of the sperical white and yolk coinicide each other at one point say “P”.

Now apply Newton’s law of gravitation i.e. F=GMm/R2 to aforementioned two masses and neglect all other local attractions.

As center to center distance b/t masses is zero, therefore F= infinity but in reality it's not.

Now how much force is required to separate aforementioned masses, infinity or less? If less then what about the Newton’s law?
 
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You seem to be ignoring density.
 
No, that's not it, he's just ignoring how forces interact:
As gravities of both Earth's cancel out and both masses exert a force which is equal but opposit in direction on each other therefore it is wrong to say that there is force of F=GM^2/d^2 between aforementioned masses.
Having an equal and opposite force pair is not cancelling out. The equation is correct.

An example: if you throw a baseball, the baseball and your hand exert equal and opposite forces on each other. Does that mean they cancel out and the ball drops straight down to the ground as soon as it leaves your hand? Of course not!

For question two, you are applying the equation incorrectly. The gravity equation does indeed assume you are dealing with point masses, so if you are not, in fact, dealing with point masses, you must adjust your usage of the equation. How to deal with this issue is, in fact, part of Newton's own gravity theory. http://en.wikipedia.org/wiki/Shell_theorem

You may want to consider that the issues you are raising (when real, anyway...) are so spectacularly obvious that not even the very first physicist to start to generate theories of motion and gravity overlooked them -- and as a result, perhaps you should adjust your posture/tone to one of accepting and questioning your own ignorance instead of questioning the theories.
 
russ_watters said:
No, that's not it, he's just ignoring how forces interact: Having an equal and opposite force pair is not cancelling out. The equation is correct.

An example: if you throw a baseball, the baseball and your hand exert equal and opposite forces on each other. Does that mean they cancel out and the ball drops straight down to the ground as soon as it leaves your hand? Of course not!

For question two, you are applying the equation incorrectly. The gravity equation does indeed assume you are dealing with point masses, so if you are not, in fact, dealing with point masses, you must adjust your usage of the equation. How to deal with this issue is, in fact, part of Newton's own gravity theory. http://en.wikipedia.org/wiki/Shell_theorem

You may want to consider that the issues you are raising (when real, anyway...) are so spectacularly obvious that not even the very first physicist to start to generate theories of motion and gravity overlooked them -- and as a result, perhaps you should adjust your posture/tone to one of accepting and questioning your own ignorance instead of questioning the theories.

Very well stated.

Claude
 
russ_watters said:
if you are not, in fact, dealing with point masses, you must adjust your usage of the equation.

That's what I meant by density, but I stated it pretty badly. Thanks for the tune-up.
 
the size is as big as Earth ,but the mass is 1kg,it's a constant.
 
cabraham said:
Very well stated.

Claude


so simple F1=GM^2/d^2= GM^2/d^2=F2 so 1=1 and in q2 just ignore the spherical boiled egg portion
 
O didn't ignore it, I pointed you to a link that discusses how to solve it!
 
please consider the center of mass
 
  • #10
Actually I am quit busy and didn't go through his link therefore I advised for instance just to ignore a portion of q2. i will be back once i go through the link regarding spherical gravity.

its weird but real

Khattak
 
  • #11
q1: Both gees (accelerations) are equal but opposite in direction
q2: Your link is irrelevant
______________
Khattak
 
  • #12
What are you talking about?
 
  • #13
The force on the first Earth is only from the second Earth and it is attractive. The force on the second Earth is only from the first Earth and it is attractive as well. If one were placed equidistant between the two bodies, then you would experience a net force of zero only if the second Earth had a mass equal to the first Earth (but you stated it had a mass of 1 kg), but you would still experience the two forces pulling you asunder. Either way, the two bodies still experience a force, the first Earth towards the second earthand the second earthto the first earth.
 

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