Problem with gravity and masses

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Discussion Overview

The discussion revolves around the interpretation of the gravitational force equation \( F = \frac{G m_1 m_2}{r^2} \) and the implications of a derived constant \( Z \) based on the masses involved. Participants explore the relationship between the gravitational force, the masses of two bodies, and the distance separating them, questioning the meaning and relevance of the constant \( Z \) in different scenarios.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that \( Z \) remains constant regardless of the distance \( r \) between two bodies, leading to confusion when considering different mass combinations.
  • Another participant argues that \( Z \) does not hold meaning unless the bodies are separated, indicating that different configurations yield different \( Z \) values.
  • There is a repeated questioning of what \( Z \) signifies, with one participant expressing uncertainty about its implications and suggesting it seems unique.
  • One participant asserts that \( Z \) is dependent on \( r \) and cannot be considered independent, comparing it to a mathematical function where changes in one variable affect the outcome.

Areas of Agreement / Disagreement

Participants express differing views on the significance and constancy of \( Z \). There is no consensus on its meaning or relevance, and the discussion remains unresolved regarding the implications of varying mass configurations on \( Z \).

Contextual Notes

Participants highlight that the interpretation of \( Z \) may depend on the specific conditions of the masses and their separation, indicating potential limitations in understanding its role in gravitational interactions.

atom888
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hi guys,

I was playing around with Newton Equation F=Gm1m2/r^2

I separate Fr^2 = Gm1m2 . This is bugging me. Fr^2 is a constant for a given 2 bodies(i call Z) of masses. That means that no matter what the distance r in between the two bodies, Z doesn't change. So i take my thought alittle further. Suppose the two bodies are almost infinite small with say ... 5 and 10 mass. so Z value is 50G. Since no matter how close u put them together, the value Z doesnt' change. I put them so close together that they almost like 1 body with a total mass of 15mass. Now I imagine what if they are 7 and 8 mass. The Z value is 56G. I put them through the same process and let them come so close together that they're almost 1 body with 15mass. Now it looks like I have two identical bodies with different Z value. It seems disturbing.
 
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but "Z" doesn't mean anything unless the bodies are separated and if you separate them in two different ways it shouldn't be surprising that you get two different "Z values".
 
I guess the question is... what does Z means. lol I imagine r^2 as a square and F go up and down to have a constant volume. Though I don't know what it means, but it seems unique.
 
atom888 said:
I guess the question is... what does Z means. lol I imagine r^2 as a square and F go up and down to have a constant volume. Though I don't know what it means, but it seems unique.

it doesn't mean a thing besides G*M_1*M_2... which has only one value for a given M_1 and M_2 but may be different for different values of M_1 and M_2... even when M_1 + M_2 =M_tot is fixed, as you see in your example. but that, too, is meaningless.
 
olgranpappy said:
it doesn't mean a thing besides G*M_1*M_2... which has only one value for a given M_1 and M_2 but may be different for different values of M_1 and M_2... even when M_1 + M_2 =M_tot is fixed, as you see in your example. but that, too, is meaningless.


Fine! I'll keep it as an souvenir. lol
 
Z is a function of r. You can't say that Z is independent of r...basically, when r changes, Z changes. It's just like saying that y=Gx^2 but y doesn't change while x can, it's just completely nonsensical.
 

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