Universal GravitationChapter 8

Explanation of satellites:

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)

To solve for the speed of an object in circular orbit:

Formula 1

V = GmE

r

Formula 2

T = 2π r3

GmE

Sorry for the shaky drawing…

Variables:

V = velocity in m/s G = 6.67 x 10-11 (this number is a

constant) mE = mass of the Earth (or any

planet – p. 178) in kg

r = radius in meters T = time period in seconds

To solve for gravitational field strength…

g = F m

Look familiar?

Gravitational strength is based on 2 factors:

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:

Important:

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

How do I determine the gravity on some other planet?

Use this formula:

g = Gm G= a constantd2 m = 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 10-11 (3.3 x 1023)

(2.44 x 106)2

Gravity on mercury = 3.7 m/s2

Last formula…

F = GmAmB d2

G = 6.67 x 10-11 (a constant)mA = mass of object AmB = mass of object Bd = distance between the objects

Which pair has more gravitational force between them?

Or…