Chapter 8

 Imagine a cannon, perched high atop a mountain, firing a cannon ball with a given horizontal speed. The cannon ball is a projectile, so it’s motion has both ___________ and ____________ components. Like all projectiles, it follows a parabolic trajectory. During its first second of flight, it falls ______ meters. If its horizontal speed is increased, it would travel farther across the Earth, but still fall______ meters in the first second.

 Because the Earth’s surface is curved, it is possible for the cannon ball to be fired with enough horizontal speed to fall 4.9 meters at a point where the Earth’s surface has curved 4.9 meters away from the horizontal. (Isaac Newton)

V = Gm E r

 T = 2π r 3 Gm E

 V = velocity in m/s  G = 6.67 x (this number is a constant)  m E = mass of the Earth (or any planet – p. 178) in kg  r = radius in meters  T = time period in seconds

g = F m Look familiar?

 1. the mass of the object(s) ▪ This is a direct relationship, which means that the larger the masses, the ____________ the gravity. ▪ Examples:

 2. the distance between the objects ▪ This is an inverse relationship, which means that the shorter the distance between them, the ___________ the amount of gravity. ▪ Examples:

Distance affects the gravitational force more than mass does!!!

Use this formula: g = GmG= a constant d 2m = mass of the planet (see the chart) d = the radius of the planet (chart) For example, to solve for gravity on the mercury, we would use 6.67 x (3.3 x ) (2.44 x 10 6 )2 Gravity on mercury = 3.7 m/s 2

F = GmAmB d 2 G = 6.67 x (a constant) mA = mass of object A mB = mass of object B d = distance between the objects