Transcript Chapter 7 Rotational Motion and the Law of Gravity

Chapter 7
Law of Gravity & Kepler’s Laws
HMH Physics Ch 7 pages 224-269
Section 6 pages 232-245
Objectives
1. Explain how Newton’s law of universal
gravitation accounts for various phenomena,
including satellite and planetary orbits, falling
objects, and the tides.
2. Apply Newton’s law of universal gravitation
to solve problems.
3. Describe Kepler’s laws of planetary motion.
4. Relate Newton’s mathematical analysis of
gravitational force to the elliptical planetary
orbits proposed by Kepler.
5. Solve problems involving orbital speed and
period.
Gravitational Force (Fg)

Gravitational force is the mutual force
of attraction between particles of
matter

Gravitational force depends on the
distance between two objects and their
mass

Gravitational force is localized to the
center of a spherical mass
G
is the constant of universal
gravitation
G = 6.673 x 10-11 N•m2/kg2
The Cavendish Experiment

Cavendish found the value for G.

He solved Newton’s equation for G and substituted his
experimental values.
◦ He used an apparatus similar to that shown above.
◦ He measured the masses of the spheres (m1 and m2), the
distance between the spheres (r), and the force of attraction
(Fg).
Chapter 7
Section 2 Newton’s Law of
Universal Gravitation
Newton’s Law of Universal
Gravitation
Ocean Tides

Newton’s law of universal gravitation is used to
explain the tides.
◦ Since the water directly below the moon is
closer than Earth as a whole, it accelerates
more rapidly toward the moon than Earth, and
the water rises.
◦ Similarly, Earth accelerates more rapidly toward
the moon than the water on the far side. Earth
moves away from the water, leaving a bulge
there as well.
◦ As Earth rotates, each location on Earth passes
through the two bulges each day.
Gravity is a Field Force



Earth, or any other
mass, creates a force
field.
Forces are caused by
an interaction
between the field and
the mass of the object
in the field.
The gravitational field
(g) points in the
direction of the force,
as shown.
Calculating the value of g

Since g is the force acting on a 1 kg
object, it has a value of 9.81 N/m (on
Earth).
◦ The same value as ag (9.81 m/s2)

The value for g (on Earth) can be
calculated as shown below.
Fg
GmmE GmE
g

 2
2
m
mr
r
Find the distance between a 0.300 kg
billiard ball and a 0.400 kg billiard ball if
the magnitude of the gravitational force
is 8.92 x 10-11 N.
Kepler’s Laws

Johannes Kepler built his ideas on planetary
motion using the work of others before him.
◦ Nicolaus Copernicus and Tycho Brahe
Kepler’s Laws

Kepler’s first law
◦ Orbits are elliptical, not circular.
◦ Some orbits are only slightly elliptical.

Kepler’s second law
◦ Equal areas are swept out in equal time intervals.

Kepler’s third law
◦ Relates orbital period (T) to distance from the
sun (r)
 Period is the time required for one revolution.
◦ As distance increases, the period increases.
 Not a direct proportion
 T2/r3 has the same value for any object orbiting
the sun
Kepler’s Laws
Equations for Planetary Motion

Using SI units, prove that the units are
consistent for each equation shown above.

A large planet orbiting a distant star is
discovered. The planet’s orbit is nearly
circular and close to the star. The orbital
distance is 7.50  1010 m and its period is
105.5 days. Calculate the mass of the
star.
◦ Answer: 3.00  1030 kg

What is the velocity of this planet as it
orbits the star?
◦ Answer: 5.17  104 m/s
Classroom Practice Problems