Law of Gravitation: F=G.m1.m2r^2?

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    Gravitation Law
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Discussion Overview

The discussion revolves around the formulation of the law of gravitation, specifically the equations F=G.m1.m2/r^2 and F=-G.m.m/r^2. Participants explore the implications of these equations, particularly in terms of vector representation and the nature of gravitational force.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question whether F=G.m1.m2/r^2 can be expressed as F=-G.m.m/r^2.
  • One participant asserts that the first version makes no sense, referencing Newton's law of universal gravitation.
  • Another participant clarifies that the negative sign in F=-G.m.m/r^2 indicates that gravity is always attractive.
  • There is a discussion about using the minus sign in vector expressions to denote attractive forces, with an example provided.
  • Some participants agree that for repulsive forces, the sign would be positive, contrasting with the treatment of gravitational forces.
  • One participant discusses the relationship between distance and force, referencing the Inverse Square Law.

Areas of Agreement / Disagreement

Participants express differing views on the formulation of the gravitational force equations and the use of the negative sign. There is no consensus on whether the equations can be interchanged or how they should be represented in vector form.

Contextual Notes

Participants highlight the importance of context in using the equations, particularly regarding the nature of the forces (attractive vs. repulsive) and the implications of vector notation. There are unresolved aspects concerning the precise definitions and applications of the equations discussed.

shounakbhatta
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I was going through a site which tells:

F=G.m1.m2r^2

Also

F=-G.m.m/r^2.

Can it be written?

Thanks.
 
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shounakbhatta said:
I was going through a site which tells:

F=G.m1.m2r^2

Also

F=-G.m.m/r^2.

Can it be written?

Thanks.
The first version makes no sense.

See: Newton's law of universal gravitation
 
Sorry,

F=G.m1.m2/r^2

Can it be written:
F=-G.m.m/r^2.
 
Yes, if and only if m1=m2=m.

EDIT: actually I just noticed the minus sign. You have to be careful that gravity is always attractive, never repulsive.
 
shounakbhatta said:
Sorry,

F=G.m1.m2/r^2

Can it be written:
F=-G.m.m/r^2.
Sometimes when writing the force as a vector expression a minus sign is used to indicate that it's an attractive force:

[tex]\vec{F} = - \frac{G m_1 m_2}{r^2} \hat{r}[/tex]
Where [itex]\vec{r}[/itex] is the position vector of m_2 with respect to m_1 and [itex]\vec{F}[/itex] is the gravitational force on m_2 due to m_1.

See: Vector form
 
Ok, so writing force as a vector we use minus.

As gravity is always attractive, so can we always use minus sign and don't use minus sign when any force is repulsive, like electric?
 
yep. As Doc Al said, the important part is if on the left-hand side, we have the force on 1 due to 2, and if on the right hand side we have the position of 1 with respect to 2, then we need the minus sign for an attractive force. (And this is the most common way it is written). And yes, for a repulsive force, it will be positive. (this is automatically taken into account by multiplying the two charges together in the case of electric force).
 
Ok. Thank you very much.
 
shounakbhatta said:
I was going through a site which tells:

F=G.m1.m2r^2

Yes, as what with the others have said, we use a minus sign to indicate (an attractive) force as a vector.

So the equation, with R2 proportional to Force, should and would be:

F = G M1M2 r-2

So that R-2 would mean to be inversely proportional to the Force (F), equal to the second equation in your original post.

The equation is derived from the Inverse Square Law: The greater the (square) distance between objects/masses, the lesser the force; and vice versa.
 

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