Universal Gravitation Chapter 12

The Falling Apple The idea that gravity extends through the universe is attributed to Sir Issac Newton He knew that if an object undergoes a change in direction or speed, a force is responsible Newton had the insight to figure out that the moon orbits Earth because it is falling towards Earth, avoiding its straight-line path

The Falling Apple

The Falling Moon The moon falls in the sense that it falls beneath the straight line it would follow if no force acted on it Newton imagined firing a cannonball from a mountain top. If he fired the cannonball with a small horizontal speed, it would follow a parabolic path and hit Earth soon. If he fired the same cannonball with greater horizontal speed, it would go farther and have a less curved path. If he fired the cannonball with great enough horizontal speed, he reasoned that the cannonball’s path would become a circle and it would circle indefinitely (orbit)

The Orbital Cannon

Launch Speed less than 8000 m/s Projectile falls to Earth Launch Speed less than 8000 m/s Projectile falls to Earth Launch Speed equal to 8000 m/s Projectile orbits Earth - Circular Path Launch Speed greater than 8000 m/s Projectile orbits Earth - Elliptical Path Cannonball in Orbit

Newton’s Law of Universal Gravitation Law of Universal Gravitation – every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object, the force also decreases as the square of the distance between the centers of mass of the objects increases The farther away the objects are from each other, the less the force of attraction between them

The Universal Gravitational Constant, G When the proportionality constant, G, is introduced, we can write the Law of Universal Gravitation in the form of an equation: F = G(m 1 )(m 2 )/d 2 G = 6.67 x N∙m²/kg² We only sense gravitation for bodies the size of a planet, smaller objects we can’t sense, but the force is there!

Law of Universal Gravitation

The Inverse-Square Law When a quantity varies as the inverse square of its distance from its source, it follows an inverse-square law The greater the distance from Earth’s center, the less an object will weigh You may weigh 300N at sea level, but only 299N at the top of Mount Everest

Inverse-Square Law

Universal Gravitation Earth is round due to gravitation, it has “attracted” itself together to create a spherical shape When planets deviate from their normal orbits, they have been pulled due to the attraction to other planets, this deviation is called perturbation This is how we found Neptune, Uranus was acting strangely, in a way that could only be accounted for by another planet perturbing its orbit

Perturbation

Assignment (due Tuesday 1/15) Read Chapter 12 (pg ) Do #15-35 (pg )