Universal Gravitation

Young Newton "I began to think of gravity extending to the Orb of the Moon, and having found out how to estimate the force with which a globe revolving within a sphere presses the surface of the sphere. From Kepler's Rule of the periodical times of the Planets, I deduced that the forces which keep the Planets in their Orbs must be reciprocally as the squares of their distances from the centres about which they revolve : and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth, and found them to answer pretty nearly". I. Newton writing about the plague years of 1665-1666

Force of Gravity The acceleration of any falling mass m is g. g = 9.81 m/s2 Galileo 1638 The force on the mass is found from F = ma. Gravitational force F = mg Newton 1687 Demonstration: drop ball and light object, compare acceleration to force Kinematic view Dynamic view

Always Falling The Moon accelerates toward the earth like it’s falling. Newton’s laws apply to the force on the Moon. Force depends on mass The Earth pulls the Moon The Moon pulls the Earth Newton used this to describe a Law of Gravity. orbital velocity Moon FEM FME centripetal acceleration Earth

Universal Gravity Newton realized that all objects obey the same universal law. Other planets Kepler’s laws Apples People The constant G is universal. G = 6.67 x 10-11 Nm2/kg2. What is the gravitational force between two students sitting in adjacent seats? Assume each mass 70 kg Assume separated by 1 m F = 3.3 x 10-7 N.

Surface Gravity Gravitational acceleration on the Earth is g = 9.81 m/s2. This value is due to the universal gravitational force. Earth’s radius r = 6.37 x 106 m Earth’s mass M = 5.97 x 1024 kg g = F/m = GM/r2 = 9.81 m/s2. Surface gravity is different on other worlds. Moon 0.165g; Mars 0.376g

Normal Force The force of gravity acts on all objects all the time. At rest: zero net force Newton’s first law The normal force pushes back. Equal and opposite Newton’s third law FN = -Fgrav = mg Demonstration: set ball on table Fgrav = -mg

Normal Force and Weight The normal force pushing up against gravity is measured as weight. Weight is a force, not a mass. Kilograms – mass Pounds – force If g is less, weight is less. Equipment: spring scale

Apparent Weight A person in an accelerating elevator feels a net force. Newton’s second law F = ma The normal force doesn’t cancel gravity. FN = m (g – a) Weight feels different

Weightlessness If the elevator accelerated downward at g, the normal force would be 0. The person would feel weightless. An object in free fall is weightless, but not massless. Demonstration: link to NASA Microgravity research at NASA