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

• shounakbhatta
In summary, the equation for Newton's law of universal gravitation can be written as F = G.m1.m2/r^2 or F = -G.m.m/r^2, depending on whether the force is attractive or repulsive. The negative sign is used to indicate an attractive force, as gravity is always attractive. This equation is derived from the Inverse Square Law, which states that the force between two objects is inversely proportional to the square of the distance between them.
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.

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:

$$\vec{F} = - \frac{G m_1 m_2}{r^2} \hat{r}$$
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

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.

## What is the Law of Gravitation?

The Law of Gravitation, also known as Newton's Law of Universal Gravitation, is a physical law that describes the force of gravitational attraction between two objects with mass. It states that every object in the universe exerts a gravitational pull on other objects, and this force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

## Who discovered the Law of Gravitation?

The Law of Gravitation was discovered by Sir Isaac Newton in the late 17th century. He developed this law based on his observations of the motion of celestial bodies, such as the moon and planets, and his theory of gravity.

## How is the Law of Gravitation related to the motion of objects?

The Law of Gravitation explains the force that causes objects to move towards each other. It is responsible for the motion of planets around the sun, as well as the motion of objects on Earth. It also explains why objects fall towards the ground when dropped.

## What is the equation for the Law of Gravitation?

The equation for the Law of Gravitation is F = G * (m1 * m2)/r^2, where F is the force of gravitational attraction, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them. This equation can be used to calculate the force of gravity between any two objects in the universe.

## How does the Law of Gravitation affect the motion of celestial bodies?

The Law of Gravitation is responsible for the orbital motion of celestial bodies, such as planets, around larger objects like stars. It explains why these bodies move in elliptical paths and how the strength of gravity affects their speed and trajectory. It also plays a crucial role in keeping our solar system stable and in maintaining the balance of the universe.

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