Question about the Derivation of the Gravitational Law

In summary, the conversation discusses the derivation of a law and the use of Newton's Third Law. The main question is why the next step requires the force to be squared and if there are other ways to calculate the force. The answer is that it is a convenient algebra trick to solve for the force in terms of other variables.
  • #1
ecastro
254
8
The derivation of the law have been put up in the forums but I have a question regarding its derivation.

I understood everything from the assumptions to the application of Newton's Third Law, but I got stocked at this step:

[tex] \frac{m}{k} = \frac{M}{k'} [/tex].

This is similar to

[tex] \frac{C}{M} = \frac{c}{m} = \frac{k}{4 \pi^2} [/tex]

at this site, http://www.relativitycalculator.com/Newton_Universal_Gravity_Law.shtml.

According to the same site, the next step requires the force to be squared. Why is this so? Is it merely to acquire the force ##F## between the two bodies? Aren't there any other ways to calculate the force other than multiplication?
 
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  • #2
ecastro said:
According to the same site, the next step requires the force to be squared. Why is this so? Is it merely to acquire the force ##F## between the two bodies? Aren't there any other ways to calculate the force other than multiplication?
It's just a convenient algebra trick to get both ##m## and ##M## into the equation for ##f##. We have ##f=f'## so we can multiply both sides of that equation by ##f## to get one equation that can be solved for ##f## in terms of ##k##, ##m##, and ##M##.
 
  • #3
Alright. Thank you for your help. :D
 

1. How was the gravitational law derived?

The gravitational law was derived by Sir Isaac Newton in the 17th century. He observed the motion of planets and objects falling towards the Earth and developed a mathematical equation to describe the force of gravity.

2. What is the mathematical equation for the gravitational law?

The mathematical equation for the gravitational law is F = G (m1m2)/r^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

3. How does the gravitational law explain the motion of objects in space?

The gravitational law explains that all objects in the universe are attracted to each other by a force called gravity. This force is directly proportional to the masses of the objects and inversely proportional to the square of the distance between them. This explains the motion of planets around the sun, as well as the motion of other celestial bodies.

4. What is the significance of the gravitational constant in the equation?

The gravitational constant, denoted by G, is a fundamental constant in physics that determines the strength of the gravitational force between two objects. Its value is approximately 6.67 x 10^-11 N*m^2/kg^2 and is used to calculate the force of gravity in the gravitational law equation.

5. Can the gravitational law be applied to all objects in the universe?

Yes, the gravitational law can be applied to all objects in the universe, regardless of their size or mass. However, for objects with very small masses, such as atoms, the force of gravity is negligible and other forces, such as electromagnetic forces, become more significant.

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