Gravitational Force Calculator

Gravitational force is one of the fundamental forces of nature that governs the attraction between two objects with mass. Whether you're a student, researcher, or someone curious about physics, calculating gravitational force can seem challenging. That’s why we’ve developed this Gravitational Force Calculator to make the process easy and accurate.

What is Gravitational Force?

Gravitational force is the attractive force between two masses. This universal force acts on all objects in the universe, pulling them toward one another. Sir Isaac Newton’s law of universal gravitation explains the concept, stating that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

The formula to calculate gravitational force is:

$$F=G\frac{m_1\cdot m_2}{r^2}$$

Where:

• $F$ = Gravitational force (measured in Newtons, N)
• $G$ = Universal gravitational constant ($6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$)
• $m_1$ = Mass of the first object (in kilograms)
• $m_2$ = Mass of the second object (in kilograms)
• $r$ = Distance between the centers of the two objects (in meters)

How to Calculate Gravitational Force

To calculate gravitational force:

1. Identify the masses of the two objects.
2. Measure the distance between the centers of the two objects.
3. Substitute the values into the formula.

For example:
If $m_1 = 5 \, \text{kg}$, $m_2 = 10 \, \text{kg}$, and $r = 2 \, \text{m}$:

$$F=G\frac{5\cdot 10}{2^2}=6.674\times 10^{-11}\frac{50}{4}=8.34\times 10^{-10}\text{N}$$

Gravitational Force on Earth

Earth’s gravitational force is what gives us weight. The force is derived from the same formula, but instead of two objects, one mass is Earth’s mass ($5.972 \times 10^{24} \, \text{kg}$) and the other is the object's mass. The distance is the radius of Earth ($6.371 \times 10^6 \, \text{m}$.

The acceleration due to gravity on Earth is $9.8 \, \text{m/s}^2$.

For an object of mass $10 \, \text{kg}$:

$$F=m\cdot g=10\cdot 9.8=98\text{N}$$

How to Use the Gravitational Force Calculator

1. Enter the masses of the two objects.
2. Input the distance between the objects.
3. Click “Calculate” to get the gravitational force, along with additional data like acceleration and escape velocity.

Gravitational Force Comparison

Final Verdict

The gravitational force is a fascinating concept that governs the motion of celestial bodies and our daily lives. Using our Gravitational Force Calculator, you can easily compute the gravitational force between objects or study the gravitational pull of planets. It’s a powerful tool for students, educators, and space enthusiasts.

FAQs

What is the gravitational force unit?

The gravitational force is measured in Newtons (N).

Can I calculate the force for celestial bodies?

Yes, you can use the masses and distances of planets or stars to calculate their gravitational force.

How does distance affect gravitational force?

The gravitational force decreases as the distance between objects increases, following an inverse-square law.

What is the gravitational constant (G)?

It is a universal constant with a value of $6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$.

Can the calculator calculate the weight of an object on a planet?

Yes, by entering the planet's mass and radius along with the object's mass.