Nevertheless, they are usually accurate enough for dense and compact objects falling over heights not exceeding the tallest man-made structures. The equations also ignore the rotation of the Earth, failing to describe the Coriolis effect for example. (In the absence of an atmosphere all objects fall at the same rate, as astronaut David Scott demonstrated by dropping a hammer and a feather on the surface of the Moon.) The effect of air resistance varies enormously depending on the size and geometry of the falling object-for example, the equations are hopelessly wrong for a feather, which has a low mass but offers a large resistance to the air. The equations ignore air resistance, which has a dramatic effect on objects falling an appreciable distance in air, causing them to quickly approach a terminal velocity. He measured elapsed time with a water clock, using an "extremely accurate balance" to measure the amount of water. He used a ramp to study rolling balls, the ramp slowing the acceleration enough to measure the time taken for the ball to roll a known distance. Galileo was the first to demonstrate and then formulate these equations. Assuming constant g is reasonable for objects falling to Earth over the relatively short vertical distances of our everyday experience, but is not valid for greater distances involved in calculating more distant effects, such as spacecraft trajectories. Assuming constant acceleration g due to Earth’s gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth’s gravitational field of strength g.
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