Planets move through the sky with More complicated paths than Stars do. We begin with Kepler’s Laws in Order to find out how.

Planets move through the sky withMore complicated paths than

Stars do.

We begin with Kepler’s Laws inOrder to find out how.

Kepler’s Laws of planetary motionAre stated as…

1)The paths of planets are ellipses,With the sun at one focus.

2) An imaginary line from the sun To a planet sweeps out equal Areas in equal time intervals.

Thus planets move faster when They are closer to the sun, and

Vise-versa.

3) The square of the ratio of the Periods of any two planets Revolving about the sun is

Equal to the cube of the ratioOf their average distances

From the sun.

TA

TB

=rA

rB

2 3

TA

TB

=rA

rB

2 3

T = the planets’ periods Of revolution

r = the average distanceFrom the sun (or another focus)

The first 2 laws apply to each Individual planet, moon, or

Satellite.

The 3rd law relates to the motionOf several satellites about a

Single body.

Io has a period of 1.8 days and is4.2 units away from Jupiter.

Callisto has a period of 16.7 days.What is the distance away

From Jupiter?

rc = 19 units

The moon has a period of 27.3 Days and a mean distance fromEarth of 3.9 X 105 km. Find thePeriod of a satellite that is in

Orbit 6.7 X 103 km.

88.6 mins

Newton also played around With a few formulas for gravitation.

Newton said that there was an Attractive force between

All objects, this is called theGravitational force.

Newton was so confidant thatHe came up with a law to find

The quantity of gravity.

The Law of Universal Gravitation

F = GmAmB

d2

F = GmAmB

d2

m = mass

d = distance between The center of the objects

G = 6.67 X 10-11 Nm2 / kg2

Without showing all the math,The force equals something else.

F = mp4π2r

T2= G

msmp

d2

And rearranged again…

T2 = 4π2

Gmsr3

Jeff (75 kg) and Racheal (60 kg)sit about 4 Meters away

from each other. Racheal looks up and feels an

Attraction. Find the gravitationalForce between them.

F = 1.87 X 10-8 N

An object that is falling at theSame rate at which the earth is

Curved is said to be in orbit.

For an object to be in orbit, air resistance Must be taken away,

which Means that it must be at least 150 km

above the earth.

Use Newton’s thought experimentOn page 179 to see how.

We can continuously derive New formulas to find out things.

v = GmE

r

T = 2πr3

GmE

These formulas only Work for the earth.

A satellite orbits Earth 225 km Above its surface. What is itsSpeed in orbit and its period?

v = 7760 m/s T = 1.5 hr

As you move farther from Earth’s Center, the acceleration due

To gravity changes.

a = grE

d

2

There are 2 kinds of mass…

Inertial mass And

Gravitational mass

Inertial mass is a measure of anObject’s resistance to an type

Of force.

minertial = Fnet

a

The gravitational mass is the sizeOf the gravitational force

Between the objects.

mgrav = r2Fgrav

Gm

Einstein proposed that gravityIs not a force, but an effect

Of space itself.

According to Einstein, massChanges space itself,

Making it curved.

Bodies are thus acceleratedBecause they follow this

Curved space toward the center.

This is Einstein’s Special Theory of Relativity.