In your opinion, how do Newton's three laws of motion lead to the law of gravitation?

How can these laws be used to describe the motion of the planets in our solar system?



First correct answer gets 10 points - please note this is a 2 part question. Thanks!In your opinion, how do Newton's three laws of motion lead to the law of gravitation?Well, Newton's third law of motion says that forces come in pairs, that is, if one planet exerts a force on another planet, the forces must be equal. This can't happen if the masses of the planets were subtracted or divided because then the forces wouldn't be equal when you calculated the force between them. So, Newton's third law says that for gravitation, the masses of two objects must be added or subtracted.



Now, Newton's second law says that F=ma. We all know that on Earth, falling objects fall with the same acceleration, no matter what its mass. Thus, a=F/m must be constant no matter what your mass is. This means that the masses in the law of gravitation can't be added, because that would make a still dependent on your mass. So Newton's second law says that in the law of gravitation, masses must be multiplied together.



Well, we know that F=ma, and that Fg(force of gravity) = GMm/r^2. So simply but, a = GM/r^2, where M is the mass of the sun in an orbit. Let's assume its in perfectly circular motion so this a = v^2/r, so v = sqrt(GM/r). In a perfectly classical sense, if we know how far away a planet is from the sun, we can know how fast its going by this equation. Of course there's other influences of gravity, so orbits like Mercury and Pluto are particularly badly predicted by this, but that requires Einstein, which is out of the fields of this question.