Chapter 7Law of Gravity & Kepler’s Laws

HMH Physics Ch 7 pages 224-269Section 6 pages 232-245

Objectives1. 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 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).

He solved Newton’s equation for G and substituted his experimental values.

Chapter 7

Newton’s Law of Universal Gravitation

Section 2 Newton’s Law of Universal Gravitation

Ocean TidesNewton’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 ForceEarth, 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 gSince 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.

2 2

g E EF Gmm Gm

gm 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 LawsJohannes Kepler built his ideas on planetary

motion using the work of others before him.◦ Nicolaus Copernicus and Tycho Brahe

Kepler’s LawsKepler’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 Laws

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

Equations for Planetary Motion

Using SI units, prove that the units are consistent for each equation shown above.

Classroom Practice Problems

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