# Gravitational Force Calculator

Calculating gravitational force for an object using the Gravitational Force Calculator is free online. STUDYQUERIES’s online gravitational force calculator tool makes it easier to calculate gravitational force and to get the result in a fraction of a second.

## How to Use the Gravitational Force Calculator?

To use the gravitational force calculator, follow these steps:

• Step 1: Enter the masses of two objects, their distance, and x for the unknown value in the input field
• Step 2: Calculate the gravitational force by clicking “Calculate x”
• Step 3: The gravitational force will be displayed in the output field

## What is Gravitational Force?

The gravitational force is explained by Newton’s Law of Universal Gravitation. Every massive particle in the universe attracts every other massive particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Observations made by induction led to the formulation of this general physical law.

One way to state the law in a more modern way is to say that every point mass is attracted to every other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

We are surrounded by gravitational force. When a basketball is thrown, it will travel a certain distance before returning to the surface, depending on how much we weigh. The gravitational force on Earth equals the force you exert on the Earth. The gravitational force equals your weight when you’re at rest on or near the surface of the Earth. If you stood on a scale on a different astronomical body like Venus or the Moon, it would show you that you weighed a different amount.

A gravitational lock occurs when the gravitational force of two objects is concentrated at a location that is not at either object’s center but at the barycenter of the system. Similar to a see-saw, the principle is the same. When two people of very different weights sit on opposite sides of the balance point, the heavier one must sit closer to it so that their masses are equal.

In this case, the heavier person must sit at half the distance from the fulcrum if they weigh twice as much. As the barycenter is the balance point of the Earth-Moon system, the balance point of the see-saw is its center of mass. In fact, it moves around the Sun in the orbit of the Earth, whereas the Earth and Moon move around the barycenter in their orbits.

Galaxy systems, and possibly the entire universe, have barycenters. The gravitational pull and push of the objects in space prevent everything in space from colliding with each other.

### The Universality of Gravity

In addition to gravitational interactions between the earth and other objects, there are interactions between the sun and the planets as well. Gravitational interactions occur between all objects with an intensity that is directly proportional to the product of their masses. As you sit in your physics classroom seat, you are gravitationally attracted to your lab partner, to the desk where you are working, and even to your physics book.

Newton’s revolutionary idea was that gravity is universal-all objects attract in proportion to their mass. Gravity is universal. Most gravitational forces are so small that they are insignificant. When the mass of objects becomes large, gravitational forces become noticeable. Calculate the force of gravity between the following familiar objects using Newton’s universal gravitation equation.

### The Universal Gravitation Equation

Newton’s law of universal gravitation extends gravity beyond the earth. Newton’s law of universal gravitation deals with gravity’s universality. Newton’s place in the Gravity Hall of Fame is not due to his discovery of gravity, but rather to his discovery that gravitation is a universal force. Every object is attracted to another by gravitation. Gravity is universal.

There is a force of gravitational attraction between two objects that is directly proportional to their masses and inversely proportional to the square of the distance between their centers. Newton’s conclusion about the magnitude of gravitational forces can be simplified as follows:

$$F\propto{\frac{M\times m}{r^2}}$$

• F is the force of gravity (measured in Newtons, N)
• G is the gravitational constant of the universe and is always the same number
• M is the mass of one object (measured in kilograms, kg)
• m is the mass of the other object (measured in kilograms, kg)
• r is the distance those objects are apart (measured in meters, m)

Because gravitational force is directly proportional to mass, more massive objects will attract each other with a greater gravitational force. Therefore, as the mass of either object increases, so does the force of gravitational attraction between them.

A doubled mass of one of the objects will double the force of gravity between them. When one of the objects’ mass is tripled, the force of gravity between them is also tripled. When the mass of both objects is doubled, then the force of gravity between them is quadrupled, and so on.

Gravitational forces are inversely proportional to the square of the separation distance between two interacting objects, so more separation distance results in weaker gravitational forces. The force of gravitational attraction between two objects decreases as they become farther apart.

The force of gravitational attraction is reduced by a factor of 4 by doubling the separation distance between two objects (increased by a factor of 2). Any separation distance between two objects is tripled (increased by a factor of 3), so the gravitational attraction between the objects is decreased by a factor of 9 (3 raised to the second power).

### Gravitational Force Formula

Newton’s law of gravitation is also known as the gravitational force formula. It also defines the magnitude of the force between two objects. In addition, the formula for gravitational force includes the gravitational constant, $$G=6.67\times 10^{-11}\frac{N\times {m^2}}{kg^2}$$ Besides, the unit of gravitational force is Newtons (N).

$$Gravitational\ Force\ (F_g) = \frac{(Gravitational\ Constant)(Mass\ Of\ Object\ 1)(Mass\ Of\ Object\ 2)}{(Distance\ Between\ Objects)^2}$$

$$F_g=G{\frac{(m_1\times m_2)}{r^2}}$$

Fg = refers to the gravitational force between two objects (N = kg⋅m/s²)

G = refers to the gravitational constant

m1 = refers to the mass of the first object in kilogram

m2 = refers to the mass of the second object also in kilogram

r = refers to the distance between the object in meters

### Gravitational Force Example

Suppose two satellites that orbit the earth passes close to each other. Also, for a moment they are 100 m apart. Furthermore, the masses of the satellites are 300 kg and 20 kg. So, calculate the magnitude of the force of gravity between these satellites?

Solution: Using the gravitational force formula, we can calculate the magnitude of the force between two satellites:

$$F_g=G{\frac{(m_1\times m_2)}{r^2}}$$

$$F_g=\frac{6.67\times 10^{-11}\frac{N\times m^2}{Kg^2}\times {2300\ Kg}{\times 20\ Kg}}{100\ m^2}$$

$$F_g=\frac{6.67\times 10^{-11}\frac{N\times m^2}{Kg^2}\times {6000\ {Kg}^2}}{10000\ m^2}$$

$$F_g=6.67\times 10^{-11}\frac{N\times m^2}{Kg^2}\times \frac{6000\ {Kg}^2}{10000\ m^2}$$

$$F_g=6.67\times {10^{-11}}{\frac{N\times m^2}{Kg^2}\times 0.6000\frac{{Kg}^2}{m^2}}$$

$$F_g=6.67\times 10^{-11}\frac{N\times m^2}{Kg^2}\times {0.6000\frac{{Kg}^2}{m^2}}$$

$$F_g={6.67\times 10^{−11}N}\times {0.600}$$

$$F_g={4.00\times {10^{−11}}N}$$

As a result, the gravitational force between the two satellites when they were at a distance of 100 is $${4.00\times 10^{−11}N}$$

Scientists put an experiment to measure the gravitational force using two large spheres. In addition, both the spheres are 1000.0 kg, and their centers of mass are 2000.0 m apart. Now, calculate the gravitational force between these two spheres?

Solution: Using the gravitational formula we can find the force of gravity between the spheres as follows:

$$F_g=G{\frac{(m_1\times m_2)}{r^2}}$$

$$F_g=\frac{6.67\times 10^{-11}\frac{N\times m^2}{Kg^2}\times {1000\ Kg}{\times 1000\ Kg}}{2000\ m^2}$$

$$F_g=\frac{6.67\times 10^{-11}\frac{N\times m^2}{Kg^2}\times {1.00\times {10^6}\ {Kg}^2}}{4.00\times {10^6}\ m^2}$$

$$F_g=6.67\times 10^{-11}\frac{N\times m^2}{Kg^2}\times \frac{{1.00\times {10^6}\ {Kg}^2}}{{4.00\times {10^6}\ m^2}}$$

$$F_g=6.67\times 10^{-11}N\times 0.25$$

$$F_g={1.66\times {10^{−11}}N}N$$

So, the magnitude of the gravitational force amid two spheres is $$1.66\times 10^{-11}N$$

## FAQs

How do you solve gravitational force problems?

Newton’s equations can be used to calculate the gravitational attraction between two objects. Newton’s equation for gravitational force is F = G (M x m) / r squared, where M is the mass of one object, m is the mass of the other object, and r is the distance between their centers.

How much is the gravitational force?

The nominal “average” value at Earth’s surface, known as standard gravity is, by definition, 9.80665 m/s2 (32.1740 ft/s2).

How do you find the mass of gravitational force?

Understand Newton’s Second Law of Motion, F = ma.

• The equation F = ma can be summarized as follows: F is the force, m is the mass, and a is the acceleration.
• Using this law, we can calculate the gravitational force of any object on the earth’s surface based on the acceleration caused by gravity.

What is gravitational force?

Gravitational force is a force exerted by the earth on all objects on it. When a ball is thrown up, it falls to the ground because of gravitational force. The water from a tap always flows downwards because of gravitational force.