Gravitational Force Formula

Gravitational Force Formula

People began to understand gravity when Newton made his discovery. Additionally, gravity is now a concept that everyone is familiar with. One can realise that every other object in the cosmos is being pulled toward itself at the same moment. Therefore, to learn more, students can read the topic to discover the gravitational force, Gravitational Force Formula, Gravitational Force Formula derivation, and solved examples based on the Gravitational Force Formula.

Gravitational Force

There are a lot of forces, pushes, and pulls in the cosmos. Additionally, humans are constantly pushing or pulling something, even if it is just the ground. However, in reality, there are just four fundamental forces in Physics, from which all other forces are generated. These forces also include Gravitational Force Formula, electromagnetic force, weak force, and strong force. 

Furthermore, any two mass-containing objects are drawn together by the Gravitational Force Formula. Additionally, this Gravitational Force Formula attracts because it never attempts to push masses apart but rather always pulls them together. Additionally, according to Newton's Universal Law of Gravitation, every object in the cosmos, including humans, pulls on every other object in the universe.

Gravitational Force Formula

Newton's law of gravitation is another name for the equation describing Gravitational Force Formula. The Gravitational Force Formula also specifies the strength of the force acting between two things. Additionally, the gravitational constant, G = 6.67 1011Nm2/kg2, is included in the equation for Gravitational Force Formula. In addition, the Gravitational Force Formula is measured in Newtons (N). 

gravitational force = (𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)(𝑚𝑎𝑠𝑠𝑜𝑓𝑜𝑏𝑗𝑒𝑐𝑡1)(𝑚𝑎𝑠𝑠𝑜𝑓𝑜𝑏𝑗𝑒𝑐𝑡2)(𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑏𝑒𝑡𝑤𝑒𝑒𝑛𝑜𝑏𝑗𝑒𝑐𝑡𝑠)2

𝐹𝑔 = 𝐺𝑚1𝑚2𝑟2

Derivation of the Gravitational Force Formula

• The Gravitational Force Formula between two objects is denoted by the symbol Fg (N = kgm/s2). 
• The gravitational constant is denoted by the symbol G (G = 6.67 1011Nm2/kg2). 
• m1 = denotes the first object's mass in kilogrammes. 
• m2 = denotes the second object's mass in kilogrammes. 
• The metres between the objects are indicated by the symbol r.

Gravity, often known as gravitation, is a phenomenon that suggests that there is a force acting between any two mass-containing objects. The Gravitational Force Formula is a constant force. 

According to the Law of Gravity, the force of gravity is directly proportional to the product of two masses, m1 and m2, and inversely proportional to the square of the distance between them if they are kept at a distance of r from one another.

The majority of the cosmos is subject to the law of gravity. Any two things gravitate toward one another like any other two galaxies. Additionally, when the distance is great enough, the attractions are tiny, perhaps even nonexistent. 

The way the stories come together can be valuable to students. They might have observed astronauts floating in space, for instance. The absence of gravity in the atmosphere is the cause of this. Students will comprehend and realise that the Gravitational Force Formula is what allows people to walk on earth.

Solved Example

Students can refer to the solved examples based on the Gravitational Force Formula that have been cited on the Extramarks website and mobile application. The notes and solutions based on the Gravitational Force Formula have been curated by Extramarks’ subject experts after great consideration and research on the past years' papers. The framework of the Gravitational Force Formula notes designed by Extramarks’ subject specialists is very easy to understand and comprehend. The Gravitational Force Formula notes are extremely internet-compatible and students can also download them for offline study and reference.

Example 1

Imagine if two earth-orbiting spacecraft come very near to one another. Furthermore, they briefly separate by 100 metres. The satellites weigh 300 kg and 20 kg, respectively. Calculate the gravitational force that exists between these satellites. 

Solution: 

By applying the Gravitational Force Formula, one may determine the strength of the force between two satellites: 

𝐹𝑔 = 𝐺𝑚1𝑚2𝑟2 

𝐹𝑔 = (6.67×10−11𝑁⋅𝑚2/𝑘𝑔2)(300𝑘𝑔)(20𝑘𝑔)(100𝑚) 

2 

𝐹𝑔 = (6.67×10−11𝑁⋅𝑚2/𝑘𝑔2)(6000𝑘𝑔2)10000𝑚2 

𝐹𝑔 = (6.67×10−11𝑁⋅𝑚2𝑘𝑔2)×6000𝑘𝑔210000𝑚2 

𝐹𝑔 = (6.67×10−11𝑁⋅𝑚2𝑘𝑔2)×(0.6000𝑘𝑔2𝑚2) 

𝐹𝑔 = (6.67×10−11𝑁⋅𝑚2𝑘𝑔2)×(0.6000𝑘𝑔2𝑚2) 

𝐹𝑔 = (6.67×10−11𝑁)× (0.600)\s𝐹𝑔 ≅ 4.00×10−11𝑁 

Therefore, the gravitational force between the two satellites at a distance of 100 is equal to 4.001011N. (Newtons).

Example 2

Two enormous spheres were used in an experiment by scientists to measure the gravitational pull. Additionally, the two spheres are 2000.0  apart and each weighs 1000.0 kg. Determine the gravitational pull between these two spheres now. 

Solution: 

So, using the Gravitational Force Formula, one can get the gravitational force between the spheres: 

𝐹𝑔 = 𝐺𝑚1𝑚2𝑟2 

𝐹𝑔 = (6.67×10−11𝑁⋅𝑚2/𝑘𝑔2)(1000𝑘𝑔)(1000𝑘𝑔)(2000𝑚) 

2 

𝐹𝑔 = (6.67×10−11𝑁⋅𝑚2/𝑘𝑔2)(1.0000×106𝑘𝑔2)4000𝑚2 

𝐹𝑔 = (6.67×10−11𝑁⋅𝑚2𝑘𝑔2)×1.0000×106𝑘𝑔24.000𝑚2 

𝐹𝑔 = (6.67×10−11𝑁⋅𝑚2𝑘𝑔2)×(2.5000×105𝑘𝑔2𝑚2) 

𝐹𝑔 =(6.67×10−11𝑁⋅𝑚2𝑘𝑔2)×(2.5000×105𝑘𝑔2𝑚2) 

𝐹𝑔 = (6.67×10−11𝑁)×(2.5000×105) 

𝐹𝑔 = 16.675×10−6𝑁 

𝐹𝑔 = 16.675×10−5𝑁 

Therefore, the gravitational force between the two spheres is 16.675 106 N in strength.