Transcript pptx
Newton and Gravity Isaac Newton (1642-1727) • Galileo found that bodies with different masses experienced the same acceleration when dropped to the ground. But he didn’t know why. • Kepler discovered that the motions of the planets were perfectly reproduced by 3 mathematical relations. Like Galileo, Kepler didn’t know why these relations worked. • Isaac Newton was able to explain the results of Galileo and Kepler, and many other phenomena in nature, with a few general principles Newton’s Concepts 1) m (mass): the amount of matter an object contains 2) v (velocity): a body’s speed and direction 3) a (acceleration): the change in a body’s velocity 4) F (force): what is needed to change a body’s velocity Newton’s Laws of Motion 1) A body’s velocity will remain constant, unless acted upon by an outside force = inertia Newton’s Laws of Motion 1) A body’s velocity will remain constant, unless acted upon by an outside force = inertia 2) A body’s acceleration depends on the force acting upon it, and will be in the direction of that force. Its resistance to acceleration depends on its mass. In equation form, this is F=ma 3) For every force, there is an equal and opposite force. Newton’s Law of Gravity Any two objects with mass experience an attractive force from gravity that tries to pull them towards each other. The strength of this force depends on the masses of the two bodies, and the distance between their centers (squared). The attractive force is greater for larger masses and smaller distances. Both objects feel the same force of gravity, even if they have different masses. G m1 m2 F = d2 Explaining Galileo’s Experiment m M = Earth’s mass Newton’s 2nd law: F=ma Newton’s law of gravity: F = G m M / d2 F = m a = G m M / d2 a = G M / d2 An object’s acceleration does not depend on its own mass. It depends on the mass of the other object (the Earth, in this case). Explaining Projectile Motion The motion of a projectile can be separated into two components: horizontal & vertical. Due to Newton’s 1st Law, the horizontal motion remains unchanged because there is no force acting on the ball in that direction (ignoring air resistance). The ball does experience a force in the vertical direction (gravity), so the vertical motion undergoes acceleration downward (Newton’s 2nd law) Explaining Projectile Motion Explaining Weight and Weightlessness You feel weight because of Newton’s third law. Gravity is pulling you down, but the ground is not allowing you to fall. It must therefore be exerting a force on you to keep you from falling. That force is the weight that you feel. If you were allowed to fall, you would not feel any weight. So when you are in free-fall, you feel weightlessness. Explaining Weight and Weightlessness As an example, a sky diver is in free fall towards the earth, and therefore feels weightlessness. gravity Explaining Weight and Weightlessness If an additional force is applied to the sky diver that is not in the direction of gravity, he will fall on a curved path because of inertia (Newton’s 1st law). inertia gravity Explaining Orbits If the size of the force is just right, the sky diver falls on a curved path that never reaches the ground and loops back on itself. This is an orbit. The sky diver (or astronaut) experiences weightlessness indefinitely. inertia gravity Explaining Orbits An orbit is a compromise between gravity and inertia. Earth coalesced from gas and dust orbiting around the Sun, so it was born with the inertia that maintains an orbit. If Earth had been born stationary relative to the Sun (no inertia), it would have fallen immediately into the Sun. Explaining Orbits Because planets are much less massive than the Sun, they induce very little acceleration in the Sun, so the Sun barely moves and has a very small “orbit”, while the planets are move a lot and have large orbits because of the strong acceleration induced by the Sun. Explaining Orbits If the Sun was orbited by larger bodies, like other stars, it would move much more in its orbit. http://astro.unl.edu/naap/esp/animations/radialVelocitySimulator.html https://phet.colorado.edu/en/simulation/gravity-and-orbits