What holds us together? Gravity

Gravity is a force Force: a push or pull exerted on an object Gravity: the attractive force between objects; force that moves objects downhill

mass: how much matter or “stuff” is in an object weight: the force that must be applied to support an object, “heaviness” acceleration: how quickly something's speed is changing

Newton’s Second Law of Motion F = ma F = force m = mass a = acceleration

Universal Law of Gravitation every object in the universe attracts every other object An equation gives the force of this attraction between any two objects:

Universal Law of Gravitation G = gravitational constant = 6.673× m 3 kg -1 s -2 m 1 = mass of object 1 m 2 = mass of object 2 d 2 = distance between the objects squared = d x d F = force of gravity

Universal Law of Gravitation In Action: You and Earth F = kg m/s 2 F = Gm 1 m 2 d 2 m 1 = you weigh 110 lbs = 50 kg m 2 = Earth = * kg d = distance to center of Earth = 6,371,000 m G = gravitational constant = 6.673× m 3 kg -1 s -2 Next Step: Newton’s 2 nd Law F = ma a = F/m 1 = m/s 2

Universal Law of Gravitation In Action: Car and Earth Will the force of gravity between the car and Earth be bigger, smaller, or the same as the force of gravity between you and Earth? F = Gm 1 m 2 d 2 m 1 = car = 2000 kg m 2 = earth = * kg d = distance to center of earth = 6,371,000 m G = gravitational constant = 6.673× m 3 kg -1 s -2

Universal Law of Gravitation In Action: Car and Earth F = kg m/s 2 Now what about acceleration due to gravity? How will it compare to acceleration due to gravity between you and Earth: bigger, smaller, or the same? m 1 = car = 2000 kg m 2 = earth = * kg d = distance to center of earth = 6,371,000 m G = gravitational constant = 6.673× m 3 kg -1 s -2 F = Gm 1 m 2 d 2

Universal Law of Gravitation In Action: Car and Earth F = kg m/s 2 Next Step: Newton’s 2 nd Law a = F/m 1 = m/s 2 F = ma

Acceleration Due to Gravity Acceleration from gravity is the same for all objects on Earth, 9.8 m/s 2 ! Math Proves It: Combine F g = m o a g and So that m o a g = solve for a g = G F g = Gm o m E d 2 Gm o m E d 2 mEd2mEd2

Acceleration Due to Gravity The weight of an object does not change how gravity acts. Gravity does not cause heavier objects to fall faster.

m 1 = moon = 7.3 x kg m 2 = earth = 6 x kg d = distance between earth and moon = 3.84 x 10 8 m G = gravitational constant = 6.673× m 3 kg -1 s -2 Force of Gravity = 1.98 x kg m/s 2 = kg m/s 2 Acceleration due to Gravity from F= ma a = F/m = * m/s 2 = m/s 2 F = Gm 1 m 2 d 2 Gravity Beyond the Classroom: Earth and Moon

Gravity Beyond the Classroom: Earth and Sun m 1 = sun = 1,988,920,000,000,000,000,000,000,000,000 kg m 2 = earth = 6,000,000,000,000,000,000,000,000 kg d = distance between earth and sun = 150 million km =1.5 * m G = gravitational constant = 6.673× m 3 kg -1 s -2 Force of Gravity = *10 24 kg m/s 2 = 3,539,000,000,000,000,000,000,000 kg m/s 2 Acceleration due to Gravity from F= ma a = F/m = m/s 2 F = Gm 1 m 2 d 2

Force of Gravity: Two Students m 1 = you weigh 110 lbs = 50 kg m 2 = student weighs 110 lbs = 50 kg d = distance between students = 5 meters (about 15 feet) G = gravitational constant = 6.673× m 3 kg -1 s -2 F = Gm 1 m 2 d 2 Force = ? Does the force of gravity depend on mass? v

Force of Gravity: Two Students Force = kg m/s 2 What about acceleration due to gravity? F= ma a = F/m = 6.6 * m/s 2 = m/s 2 F = Gm 1 m 2 d 2

The distance between any two objects and their masses determines the force of gravity between them

Force of Gravity Depends on Mass Between you and Earth: Force = kg m/s 2 Acceleration = Force/Mass = 9.8 m/s 2 What about between you and the moon? The moon is 1/80 th the mass of Earth. Force = ? a = F/m = ?

Force of Gravity Depends on Mass Between you and Earth: Force = kg m/s 2 Acceleration = Force/Mass = 9.8 m/s 2 Between you and the Moon Force = 1.65 * kg m/s 2 = kg m/s 2 a = F/m = 3.2 * m/s 2 = m/s 2

Force of Gravity Depends on Distance Between Earth and the moon: Force = 1.98 x kg m/s 2 Acceleration = Force/Mass = m/s 2 What would happen to the force of gravity if we doubled the distance between Earth and the moon?

Force of Gravity Depends on Distance Between Earth and the moon: Force = 1.98 x kg m/s 2 and a = m/s 2 Force = kg m/s 2 a = F/m = 6.78 * m/s 2 = m/s 2 If we double the distance to the moon the force of gravity is ¼ of what it was!

Inertia The tendency of an object to resist a change in motion

Newton’s First Law of Motion (Inertia) An object at rest will stay at rest and an object in motion will stay in motion with a constant speed unless acted on by a force

Orbits Inertia and gravity combine to keep objects in orbit.