2/20/2023 0 Comments Sir isaac newton laws of motion![]() ![]() This equation assumes that m 1 is orbiting around m 2. V = d / Δ t, where the time period (Δ t) is the period of one orbit ( P) and distance is the circumference of a circle (2 πr) giving, If it’s faster than the escape velocity - when the kinetic energy is equal to the gravitational potential energy (discussed in Chapter 14) - then it will leave the Earth’s orbit. If it reaches the orbital velocity (discussed in Section 5.3) - where the gravitational force equals the centripetal force - then it will orbit the Earth in a circle or ellipse. If it’s slow, then it will fall straight down. ![]() If gravity is present, then its path will depend on its velocity. Without gravity, the cannonball should move in a straight line. Here Newton imagined a cannon on top of a mountain. In 1728, Newton demonstrated the universality of the force of gravity with his cannonball thought-experiment. 5.2.1 Newton’s cannonball thought experiment This means that it can account for both the force that causes the planets to orbit the Sun - as described by Kepler - and the downward force that causes objects to accelerate towards the Earth - as described by Galileo. Most importantly, it affects everything with mass - and has nothing to do with an object’s charge or chemical composition. Newton stated that the force of gravity is always attractive, works instantaneously at a distance, and has an infinite range. ![]() Finally, G is a constant that is the same for everything in the universe. r is the distance between the two masses. F 1 is the gravitational force produced by m 1, and F 2 is the gravitational force produced by m 2. Here, for two objects that are orbiting a common centre of mass (like the Earth and the Sun), m 1 is the mass of the less massive object (like the Earth) and m 2 is the mass of the more massive object (like the Sun). ![]()
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