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Given Kepler's Laws how do you derive Newton's Law of Gravitation?
AUK 1138 said:I don't believe any of Kepler's laws were used to create Newton's law. Newton added an expression to one of Kepler's laws to allow it to work in standard SI units as opposed to only years/ AU, but i think that's where the "teamwork" ends. I could be wrong, though.
lavinia said:Given Kepler's Laws how do you derive Newton's Law of Gravitation?
lavinia said:going from inverse square to ellipse is classical.
the other way around seems hard. I agree that equal area in equal time seems like a good starting place.
Cleonis said:Well, Kepler's second law, that equal areas are swept out in equal intervals of time, is equivalent to conservation of angular momentum.
Conservation of angular momentum applies for any central force, not specifically for the inverse square law of gravity. So you can't bring the area law to bear on this question; the area law doesn't single out the inverse square law.
lavinia said:Given Kepler's Laws how do you derive Newton's Law of Gravitation?
lavinia said:Given Kepler's Laws how do you derive Newton's Law of Gravitation?
Cleonis said:A Google search with the keywords "gravity" "kepler" "integrate" "ellipse" gave several promising links,
Newton's Law of Gravitation is a fundamental law of physics that describes the force of gravitational attraction between two objects. It states that every object in the universe exerts a force of attraction on every other object, and this force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Newton derived his law of gravitation through a combination of mathematical reasoning and observations of the motions of celestial bodies. He used his laws of motion and the concept of universal gravitation to develop a mathematical formula that accurately described the gravitational force between two objects.
The key components of Newton's Law of Gravitation are the masses of the two objects, the distance between them, and the gravitational constant (G). The masses of the objects determine the strength of the gravitational force, while the distance between them and the value of G determine the magnitude of the force.
Newton's Law of Gravitation is a simplified version of Einstein's theory of general relativity, which provides a more comprehensive understanding of gravity. While Newton's law works well for most everyday situations, it breaks down at extremely large distances or in the presence of very massive objects. Einstein's theory takes into account the curvature of space-time caused by the presence of mass, providing a more accurate description of gravity.
Yes, there are some limitations to Newton's Law of Gravitation. It is only accurate for objects with masses that are relatively small compared to the masses of planets or stars. It also does not take into account the effects of relativity or the presence of other forces, such as electromagnetic forces, which can also influence the motion of objects.