Gravity Don’t Let It Get You Down!

The Truth About Gravity u Gravity is a phenomenon u The phenomenon results in a force which can accelerate objects with mass u “g” represents the acceleration due to the force caused by the phenomenon of gravity

Back to the Beginning u Astronomy drove our understanding and discovery u It did so without knowing it, however

The Importance of Being Gravity u Gravity has basic properties that set it apart from the other forces: (1) it is long-ranged and thus can act over cosmological distances; (2) it always supplies an attractive force between any two pieces of matter in the Universe. u Thus, although extremely weak, it always wins over cosmological distances and is the most important force for the understanding of the large scale structure and evolution of the Universe.

So, let us deal with GRAVITY We’ll need a bit of a history lesson: Brahe Kepler Newton Einstein Pay close attention, gravity has many implications!

Tycho Brahe A wild Dane, but he made and recorded large quantities of accurate measurements of the motions of the planets around the Sun Began working with Johannes Kepler in 1600.

1) The planets move abort the sun in elliptical orbits with the Sun at one focus. 2) The radius vector joining a planet to the sun sweeps over equal areas in equal intervals of time. The empirical discovery of these laws from Tycho Brahe's mass of data constitutes one of the most remarkable inductions ever made in science. T 1 2 / T 2 2 =R 1 3 / R 2 3 or T 2 =k. R 3 3) The square of the time of one compete revolution of a planet about its orbit is proportional to the cube of the orbit's semi-major axis Kepler’s “Laws” of Planetary Motion

Isaac Newton u Born 1642, the year Galileo died u Loner, tinkerer, paranoid u Plague was very good for him u Suffered mental breakdown 1675 u Math, Chemistry, Theology, Parliament u Died 1727 u Has his picture on the British pound note He put the physics and mathematics to Kepler’s Laws!

Newton’s Laws of Motion u First Law - A body remains in its state of motion unless acted upon by an outside force u Second Law - A body acted upon by an external force will change its momentum in the direction of the force such that the greater the force the greater the change in momentum (F= ma). u Third Law - Forces always occur in pairs, i.e. for every action there is an equal and opposite reaction

Universal Law of Gravitation u All objects in the Universe attract each other with a force that varies directly as the product of their masses and inversely as the square of their separation from each other. F = G m m F = G m m r gravity 1 2 2

General Relativity u Einstein’s Theory of Gravity, published 1915 u Principle of Equivalence: Accelerations are indistinguishable from gravitational fields. They are equivalent. u So, for example, when you are in freefall (like in an orbiting Shuttle), your downward acceleration is just enough to cancel the gravitational force.

Einstein’s View of Gravity u Gravity is due to the curvature of spacetime. u Spacetime is curved by mass.

Applications of Newton’s 2nd Law and Einstein’s GR u Projectile Motion u Pendulums u Black Holes

Projectile Motion Projectile - any object given an initial velocity which subsequently follows a path determined by the gravitational force acting on it, and by the frictional resistance of the atmosphere bullet shot from a gun, rocket after the fuel is exhausted, thrown or batted baseball

Trajectory Trajectory - the path followed by a projectile

Our Assumptions We will consider only short length trajectories so that: u Gravitational force is considered constant in magnitude and direction u Earth is an inertial system u Air resistance is negligible In other words, we will examine motion in a vacuum on a flat, non-rotating Earth. In physics, we call this creating an

First, the Forces u Only force acting on the projectile is its weight…remember we are in the Ideal Case. u X-axis is horizontal; y-axis is vertical; origin is point where projectile starts its free flight u So x-component of the force on the projectile is zero and y-component of the force is the weight, mg.

Acceleration Netwon’s 2nd law then tells us that the x- component of the acceleration is zero and the y- component is -g. In other words, trajectory is a combination of a horizontal motion with constant velocity and a vertical component with constant acceleration.

Result u Under these conditions, projectiles travel in trajectories which are parabolas. u You can derive the equation for the parabolic motion from Newton’s Laws!

Pendulums   mg T mg sin  For small angles, sin  Simple Harmonic Motion L x Period = 2  L/g Measure period of oscillation and length of pendulum, determine g!

Energy and Pendulums u Since energy is never created nor destroyed, the energy of a pendulum moving changes form. u When it is at its highest, is has only potential energy (PE) based on gravity potentially pulling it to the earth. u When it is at its lowest, it has only kinetic energy (KE) since that is the closest movement allowed by the string. u In between these two, it has both types of energy (KE+PE)

Black Holes A huge great enormous thing, like — like nothing. A huge big — well, like a — I don’t know — like an enormous big nothing … Piglet describes the Heffalump, Piglet describes the Heffalump, in Winnie the Pooh by A.A. Milne in Winnie the Pooh by A.A. Milne