Why? A Calculus was invented by Newton and Leibnitz and others because there were not ways of doing it 'simply'. If you have a problem with calculus then the best way to deal with that is to learn about it and get to love it. You cannot do without it.Nousher Ahmed said:I want to evaluate it with another simple way except calculas.
One way to prove V=-(GM)/r without using calculus is by using the definition of potential energy, which states that the potential energy of an object is equal to the negative of the work done by an external force in bringing the object from infinity to its current position. By considering the gravitational force between two objects at different distances, the potential energy can be calculated and shown to be equal to -(GM)/r.
Aside from using the definition of potential energy, other mathematical methods that can be used to prove V=-(GM)/r include using the inverse square law for gravitational force, using the concept of conservative forces, and using the concept of equipotential surfaces.
The concept of conservative forces is related to proving V=-(GM)/r because gravitational force is a conservative force, meaning that the work done by the force is independent of the path taken. This allows us to calculate the potential energy at any point in space without needing to know the exact path of the object.
No, it is not possible to prove V=-(GM)/r without any mathematical calculations. The concept of potential energy and gravitational force are mathematical concepts that require calculations to prove their relationship. However, the proof can be simplified and shown visually through diagrams and illustrations.
Proving V=-(GM)/r without using calculus can benefit our understanding of the concept by providing a more intuitive and visual approach. It allows us to understand the relationship between distance and potential energy without needing to know complex mathematical calculations. Additionally, it can also help us understand the limitations and assumptions of the equation.