Why does gravitational force have two different forms?

[shounakbhatta]

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.

 

[Doc Al]

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

 

[shounakbhatta]

Sorry,

F=G.m1.m2/r^2

Can it be written:
F=-G.m.m/r^2.

 

[Dale]

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.

 

[Doc Al]

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:

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

See: Vector form

 

[shounakbhatta]

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?

 

[BruceW]

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).

 

[shounakbhatta]

Ok. Thank you very much.

 

[kweba]

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.