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Gravitational Force Calculator

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Gravitational force calculator

Gravitational force calculator is used to calculate the gravitational force, the mass of the objects, and the distance between the objects using Newton’s law of gravitational force.

What is gravitational force?

Gravitational force is the force that occurs between any two objects having mass. It is responsible for the phenomenon of weight and is the reason objects fall to the ground when dropped.

There were various theories about the nature of planetary motion and celestial body interactions before this law. Newton's law of gravitation revolutionized our understanding of the universe and became a cornerstone of classical physics.

Formulation of the law

The newton law of gravitation states that:

The force of attraction or repulsion between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Mathematical expression:

F = (G * m1 * m2) / r2

Where:

  • F is the force between the two objects.
  • m1 is the Mass of the first object.
  • m2 is the Mass of the second object.
  • G is the Gravitational constant.
  • r is the Distance between the centers of m1 and m2.

Gravitational constant (G):

The gravitational constant G is a fundamental constant that appears in Newton's law of gravitation. Its value is approximately 6.67430 * 10-11 m3 kg-1 s-2. The precise determination of G was a significant scientific achievement and required meticulous experimentation.

Inverse square law:

The inverse square law in Newton's law of gravitation means that the force weakens with the square of the distance between the two masses. Consequently, the force decreases rapidly as objects move apart from each other.

Examples of gravitational force:

The gravitational force on Earth:

On Earth, the gravitational force is responsible for keeping everything anchored to its surface and giving objects their weight. It is the reason objects fall when dropped and the foundation of various natural phenomena.

The gravitational force between celestial bodies:

Gravitational force plays a crucial role in celestial mechanics. It governs the orbits of planets around the Sun, moons around planets, and even interactions between galaxies.

Gravitational force in space exploration:

Understanding gravitational force is essential for space exploration. It is used to calculate trajectories, plan space missions, and execute complex maneuvers.

How to solve gravitational force problems?

Example

Find out the mass m2 if the mass of the first object is 9 Kg, the force of attraction between them is 13N, and the distance between the masses is 7m.

Solution:

Step 1: Extract the given data

Mass of the 1st object = m1 = 9 Kg

Force = f = 13 N

Distance = r = 7 meters

G = 6.67430 * 10-11

Mass of the 2nd object = m2 =?

Step 2: Calculation

According to Newton’s law of gravitation.

F = (G * m1 * m2) / r2

Re-arranging the formula:

m2 = (F * r2) / (G * m1)

Plugging in the values:

m2 = (13 * (7)2) / (6.67430 * 10-11 * 9)

m2 = (13 * 49) / (6.67430 * 10-11 * 9)

m2 = (637) / (6.67430 * 10-11 * 9)

m2 = (637) / (60.087 * 10-11)

m2 = 1.060 * 1012

Hence the mass of the second object is 1.060 * 1012 Kg

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