Law of gravitation


by shounakbhatta
Tags: gravitation
shounakbhatta
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#1
Jan7-13, 12:59 PM
P: 268
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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Doc Al
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#2
Jan7-13, 01:04 PM
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Quote Quote by shounakbhatta View Post
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
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#3
Jan7-13, 01:11 PM
P: 268
Sorry,

F=G.m1.m2/r^2

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

DaleSpam
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#4
Jan7-13, 01:35 PM
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Law of gravitation


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
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#5
Jan7-13, 01:36 PM
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Quote Quote by shounakbhatta View Post
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
shounakbhatta
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#6
Jan7-13, 02:57 PM
P: 268
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
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#7
Jan8-13, 02:10 PM
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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
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#8
Jan9-13, 01:27 AM
P: 268
Ok. Thank you very much.
kweba
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#9
Jan9-13, 07:13 AM
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Quote Quote by shounakbhatta View Post
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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