In this article, we shall discuss whether is gravitational force positive or negative and why gravitational force is denoted with a negative sign.

**The gravitational force is always positive, but since it is an attractive force between the two objects, it can be denoted by the negative sign. Negative gravity is the antigravity between two objects that push them away from each other.**

**What is Negative Gravitational Force?**

The gravitational force is an attractive force exerted between the two bodies having mass and that keeps them bonded together.

**If the gravitational pull exerted by the body is minute then the distance of separation between the two objects will expand due to some circumstances or external forces then it is called a negative gravitational force.**

If we look into the electrostatics, based on the charges between which this force of attraction of repulsion comes into the picture, we can say whether the force is positive or negative.

Here, it becomes difficult to say whether the gravitational force is positive or negative because mass can’t be a negative quantity. Hence, it is a theoretical explanation of the positive and negative gravitational pull of attraction.

The gravity of any object depends upon its mass. If the mass of the object is less, then the gravitational force that it can exert on other objects is very less, or zero. These objects can be easily pulled due to the gravitational attraction; hence the negative gravitational force is in terms of the lighter objects also.

**Read more on How to Calculate Mass from Gravitational Force: Several Approaches and Problem Examples.**

**Is Gravitational Force is Positive?**

The gravitational force is given by the formula F=Gm_{1}m_{2}/r^{2}

Where G=6.67*10^{-11}

m_{1} is mass of object 1

m_{2} is mass of object 2

‘r’ is a shortest path joining the two objects

**The gravitational force is always positive, but theoretically, we can write it as negative in vector form as the force of attraction between the two objects is exerted in two opposite directions.**

Consider two objects having mass M_{1} and M_{2} exerting a force F_{1} on mass M_{2} and force F_{2} on mass M_{1} respectively as shown in the below figure.

The gravitational force follows Newton’s Third Law of Motion, according to which,

“Every action has the equal and opposite reaction.”

The force reacting on each of the objects is equal but exerted in the opposite direction.

**Read more on How To Find Gravitational Acceleration: Several Approaches and Problem Examples.**

**When is Gravitational Force Positive?**

It is a very tiny force of attraction between two objects comprising a mass.

**The gravitational force is positive if that force keeps binding the two objects together and shows the force of attraction towards each other.**

When the gravitational force is exerted on the object towards each other in the two opposite directions to keep the objects bonded together with a fixed distance or approaching each other then the gravitational force is said to be positive.

**The magnitude of the gravitational force always depends upon the product of the masses of the objects and the shortest length connecting them both.**

The gravitational potential energy of the objects is given as

The negative sign indicates that the gravitational force is a force of attraction between the two bodies.

**Read more on How to find Gravitational Acceleration without Mass: Several Approaches and Problem Examples.**

**How is Gravitational Force Positive?**

If there is some work done due to the presence of the gravitational pull exertion, then the gravitational force is positive.

**The work done will be positive if there is a displacement of the two bodies between which the gravitational force acts, and the objects move towards each other due to the exertion of the gravitational pull on each body.**

Work done by the gravitational force is depicted by the formula,

Work done=F*displacement

Work done=G m_{1}m_{2}/r^{2} d

If there is work done by the bodies, then we can say that the gravitational force is positive. We can take an example of the high tides and low tides of ocean currents on the Earth due to the gravitational pull of the Moon experienced on the Earth. The high tide is seen in the area when the Moon reaches closest to that particular side of the Earth, and when the Moon moves away from that area the low tides are observed.

**Read more on Gravitational Acceleration Example: Detailed Insights.**

**Is Gravitational Force is Negative?**

The gravitational force becomes zero if the object collides with the heavy mass due to the gravitational pull.

**The gravitational force is actually not negative, but since the gravitational force is exerted equally and in the opposite direction by the two bodies having mass, the negative sign denotes the same.**

The magnitude of the gravitational force is given by the equation,

F = G m_{1}m_{2}/r^{2}

In vector form, the gravitational force is,

Where

The negative sign is because the force is an attractive force and acts along with the ‘–r’ distance.

If we consider two objects binding together with the force of gravitation as shown in the below diagram:

Then, based on the direction we can say that the force exerted on the mass ‘M_{2}’ due to mass ‘M_{1}’ is positive if we consider both masses on the x-axis. That is,

F=Gm_{1}m_{2}/r^{2}

And, the force exerted on the mass ‘M_{1}’ due to mass ‘M_{2}’ is negative as it is directed in the negative x-axis.

F= – Gm_{1}m_{2}/r^{2}

**Read more on Gravitational Force a Contact Force: Why, How, When and Detailed Facts.**

**When is Gravitational Force Negative?**

The negative gravitational force is a minute force required for an object to repel away from each other.

**This may be the case if the two objects are separated from each other at an infinite distance, or the distance of separation between the two objects increases due to internal or external effects.**

The negative gravitational force is called antigravity, a place where there is no existence of the gravitational force theoretically. Examples of the negative gravitational forces are the explosion of supernovas, the expanding universe due to dark energy.

The gravitational force on the objects surrounding the Earth is always pointing at the center of the Earth and therefore is called a center force too. But during the explosion of any supernova, the centrifugal force comes into a scenario that impacts the supernovas to explode. The centrifugal force is very high as compared to the central force.

The centrifugal force is given by the formula

F_{c} = mv^{2}/r

If the centrifugal force is equal to the gravitational force, then

mv^{2}/r =GMm/r^{2}

v=√GMm/r

This is the velocity of the object in the presence of the gravitational force, if the gravitational force is absent, then the object will sway away at an infinite distance with the energy that it receives on an explosion.

**Read more on Is Gravitational Field Strength A Vector: Why, How, Detailed Facts.**

**How is Gravitational Force Negative?**

The positive gravitational force of attraction keeps the two bodies binding together.

**The work done by the two bodies exerting a minute gravitational attraction to repel away from each other, then the gravitational force is negative.**

The attractive force between the two bodies will always try to bring them closer to each other. Certain work is done on each object to displace it towards each other. This is in the case of positive gravitational force, where the work done is positive.

**But if the separation between the two bodies keeps on increasing, and the force between the two is not constantly acting towards the center then the work done between the two will be negative and thus the two bodies will repel away from each other. Hence, the gravitational force is said to be negative.**

That is the work done will be,

Work done=-Gm_{1}m_{2}/r^{2} d

In this case, the circumstantial force acting outward that drags the bodies away from each other is more compared to the gravitational force acting equal and opposing between the two bodies. This may be the result when the two objects at separated at a wider distance from each other.

We will see another case where gravitational force can be negative. Let us consider an object having a huge mass ‘M’ and another object of very small size having a lighter mass ‘m’.

The Gravitational pull of mass ‘M’ exerted on the lighter mass ‘m’ will be far greater than the gravitational force by the mass ‘m’ on the mass ‘M’, due to this the object of mass ‘m’ will move closer and closer towards the object of mass ‘M’, thus increasing the gravitational pull on the object of mass ‘m’.

**Read more on Is Gravitational Force A Central Force: Why, How And Detailed Insights.**

**Is gravitational constant negative or positive?**

The gravitational constant is obviously a positive quantity and can’t be negative.

**The gravitational constant G=6.67*10 ^{-11} is a proportionality constant that relates the square of the distance separating the two bodies and the product of their masses equating to the gravitational force.**

**Read more on Gravitational Constant.**

Consider an object of mass ‘m’ on the Earth exerting the gravitational pull due to the Earth. Let ‘M’ be the mass of the Earth and ‘r’ be the radius of the Earth.

The gravitational force is denoted by the relation as below,

F=G Mm/ r^{2}

Where F is a gravitational force

G is a gravitational constant

M is a mass of the Earth

m is a mass of the object orbiting around the Earth

r is a radius of the Earth

**According to Newton’s Second Law of motion, the force acting on the object due to gravity is F=mg.**

Here, the force due to gravity by the Earth exerted on the object of mass ‘m’ is greater as the mass ‘M’ is bigger than the mass ‘m’. Hence, the force due to gravity by the mass ‘M’ is F=Mg. On equating this with the gravitational force equation, we have

Mg=Mm/r^{2}

So we get

g=Gm/r^{2}

Hence, we have

G=gr^{2}/m

Substituting the values in this equation, we can get the value of the gravitational constant.

We have, g=9.8m/s^{2}

The radius of the Earth r=6400km

The mass of the Earth is m= 6*10^{24}kg

Inserting these values in the above equation, we get,

G= 9.8*(6400*10^{3})^{2}/6*10^{24}

= 9.8*6400*6400*10^{-18}/6

=6.67*10^{7}*10^{-18}

=6.67*10^{-11} Nm^{2}/kg^{2}

Thus we have seen that the gravitational constant is positive.

**Read more on 10+ Examples of Gravitational Potential Energy.**

**Frequently Asked Questions**

**What is a gravitational force between the objects having mass 105kg and 2.5 × 10**^{3} kg separated by the distance 10^{3}km?

^{3}kg separated by the distance 10

^{3}km?

**Given:** m=105kg

M= 2.5 × 10^{3} kg

r= 10^{3}km

G=6.67*10^{-11}Nm^{2}/kg^{2}

We have,

F=GmM/r^{2}

=6.67* 10^{-11}{10^{5}*2.5*10^{3}/(10^{3})^{2}

=1750.9*10^{-14}

=1.75*10^{-11} N

Hence, the gravitational force between the two objects is

1.75*10^{-11} N.

**What is the escape velocity of our planet Earth?**

Escape velocity is given as vesc=√2GM/r

We know that g=GM/r^{2}.

Using this in the above equation,

v_{esc}=√2gr

Radius of the Earth r=6400km=6400*10^{3} m

=√2*9.8*6400*10^{3}

=√125.44*10^{6}

=11.2*10^{3}m/s

=11.2 km/s

**Hence, the escape velocity of the Earth is 11.2 km/s.**

**What is the gravity of the object having a mass 10**^{4}kg of radius 10m present on the Earth?

^{4}kg of radius 10m present on the Earth?

**Given:** m=10^{4}kg

r=10m

G=6.67* 10^{-11}Nm^{2}/kg^{2}

We have, g=GM/r^{2}

=6.67*10^{-11}*10^{4}/10^{2}

=6.67*10^{-9}N/kg

Hence, the gravity of the object is 6.67*10^{-9}N/kg.

**What is an escape velocity?**

The escape velocity is given by the formula

v=√2GM/r

**It is the minimum velocity required by any object to overcome the gravitational force imposed on it. This is when the potential energy gained by the object at a certain height becomes equal to its kinetic energy.**