Calculation of Gravitational Force

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Welcome to class! 

In today’s class, we will be talking about the calculation of gravitational force. Enjoy the class!

Calculation of Gravitational Force

A gravitational force is experienced by any mass in a gravitational field. Masses are attracted towards each other by gravitational force. The force is there and we can calculate it.

Universal gravitational force

This equation describes the force between any two objects in the universe:

In the equation:

• 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)

So if you know how massive two objects are and how far they are apart, you can figure out the force between them.

Gravitationalforce=[ (gravitational constant)*(mass of object 1)*(mass of object 2)] / (Distance between objects)²

F_g = (G*m1*m2) / r2

Example 1

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

Solution:

So, by using gravitational formula we can find the force of gravity amid the spheres:

F_g = (G*m1*m2) / r2

F_g = [(6.67×10⁻¹¹N⋅m²/kg²)*(1000kg)*(1000kg)] / (2000m)²

F_g = [(6.67×10⁻¹¹N⋅m2/kg²)*(1.0000×106kg²)] / 4000m²

F_g = (6.67×10⁻¹¹N⋅m²/kg²)×1.0000×10⁶kg² /4.000m²

F_g = (6.67×10⁻¹¹N⋅m² /kg²)×(2.5000×105kg²/m²)

F_g =(6.67×10⁻¹¹N⋅m² /kg²)×(2.5000×105kg²/m²)

F_g = (6.67×10⁻¹¹N)×(2.5000×105)

F_g = 16.675×10⁻⁶N
F_g = 16.675×10⁻⁵N

So, the magnitude of the gravitational force amid two spheres is 16.675×10⁻⁶N.

Example 2

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:

We can calculate the magnitude of the force between two satellites using the gravitational force formula:

F_g = (G*m1*m2) / r2

F_g = [(6.67×10⁻¹¹N⋅m² /kg²)*(300kg)(20kg)] / (100m)²

F_g = [(6.67×10⁻¹¹N⋅m² /kg²) × (6000kg²)] / 10000m²

F_g = (6.67×10⁻¹¹N⋅m² /kg²)×(0.6000kg² /m²)

F_g = (6.67×10⁻¹¹N⋅m² /kg²)×(0.6000kg² /m²)

F_g = (6.67×10⁻¹¹N)× (0.600)
F_g ≅ 4.00×10⁻¹¹N

So, the magnitude of the gravitational force between the two satellites when they were at a distance of 100 is 4.00×10⁻¹¹N (Newton).

 

In our next class, we will be talking about Space Travel.  We hope you enjoyed the class.

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