
#1
Feb2510, 01:58 PM

P: 112

If we consider the classical formula of gravitational force F = [tex]\frac{Gm_{1}m_{2}}{r^{2}}[/tex], then can the antigravitational force responsible for the accelerated expansion of the universe be represented by F = [tex]\frac{r^{2}}{Gm_{1}m_{2}}[/tex] ?
Thus, since the (MKS) magnitude of G = 10 [tex]^{11}[/tex], would the antigravitational force be smaller than the gravitational force by a factor of 10 [tex]^{11}[/tex] ? 



#2
Feb2510, 02:02 PM

Sci Advisor
P: 1,883

No, you switch signs, and let the equation otherwise unchanged.




#3
Feb2510, 03:29 PM

P: 2,043

I don't think there's a well defined "antigravitational force" at all...Dark energy is quite mysterious at this point. There is no indication that a modified gravitational theory is needed. 



#4
Feb2510, 04:02 PM

Sci Advisor
P: 1,547

Formula of antigravitational force
Also want to mention that one does not need to modify gravitational theory to get "antigravitational force". By the way, I hate that phrase, considering there isn't any cosmological scale gravitational force affecting the expansion (the Newtonian potential is zero in a homogeneous universe) and the word "antigravity" has crackpot written all over it. In any case, you can get "antigravitational phenomena" (ie accelerated expansion) by just playing with the kind of gravitational source that you plug into the regular old equations of GR. In GR, one can get accelerated expansion by sourcing gravity with a negative pressure fluid.




#5
Feb2610, 02:43 AM

P: 112





#6
Feb2610, 03:02 AM

Sci Advisor
P: 1,883





#7
Feb2610, 03:55 AM

P: 112

When it comes to the formula of interaction between two discrete masses over an unit distance, F = [tex]\frac{Gm_{1}m_{2}}{r^{2}}[/tex]......(2), switched signs alone merely indicate opposite directions  the negative signed formula of antigravitational force between discrete masses does not represent increase of force over distance, unlike the volume formula (1) of antigravitational force, which describes the increase of antigravitational force over distance. So I am wondering what would be the formula/condition for antigravitational force to increase between discrete masses over unit distance? 



#8
Feb2610, 08:33 AM

Sci Advisor
P: 1,883

And there's no difference in whether you consider gravitation or "antigravitation". 



#9
Feb2610, 10:41 AM

P: 112

In the ~r equation we mandate the mass density is to remain constant for antigravitational force to increase with distance. What do we mandate in the 1/r[tex]^{2}[/tex] equation for the antigravitational force between two discrete masses to increase with distance, even though distance goes as 1/r[tex]^{2}[/tex] ? Do we mandate mass [tex]\propto[/tex] r or r[tex]^{2}[/tex]? 


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